diff --git a/.travis.yml b/.travis.yml
index 731354f..c9e1716 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,88 +1,92 @@
language: cpp
dist: trusty
env:
matrix:
fast_finish: true
include:
- os: linux
addons:
apt:
sources:
- ubuntu-toolchain-r-test
packages:
- g++-4.9
- libeigen3-dev
env: COMPILER=gcc GCC=4.9
- os: linux
addons:
apt:
sources:
- ubuntu-toolchain-r-test
packages:
- g++-5
- libeigen3-dev
env: COMPILER=gcc GCC=5
- os: linux
addons:
apt:
sources:
- ubuntu-toolchain-r-test
packages:
- g++-6
- libeigen3-dev
env: COMPILER=gcc GCC=6
env:
global:
- MINCONDA_VERSION="latest"
- MINCONDA_LINUX="Linux-x86_64"
- MINCONDA_OSX="MacOSX-x86_64"
before_install:
- |
# Configure build variables
if [[ "$TRAVIS_OS_NAME" == "linux" ]]; then
if [[ "$COMPILER" == "gcc" ]]; then
export CXX=g++-$GCC CC=gcc-$GCC;
fi
if [[ "$COMPILER" == "clang" ]]; then
export CXX=clang++-$CLANG CC=clang-$CLANG;
fi
elif [[ "$TRAVIS_OS_NAME" == "osx" ]]; then
export CXX=clang++ CC=clang;
fi
install:
# Define the version of miniconda to download
- if [[ "$TRAVIS_OS_NAME" == "linux" ]]; then
MINCONDA_OS=$MINCONDA_LINUX;
elif [[ "$TRAVIS_OS_NAME" == "osx" ]]; then
MINCONDA_OS=$MINCONDA_OSX;
fi
- wget "http://repo.continuum.io/miniconda/Miniconda3-$MINCONDA_VERSION-$MINCONDA_OS.sh" -O miniconda.sh;
- bash miniconda.sh -b -p $HOME/miniconda
- export PATH="$HOME/miniconda/bin:${PATH}"
- export INCLUDE_PATH="$HOME/miniconda/include:${INCLUDE_PATH}"
- hash -r
- conda config --set always_yes yes --set changeps1 no
- conda update -q conda
- conda install cmake -c conda-forge
- conda install xtl -c conda-forge
- conda install xsimd -c conda-forge
- conda install xtensor -c conda-forge
+ # store relevant
+ - build_dir="${PWD}/build"
+ - example_dir="${PWD}/docs/examples"
# build path
- - mkdir build
- - cd build
+ - mkdir "${build_dir}"
+ - cd "${build_dir}"
# install catch
- git clone https://github.com/catchorg/Catch2.git
- cd Catch2
- mkdir build
- cd build
- mkdir opt
- cmake .. -DCATCH_BUILD_TESTING=OFF -DCMAKE_INSTALL_PREFIX:PATH="${PWD}"/opt
- make install
- export INCLUDE_PATH="${PWD}"/opt/include:"${INCLUDE_PATH}"
- - cd ../..
# make test-cases
+ - cd "${build_dir}"
- cmake .. -DBUILD_TESTS=ON
- make
- - cd test
script:
+ # run tests
+ - cd "${build_dir}/test"
- ./test
diff --git a/docs/conventions/allocation.rst b/docs/conventions/allocation.rst
index a5b7210..882bb31 100644
--- a/docs/conventions/allocation.rst
+++ b/docs/conventions/allocation.rst
@@ -1,22 +1,22 @@
.. _conventions_allocation:
Data allocation
===============
Most of GooseFEM's functions provided an interface to:
1. Allocate output arrays: names start with a **upper-case** letter. For example:
.. code-block:: cpp
ue = GooseFEM::Vector::AsElement(disp);
2. Directly write to output arrays, without allocation them and copying them, by taking a pointer the externally allocated array as the last input argument(s): names start with a **lower-case** letter. For example:
.. code-block:: cpp
GooseFEM::Vector::asElement(disp, ue);
.. note::
- The Python API only option 1. Option 2 is only available in the C++ API.
+ The Python API only provides option 1. Option 2 is only available in the C++ API.
diff --git a/docs/conventions/matrix.rst b/docs/conventions/matrix.rst
index 7c96130..2747c74 100644
--- a/docs/conventions/matrix.rst
+++ b/docs/conventions/matrix.rst
@@ -1,40 +1,42 @@
.. _conventions_matrix:
Matrix representation
=====================
Element system matrix
---------------------
The element system matrix collects individual system matrices as a multi-dimensional array of shape :math:`\left[ n_\text{elements} \times n_\text{nodes-per-element} n_\text{dim} \times n_\text{nodes-per-element} n_\text{dim} \right]``. An element system matrix
.. code-block:: python
Ke = K[e,:,:]
obeys the following convention:
.. math::
\underline{f} = \underline{\underline{K}} \underline{u}
where
- \underline{f_(n + i d)} = f_i^{(n)}
+.. math::
+
+ f_{(n + i d)} \equiv f_i^{(n)}
with :math:`n` the node number, :math:`i` the dimension, and :math:`d` the number of dimensions. For example for a two-dimensional quadrilateral element
.. math::
\underline{f} =
\big[
f_x^{(0)},
f_y^{(0)},
f_x^{(1)},
f_y^{(1)},
f_x^{(2)},
f_y^{(2)},
f_x^{(3)},
f_y^{(3)}
\big]^T
diff --git a/docs/conventions/storage.rst b/docs/conventions/storage.rst
index 8078aaf..c770c17 100644
--- a/docs/conventions/storage.rst
+++ b/docs/conventions/storage.rst
@@ -1,77 +1,77 @@
.. _conventions_storage:
Data storage
============
Glossary
--------
+---------+-------------------------------+-------------------------------------+
| Alias | Shape | Description |
+=========+===============================+=====================================+
| dofval | [ndof] | degrees of freedom |
+---------+-------------------------------+-------------------------------------+
| nodevec | [nnode, ndim] | nodal vector |
+---------+-------------------------------+-------------------------------------+
| elemvec | [nelem, nne, ndim] | nodal vector stored per element |
+---------+-------------------------------+-------------------------------------+
| elemmat | [nelem, nne*ndim, nne*ndim] | matrix stored per element |
+---------+-------------------------------+-------------------------------------+
| qscalar | [nelem, nip] | scalar stored per integration point |
+---------+-------------------------------+-------------------------------------+
| qtensor | [nelem, nip, tdim, tdim, ...] | tensor stored per integration point |
+---------+-------------------------------+-------------------------------------+
dofval
------
* Degrees-of-freedom
-* [ndof]
+* Shape [ndof]
* :code:`xt::xtensor<double,1>`
nodevec
-------
* Nodal vectors
-* [nnode, ndim]
+* Shape [nnode, ndim]
* :code:`xt::xtensor<double,2>`
elemvec
-------
* Nodal vectors stored per element
* Allows treatment of all elements independently, no connectivity needed
-* [nelem, nne, ndim]
+* Shape [nelem, nne, ndim]
* :code:`xt::xtensor<double,3>`
elemmat
-------
* Matrices stored per element
-* [nelem, nne*ndim, nne*ndim]
+* Shape [nelem, nne*ndim, nne*ndim]
* :code:`xt::xtensor<double,3>`
qscalar
-------
* Scalars stored per integration point
-* [nelem, nip]
+* Shape [nelem, nip]
* :code:`xt::xtensor<double,2>`
qtensor (2nd order)
-------------------
* 2nd-order tensors stored per integration point
-* For certain element the number of dimensions of the tensor can be larger than the number of dimensions of the element
-* [nelem, nip, tdim, tdim]
+* For certain elements, the number of dimensions of the tensor can be larger than the number of dimensions of the element (tdim >= ndim)
+* Shape [nelem, nip, tdim, tdim]
* :code:`xt::xtensor<double,4>`
qtensor (4th order)
-------------------
* 4th-order tensors stored per integration point
-* For certain element the number of dimensions of the tensor can be larger than the number of dimensions of the element
-* [nelem, nip, tdim, tdim, tdim, tdim]
+* For certain elements, the number of dimensions of the tensor can be larger than the number of dimensions of the element (tdim >= ndim)
+* Shape [nelem, nip, tdim, tdim, tdim, tdim]
* :code:`xt::xtensor<double,4>`
diff --git a/docs/conventions/terminology.rst b/docs/conventions/terminology.rst
index 8d4b4da..f25226a 100644
--- a/docs/conventions/terminology.rst
+++ b/docs/conventions/terminology.rst
@@ -1,81 +1,81 @@
.. _conventions_terminology:
Terminology
===========
Glossary
--------
+---------+---------+-------------------------------------+
| Alias | Type | Description |
+=========+=========+=====================================+
| nnode | size | number of nodes |
+---------+---------+-------------------------------------+
| ndim | size | number of dimensions |
+---------+---------+-------------------------------------+
| nelem | size | number of elements |
+---------+---------+-------------------------------------+
| nne | size | number of nodes per element |
+---------+---------+-------------------------------------+
-| tdim | size | number of dimensions of tensor |
+| tdim | size | number of dimensions of a tensor |
+---------+---------+-------------------------------------+
| --- | --- | --- |
+---------+---------+-------------------------------------+
| dofval | array | degrees of freedom |
+---------+---------+-------------------------------------+
| nodevec | array | nodal vector |
+---------+---------+-------------------------------------+
| elemvec | array | nodal vector stored per element |
+---------+---------+-------------------------------------+
| elemmat | array | matrix stored per element |
+---------+---------+-------------------------------------+
| qscalar | array | scalar stored per integration point |
+---------+---------+-------------------------------------+
| qtensor | array | tensor stored per integration point |
+---------+---------+-------------------------------------+
| --- | --- | --- |
+---------+---------+-------------------------------------+
| coor | name | nodal coordinates |
+---------+---------+-------------------------------------+
| conn | name | connectivity |
+---------+---------+-------------------------------------+
| --- | --- | --- |
+---------+---------+-------------------------------------+
| Tri3 | element | 2-d triangular element (3 nodes) |
+---------+---------+-------------------------------------+
| Quad4 | element | 2-d quadrilateral element (4 nodes) |
+---------+---------+-------------------------------------+
| Hex8 | element | 3-d hexahedral element (8 nodes) |
+---------+---------+-------------------------------------+
Coordinates
-----------
* Nodal coordinates: each node has one row
-* Shape :math:`\left[ n_\text{node} \times n_\text{dim} \right]`
+* Shape [nnode, ndim]
* Denoted: *coor*
Connectivity
------------
* Node numbers per element: each element has one row
-* Shape :math:`\left[ n_\text{elem} \times n_\text{nodes-per-element} \right]`
+* Shape [nelem, nne]
* Denoted: *conn*
Sizes
-----
-+-------+---------------------------------+------------------------------------+
-| Alias | Description | |
-+=======+=================================+====================================+
-| nnode | number of nodes | :math:`n_\text{nodes}` |
-+-------+---------------------------------+------------------------------------+
-| ndim | number of dimensions | :math:`n_\text{ndim}` |
-+-------+---------------------------------+------------------------------------+
-| nelem | number of elements | :math:`n_\text{elements}` |
-+-------+---------------------------------+------------------------------------+
-| nne | number of nodes per element | :math:`n_\text{nodes-per-element}` |
-+-------+---------------------------------+------------------------------------+
-| tdim | number of dimensions of tensor | :math:`n_\text{ndim}` |
-+-------+---------------------------------+------------------------------------+
++-------+---------------------------------+
+| Alias | Description |
++=======+=================================+
+| nnode | number of nodes |
++-------+---------------------------------+
+| ndim | number of dimensions |
++-------+---------------------------------+
+| nelem | number of elements |
++-------+---------------------------------+
+| nne | number of nodes per element |
++-------+---------------------------------+
+| tdim | number of dimensions of tensor |
++-------+---------------------------------+
diff --git a/docs/conventions/vector.rst b/docs/conventions/vector.rst
index ab86cbc..1dae11d 100644
--- a/docs/conventions/vector.rst
+++ b/docs/conventions/vector.rst
@@ -1,238 +1,241 @@
.. _conventions_vector:
Vector representation
=====================
In GooseFEM there are three ways to represent vectors. In particular, a vector field (e.g. the displacement) can be collected:
* per node (denoted "nodevec", :ref:`see below <conventions_storage>`),
* per degree-of-freedom (denoted "dofval", :ref:`see below <conventions_storage>`),
* per element (denoted "elemvec", :ref:`see below <conventions_storage>`).
.. warning::
- Care has to be taken in the conversion from one representation to the other as 'down-sizing' can be done in more than one way, see :ref:`conventions_vector_conversion`.
+ Watch out with the conversion from one representation to the other as downsizing can be done in more than one way, see :ref:`conventions_vector_conversion`.
Consider a simple two-dimensional mesh of just two elements, and a displacement vector per node:
.. image:: figures/data-representation.svg
:width: 400px
:align: center
|
-Collected per node
-------------------
+Collected per node (nodevec)
+----------------------------
.. math::
\texttt{disp} =
\begin{bmatrix}
u_x^{(0)} & u_y^{(0)} \\
u_x^{(1)} & u_y^{(1)} \\
u_x^{(2)} & u_y^{(2)} \\
u_x^{(3)} & u_y^{(3)} \\
u_x^{(4)} & u_y^{(4)} \\
u_x^{(5)} & u_y^{(5)}
\end{bmatrix}
-Collected per degree-of-freedom
--------------------------------
+Collected per degree-of-freedom (dofval)
+----------------------------------------
The following definition
.. math::
\texttt{dofs} =
\begin{bmatrix}
0 & 1 \\
2 & 3 \\
4 & 5 \\
6 & 7 \\
8 & 9 \\
10 & 11
\end{bmatrix}
gives:
.. math::
\texttt{u} =
\big[
u_x^{(0)} \,
u_y^{(0)} \,
u_x^{(1)} \,
u_y^{(1)} \,
u_x^{(2)} \,
u_y^{(2)} \,
u_x^{(3)} \,
u_y^{(3)} \,
u_x^{(4)} \,
u_y^{(4)} \,
u_x^{(5)} \,
u_y^{(5)}
\big]^T
Whereby "dofs" can be used to:
* **Reorder** "u" such that is can be easily (even directly) partitioned. For example, consider that all :math:`x`-coordinates are *Prescribed* and all :math:`y`-coordinates are *Unknown*. In particular,
.. math::
\texttt{dofs} =
\begin{bmatrix}
6 & 0 \\
7 & 1 \\
8 & 2 \\
9 & 3 \\
10 & 4 \\
11 & 5
\end{bmatrix}
gives
.. math::
\texttt{u} =
\big[
u_y^{(0)} \,
u_y^{(1)} \,
u_y^{(2)} \,
u_y^{(3)} \,
u_y^{(4)} \,
u_y^{(5)} \, \;
u_x^{(0)} \,
u_x^{(1)} \,
u_x^{(2)} \,
u_x^{(3)} \,
u_x^{(4)} \,
u_x^{(5)}
\big]^T
=
\big[
\texttt{u}_u \, \;
\texttt{u}_p
\big]^T
which allows
.. math::
\texttt{u}_u &= \texttt{u[:6]} \\
\texttt{u}_p &= \texttt{u[6:]}
|
* **Eliminate** dependent nodes. For example, suppose that the displacement of all top nodes is equal to that of the bottom nodes. In this one could:
.. math::
\texttt{dofs} =
\begin{bmatrix}
0 & 1 \\
2 & 3 \\
4 & 5 \\
0 & 1 \\
2 & 3 \\
4 & 5
\end{bmatrix}
\qquad
\rightarrow
\qquad
\texttt{u} =
\begin{bmatrix}
u_0 \\
u_1 \\
u_2 \\
u_3 \\
u_4 \\
u_5
\end{bmatrix}
\quad
\leftrightarrow
\quad
\texttt{disp} =
\begin{bmatrix}
u_0 & u_1 \\
u_2 & u_3 \\
u_4 & u_5 \\
u_0 & u_1 \\
u_2 & u_3 \\
u_4 & u_5
\end{bmatrix}
+.. note::
+
+ :ref:`Vector` applies the reordering itself. One does not need to change "dofs", but one simply supplies "iip".
-Collected per element
----------------------
+Collected per element (elemvec)
+-------------------------------
For this example:
.. math::
\texttt{conn} =
\begin{bmatrix}
0 & 1 & 4 & 3 \\
1 & 2 & 5 & 4
\end{bmatrix}
The storage per node proceeds in
.. math::
\texttt{shape(ue)}
&= \left[ n_\text{elements} \times n_\text{nodes-per-element} \times n_\text{dim} \right]
\\
&= \left[ 2 \times 4 \times 2 \right]
In particular:
.. math::
\texttt{ue[0,:,:]} =
\begin{bmatrix}
u_x^{(0)} & u_y^{(0)} \\
u_x^{(1)} & u_y^{(1)} \\
u_x^{(4)} & u_y^{(4)} \\
u_x^{(3)} & u_y^{(3)} \\
\end{bmatrix}
and
.. math::
\texttt{ue[1,:,:]} =
\begin{bmatrix}
u_x^{(1)} & u_y^{(1)} \\
u_x^{(2)} & u_y^{(2)} \\
u_x^{(5)} & u_y^{(5)} \\
u_x^{(4)} & u_y^{(4)} \\
\end{bmatrix}
.. _conventions_vector_conversion:
Conversion
----------
-Conversion to a larger representation (up-sizing) can always be done uniquely, however, conversion to a more compact representation (down-sizing) can be done in two ways. In particular:
+Conversion to a larger representation (upsizing) can always be done uniquely, however, conversion to a more compact representation (downsizing) can be done in two ways. In particular:
+---------+---------+-------------------+------------------------------+
| From | To | Function | Remarks |
+=========+=========+===================+==============================+
| dofval | nodevec | asNode(...) | unique |
+---------+---------+-------------------+------------------------------+
| dofval | elemvec | asElement(...) | unique |
+---------+---------+-------------------+------------------------------+
| nodevec | elemvec | asElement(...) | unique |
+---------+---------+-------------------+------------------------------+
| nodevec | dofval | asDofs(...) | overwrites reoccurring items |
+---------+---------+-------------------+------------------------------+
| elemvec | dofval | asDofs(...) | overwrites reoccurring items |
+---------+---------+-------------------+------------------------------+
| elemvec | nodevec | asNode(...) | overwrites reoccurring items |
+---------+---------+-------------------+------------------------------+
| nodevec | dofval | assembleDofs(...) | adds reoccurring items |
+---------+---------+-------------------+------------------------------+
| elemvec | dofval | assembleDofs(...) | adds reoccurring items |
+---------+---------+-------------------+------------------------------+
| elemvec | nodevec | assembleNode(...) | adds reoccurring items |
+---------+---------+-------------------+------------------------------+
diff --git a/docs/details/Element.rst b/docs/details/Element.rst
index 5273490..00bbfd4 100644
--- a/docs/details/Element.rst
+++ b/docs/details/Element.rst
@@ -1,47 +1,28 @@
+.. _Element:
*******
Element
*******
| :download:`GooseFEM/Element.h <../../include/GooseFEM/Element.h>`
| :download:`GooseFEM/Element.hpp <../../include/GooseFEM/Element.hpp>`
-.. tip::
-
- To take the gradients and integral with respect to updated coordinates (i.e. to do updated Lagrange), use the ".update_x(...)" method to update the nodal coordinates and re-evaluate the shape function gradients and integration volumes.
-
Element::asElementVector
========================
Convert nodal vector "[nnode, ndim]" to nodal vector stored per element "[nelem, nne, ndim]".
-.. todo::
-
- Describe.
-
Element::assembleNodeVector
===========================
Assemble nodal vector stored per element "[nelem, nne, ndim]" to nodal vector "[nnode, ndim]".
-.. todo::
-
- Describe.
-
Element::isSequential
=====================
Check that DOFs leave no holes.
-.. todo::
-
- Describe.
-
Element::isDiagonal
===================
-Check structure of the matrices stored per element "[nelem, nne*ndim, nne*ndim]".
-
-.. todo::
-
- Describe.
+Check structure of the matrices stored per element "[nelem, nne*ndim, nne*ndim]" to be diagonal (check that all off-diagonal entries have a value lower than a small numerical tolerance).
diff --git a/docs/details/ElementHex8.rst b/docs/details/ElementHex8.rst
index 5d71404..68d102f 100644
--- a/docs/details/ElementHex8.rst
+++ b/docs/details/ElementHex8.rst
@@ -1,35 +1,188 @@
+.. _ElementHex8:
*************
Element::Hex8
*************
| :download:`GooseFEM/ElementHex8.h <../../include/GooseFEM/ElementHex8.h>`
| :download:`GooseFEM/ElementHex8.hpp <../../include/GooseFEM/ElementHex8.hpp>`
Element::Hex8::Quadrature
-==========================
+=========================
-Element definition.
+Element definition to numerically interpolate and integrate.
-.. todo::
+.. note::
- Describe.
+ This function evaluates the shape function gradients upon construction, they are not recomputed upon evaluation. To evaluate them with respect to updated coordinates (e.g. to do updated Lagrange), use ".update_x(...)" to update the nodal coordinates and re-evaluate the shape function gradients and integration volumes.
+
+.. note::
+
+ By default integration is done using Gauss points. To use a different scheme one has to supply the position (in isoparametric coordinates) and weight of the integration points (their number is inferred from the input).
+
+.. note::
+
+ Most functions take the output as the last input-argument, as to write directly to a pre-allocated array, avoiding their re-allocation. All these functions have a wrapper that does the allocation for you (and thus returns the output rather than taking it as input). All function of this kind are indicated here with a *
+
+Element::Hex8::Quadrature::update_x(...)
+----------------------------------------
+
+Update the nodal coordinates (elemvec: [nelem, nne, ndim]).
+
+Element::Hex8::Quadrature::nelem()
+----------------------------------
+
+Number of elements.
+
+Element::Hex8::Quadrature::nne()
+--------------------------------
+
+Number of nodes per element.
+
+Element::Hex8::Quadrature::ndim()
+---------------------------------
+
+Number of dimensions.
+
+Element::Hex8::Quadrature::nip()
+--------------------------------
+
+Number of integration points.
+
+Element::Hex8::Quadrature::GradN()
+----------------------------------
+
+(Current) Shape function gradient (w.r.t. real coordinates): [nelem, nip, nne, ndim]
+
+Element::Hex8::Quadrature::dV(...)*
+-----------------------------------
+
+(Current) Volume of each integration point (qscalar: [nelem, nip]). An overload is available to get the same result as a tensor per integration point (qtensor: [nelem, nip, tdim, tdim]) with all tensor-components having the same value.
+
+Element::Hex8::Quadrature::gradN_vector(...)*
+---------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \vec{\nabla} N_m \vec{u}_m
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ij} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Hex8::Quadrature::gradN_vector_T(...)*
+-----------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ji} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Hex8::Quadrature::symGradN_vector(...)*
+------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \tfrac{1}{2} \left(
+ \vec{\nabla} N_m \vec{u}_m + \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+ \right)
+
+Element::Hex8::Quadrature::int_N_scalar_NT_dV(...)*
+---------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ M_{mn}
+ =
+ \int\limits_{\Omega^h} N_m \; \rho \; N_n \; \mathrm{d}\Omega^h
+ \equiv
+ \sum\limits_q \; N_m \; \rho \; N_n \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim]. This implies that all dimensions are the same.
+
+Element::Hex8::Quadrature::int_gradN_dot_tensor2_dV(...)*
+---------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \vec{f}_m = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \bm{\sigma} \; \mathrm{d}\Omega^h
+
+or in index notation
+
+.. math::
+
+ f_{mj} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} \sigma_{ij} \; \delta\Omega_q
+
+Element::Hex8::Quadrature::int_gradN_dot_tensor4_dot_gradNT_dV(...)*
+--------------------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \bm{K}_{mn} = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \mathbb{C} \cdot \vec{\nabla} N_n \; \mathrm{d}\Omega^h
+
+or in index notation
+
+.. math::
+
+ K_{m+id, n+kd} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} C_{ijkl} \frac{\partial N_n}{\partial x_l} \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim].
Element::Hex8::Gauss
-=====================
+====================
-Integration definition.
+Integration points according to exact integration using Gauss points.
-.. todo::
+Element::Hex8::Gauss::nip()
+---------------------------
- Describe.
+Returns the number of integration points.
+
+Element::Hex8::Gauss::xi()
+--------------------------
+
+Returns the position of the integration points in isoparametric coordinates [nip, ndim] (with ndim = 3).
+
+Element::Hex8::Gauss::w()
+-------------------------
+
+Returns the weights of the integration points [nip].
Element::Hex8::Nodal
-=====================
+====================
+
+Integration points that coincide with the nodes (equally weight). This scheme can for example be used to obtain a diagonal mass matrix.
+
+Element::Hex8::Nodal::nip()
+---------------------------
+
+Returns the number of integration points.
-Integration definition.
+Element::Hex8::Nodal::xi()
+--------------------------
-.. todo::
+Returns the position of the integration points in isoparametric coordinates [nip, ndim] (with ndim = 3).
- Describe.
+Element::Hex8::Nodal::w()
+-------------------------
+Returns the weights of the integration points [nip].
diff --git a/docs/details/ElementQuad4.rst b/docs/details/ElementQuad4.rst
index 2a73ccb..0b705c1 100644
--- a/docs/details/ElementQuad4.rst
+++ b/docs/details/ElementQuad4.rst
@@ -1,66 +1,492 @@
+.. _ElementQuad4:
**************
Element::Quad4
**************
| :download:`GooseFEM/ElementQuad4.h <../../include/GooseFEM/ElementQuad4.h>`
| :download:`GooseFEM/ElementQuad4.hpp <../../include/GooseFEM/ElementQuad4.hpp>`
| :download:`GooseFEM/ElementQuad4Planar.h <../../include/GooseFEM/ElementQuad4Planar.h>`
| :download:`GooseFEM/ElementQuad4Planar.hpp <../../include/GooseFEM/ElementQuad4Planar.hpp>`
| :download:`GooseFEM/ElementQuad4Axisymmetric.h <../../include/GooseFEM/ElementQuad4Axisymmetric.h>`
| :download:`GooseFEM/ElementQuad4Axisymmetric.hpp <../../include/GooseFEM/ElementQuad4Axisymmetric.hpp>`
Element::Quad4::Quadrature
==========================
-Element definition.
+Element definition to numerically interpolate and integrate.
-.. todo::
+.. note::
- Describe.
+ This function evaluates the shape function gradients upon construction, they are not recomputed upon evaluation. To evaluate them with respect to updated coordinates (e.g. to do updated Lagrange), use ".update_x(...)" to update the nodal coordinates and re-evaluate the shape function gradients and integration volumes.
-Element::Quad4::QuadratureAxisymmetric
-======================================
+.. note::
+
+ By default integration is done using Gauss points. To use a different scheme one has to supply the position (in isoparametric coordinates) and weight of the integration points (their number is inferred from the input).
+
+.. note::
+
+ Most functions take the output as the last input-argument, as to write directly to a pre-allocated array, avoiding their re-allocation. All these functions have a wrapper that does the allocation for you (and thus returns the output rather than taking it as input). All function of this kind are indicated here with a *
+
+Element::Quad4::Quadrature::update_x(...)
+-----------------------------------------
+
+Update the nodal coordinates (elemvec: [nelem, nne, ndim]).
+
+Element::Quad4::Quadrature::nelem()
+-----------------------------------
+
+Number of elements.
+
+Element::Quad4::Quadrature::nne()
+---------------------------------
+
+Number of nodes per element.
+
+Element::Quad4::Quadrature::ndim()
+----------------------------------
+
+Number of dimensions.
+
+Element::Quad4::Quadrature::nip()
+---------------------------------
+
+Number of integration points.
+
+Element::Quad4::Quadrature::GradN()
+-----------------------------------
+
+(Current) Shape function gradient (w.r.t. real coordinates): [nelem, nip, nne, ndim]
+
+Element::Quad4::Quadrature::dV(...)*
+------------------------------------
+
+(Current) Volume of each integration point (qscalar: [nelem, nip]). An overload is available to get the same result as a tensor per integration point (qtensor: [nelem, nip, tdim, tdim]) with all tensor-components having the same value.
+
+Element::Quad4::Quadrature::gradN_vector(...)*
+----------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \vec{\nabla} N_m \vec{u}_m
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ij} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Quad4::Quadrature::gradN_vector_T(...)*
+------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ji} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Quad4::Quadrature::symGradN_vector(...)*
+-------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \tfrac{1}{2} \left(
+ \vec{\nabla} N_m \vec{u}_m + \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+ \right)
+
+Element::Quad4::Quadrature::int_N_scalar_NT_dV(...)*
+----------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ M_{mn}
+ =
+ \int\limits_{\Omega^h} N_m \; \rho \; N_n \; \mathrm{d}\Omega^h
+ \equiv
+ \sum\limits_q \; N_m \; \rho \; N_n \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim]. This implies that all dimensions are the same.
+
+Element::Quad4::Quadrature::int_gradN_dot_tensor2_dV(...)*
+----------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \vec{f}_m = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \bm{\sigma} \; \mathrm{d}\Omega^h
-Element definition.
+or in index notation
-.. todo::
+.. math::
- Describe.
+ f_{mj} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} \sigma_{ij} \; \delta\Omega_q
+Element::Quad4::Quadrature::int_gradN_dot_tensor4_dot_gradNT_dV(...)*
+---------------------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \bm{K}_{mn} = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \mathbb{C} \cdot \vec{\nabla} N_n \; \mathrm{d}\Omega^h
+
+or in index notation
+
+.. math::
+
+ K_{m+id, n+kd} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} C_{ijkl} \frac{\partial N_n}{\partial x_l} \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim].
Element::Quad4::QuadraturePlanar
================================
-Element definition.
+Element definition to numerically interpolate and integrate under a planar assumption. This implies that all the tensors are 3-d, but that the third dimension is ignored by all functions (although for output these components are zero-initialised).
+
+.. note::
+
+ This function evaluates the shape function gradients upon construction, they are not recomputed upon evaluation. To evaluate them with respect to updated coordinates (e.g. to do updated Lagrange), use ".update_x(...)" to update the nodal coordinates and re-evaluate the shape function gradients and integration volumes.
+
+.. note::
+
+ By default integration is done using Gauss points. To use a different scheme one has to supply the position (in isoparametric coordinates) and weight of the integration points (their number is inferred from the input).
+
+.. note::
+
+ Most functions take the output as the last input-argument, as to write directly to a pre-allocated array, avoiding their re-allocation. All these functions have a wrapper that does the allocation for you (and thus returns the output rather than taking it as input). All function of this kind are indicated here with a *
+
+Element::Quad4::QuadraturePlanar::update_x(...)
+-----------------------------------------------
+
+Update the nodal coordinates (elemvec: [nelem, nne, ndim]).
+
+Element::Quad4::QuadraturePlanar::nelem()
+-----------------------------------------
+
+Number of elements.
+
+Element::Quad4::QuadraturePlanar::nne()
+---------------------------------------
+
+Number of nodes per element.
+
+Element::Quad4::QuadraturePlanar::ndim()
+----------------------------------------
+
+Number of dimensions.
+
+Element::Quad4::QuadraturePlanar::nip()
+---------------------------------------
+
+Number of integration points.
+
+Element::Quad4::QuadraturePlanar::GradN()
+-----------------------------------------
+
+(Current) Shape function gradient (w.r.t. real coordinates): [nelem, nip, nne, ndim]
+
+Element::Quad4::QuadraturePlanar::dV(...)*
+------------------------------------------
+
+(Current) Volume of each integration point (qscalar: [nelem, nip]). An overload is available to get the same result as a tensor per integration point (qtensor: [nelem, nip, tdim, tdim]) with all tensor-components having the same value.
+
+Element::Quad4::QuadraturePlanar::gradN_vector(...)*
+----------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \vec{\nabla} N_m \vec{u}_m
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ij} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Quad4::QuadraturePlanar::gradN_vector_T(...)*
+------------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ji} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Quad4::QuadraturePlanar::symGradN_vector(...)*
+-------------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \tfrac{1}{2} \left(
+ \vec{\nabla} N_m \vec{u}_m + \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+ \right)
+
+Element::Quad4::QuadraturePlanar::int_N_scalar_NT_dV(...)*
+----------------------------------------------------------
-.. todo::
+Implementation of
- Describe.
+.. math::
+
+ M_{mn}
+ =
+ \int\limits_{\Omega^h} N_m \; \rho \; N_n \; \mathrm{d}\Omega^h
+ \equiv
+ \sum\limits_q \; N_m \; \rho \; N_n \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim]. This implies that all dimensions are the same.
+
+Element::Quad4::QuadraturePlanar::int_gradN_dot_tensor2_dV(...)*
+----------------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \vec{f}_m = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \bm{\sigma} \; \mathrm{d}\Omega^h
+
+or in index notation
+
+.. math::
+
+ f_{mj} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} \sigma_{ij} \; \delta\Omega_q
+
+Element::Quad4::QuadraturePlanar::int_gradN_dot_tensor4_dot_gradNT_dV(...)*
+---------------------------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \bm{K}_{mn} = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \mathbb{C} \cdot \vec{\nabla} N_n \; \mathrm{d}\Omega^h
+
+or in index notation
+
+.. math::
+
+ K_{m+id, n+kd} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} C_{ijkl} \frac{\partial N_n}{\partial x_l} \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim].
+
+Element::Quad4::QuadratureAxisymmetric
+======================================
+
+Element definition to numerically interpolate and integrate in an axisymmetric cylindrical coordinate system. This implies that all tensors (stress, strain, stiffness, ...) are fully three dimensional, but the discretisation is two-dimensional.
+
+.. note::
+
+ This function evaluates the shape function gradients upon construction, they are not recomputed upon evaluation. To evaluate them with respect to updated coordinates (e.g. to do updated Lagrange), use ".update_x(...)" to update the nodal coordinates and re-evaluate the shape function gradients and integration volumes.
+
+.. note::
+
+ By default integration is done using Gauss points. To use a different scheme one has to supply the position (in isoparametric coordinates) and weight of the integration points (their number is inferred from the input).
+
+.. note::
+
+ Most functions take the output as the last input-argument, as to write directly to a pre-allocated array, avoiding their re-allocation. All these functions have a wrapper that does the allocation for you (and thus returns the output rather than taking it as input). All function of this kind are indicated here with a *
+
+Element::Quad4::QuadratureAxisymmetric::update_x(...)
+-----------------------------------------------------
+
+Update the nodal coordinates (elemvec: [nelem, nne, ndim]).
+
+Element::Quad4::QuadratureAxisymmetric::nelem()
+-----------------------------------------------
+
+Number of elements.
+
+Element::Quad4::QuadratureAxisymmetric::nne()
+---------------------------------------------
+
+Number of nodes per element.
+
+Element::Quad4::QuadratureAxisymmetric::ndim()
+----------------------------------------------
+
+Number of dimensions.
+
+Element::Quad4::QuadratureAxisymmetric::nip()
+---------------------------------------------
+
+Number of integration points.
+
+Element::Quad4::QuadratureAxisymmetric::GradN()
+-----------------------------------------------
+
+(Current) Shape function gradient (w.r.t. real coordinates): [nelem, nip, nne, ndim]
+
+Element::Quad4::QuadratureAxisymmetric::dV(...)*
+------------------------------------------------
+
+(Current) Volume of each integration point (qscalar: [nelem, nip]). An overload is available to get the same result as a tensor per integration point (qtensor: [nelem, nip, tdim, tdim]) with all tensor-components having the same value.
+
+Element::Quad4::QuadratureAxisymmetric::gradN_vector(...)*
+----------------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \vec{\nabla} N_m \vec{u}_m
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ij} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Quad4::QuadratureAxisymmetric::gradN_vector_T(...)*
+------------------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+
+or in index notation
+
+.. math::
+
+ \varepsilon_{ji} = \frac{\partial N_m}{\partial x_i} u_{mj}
+
+Element::Quad4::QuadratureAxisymmetric::symGradN_vector(...)*
+-------------------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ \bm{\varepsilon} = \tfrac{1}{2} \left(
+ \vec{\nabla} N_m \vec{u}_m + \left( \vec{\nabla} N_m \vec{u}_m \right)^T
+ \right)
+
+Element::Quad4::QuadratureAxisymmetric::int_N_scalar_NT_dV(...)*
+----------------------------------------------------------------
+
+Implementation of
+
+.. math::
+
+ M_{mn}
+ =
+ \int\limits_{\Omega^h} N_m \; \rho \; N_n \; \mathrm{d}\Omega^h
+ \equiv
+ \sum\limits_q \; N_m \; \rho \; N_n \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim]. This implies that all dimensions are the same.
+
+Element::Quad4::QuadratureAxisymmetric::int_gradN_dot_tensor2_dV(...)*
+----------------------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \vec{f}_m = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \bm{\sigma} \; \mathrm{d}\Omega^h
+
+or in index notation
+
+.. math::
+
+ f_{mj} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} \sigma_{ij} \; \delta\Omega_q
+
+Element::Quad4::QuadratureAxisymmetric::int_gradN_dot_tensor4_dot_gradNT_dV(...)*
+---------------------------------------------------------------------------------
+
+Implementation of:
+
+.. math::
+
+ \bm{K}_{mn} = \int\limits_{\Omega^h} ( \vec{\nabla} N_m ) \cdot \mathbb{C} \cdot \vec{\nabla} N_n \; \mathrm{d}\Omega^h
+
+or in index notation
+
+.. math::
+
+ K_{m+id, n+kd} = \sum\limits_q \; \frac{\partial N_m}{\partial x_i} C_{ijkl} \frac{\partial N_n}{\partial x_l} \; \delta\Omega_q
+
+Note that the output is an "elemmat", which has shape [nelem, nne*ndim, nne*ndim].
Element::Quad4::Gauss
=====================
-Integration definition.
+Integration points according to exact integration using Gauss points.
+
+Element::Quad4::Gauss::nip()
+----------------------------
-.. todo::
+Returns the number of integration points.
- Describe.
+Element::Quad4::Gauss::xi()
+---------------------------
+
+Returns the position of the integration points in isoparametric coordinates [nip, ndim] (with ndim = 3).
+
+Element::Quad4::Gauss::w()
+--------------------------
+
+Returns the weights of the integration points [nip].
Element::Quad4::Nodal
=====================
-Integration definition.
+Integration points that coincide with the nodes (equally weight). This scheme can for example be used to obtain a diagonal mass matrix.
+
+Element::Quad4::Nodal::nip()
+----------------------------
+
+Returns the number of integration points.
+
+Element::Quad4::Nodal::xi()
+---------------------------
-.. todo::
+Returns the position of the integration points in isoparametric coordinates [nip, ndim] (with ndim = 3).
- Describe.
+Element::Quad4::Nodal::w()
+--------------------------
+
+Returns the weights of the integration points [nip].
Element::Quad4::MidPoint
========================
-Integration definition.
+Single integration point in the middle of the element.
+
+Element::Quad4::MidPoint::nip()
+-------------------------------
+
+Returns the number of integration points.
+
+Element::Quad4::MidPoint::xi()
+------------------------------
+
+Returns the position of the integration points in isoparametric coordinates [nip, ndim] (with ndim = 3).
-.. todo::
+Element::Quad4::MidPoint::w()
+-----------------------------
- Describe.
+Returns the weights of the integration points [nip].
diff --git a/docs/details/Iterate.rst b/docs/details/Iterate.rst
index de2cc4f..e44af6c 100644
--- a/docs/details/Iterate.rst
+++ b/docs/details/Iterate.rst
@@ -1,12 +1,23 @@
+.. _Iterate:
+
*******
Iterate
*******
+| :download:`GooseFEM/Iterate.h <../../include/GooseFEM/Iterate.h>`
+| :download:`GooseFEM/Iterate.hpp <../../include/GooseFEM/Iterate.hpp>`
+
Iterate::StopList
=================
-Convergence check.
+Convergence check to check that a residual is smaller than a certain value of a certain number of consecutive steps. The class is constructed with the number of consecutive to enforce the residual.
+
+Iterate::StopList::reset(...)
+-----------------------------
+
+Reset all residuals to infinity.
-.. todo::
+Iterate::StopList::stop(...)
+----------------------------
- Complete.
+Append the list with residuals, return "true" if all residuals are below the tolerance (argument).
diff --git a/docs/details/Matrix.rst b/docs/details/Matrix.rst
index 469653b..08ecd53 100644
--- a/docs/details/Matrix.rst
+++ b/docs/details/Matrix.rst
@@ -1,108 +1,474 @@
+.. _Matrix:
+
******
Matrix
******
-.. _sparse:
+| :download:`GooseFEM/Matrix.h <../../include/GooseFEM/Matrix.h>`
+| :download:`GooseFEM/Matrix.hpp <../../include/GooseFEM/Matrix.hpp>`
+| :download:`GooseFEM/MatrixPartitioned.h <../../include/GooseFEM/MatrixPartitioned.h>`
+| :download:`GooseFEM/MatrixPartitioned.hpp <../../include/GooseFEM/MatrixPartitioned.hpp>`
+| :download:`GooseFEM/MatrixPartitionedTyings.h <../../include/GooseFEM/MatrixPartitionedTyings.h>`
+| :download:`GooseFEM/MatrixPartitionedTyings.hpp <../../include/GooseFEM/MatrixPartitionedTyings.hpp>`
+| :download:`GooseFEM/MatrixDiagonal.h <../../include/GooseFEM/MatrixDiagonal.h>`
+| :download:`GooseFEM/MatrixDiagonal.hpp <../../include/GooseFEM/MatrixDiagonal.hpp>`
+| :download:`GooseFEM/MatrixDiagonalPartitioned.h <../../include/GooseFEM/MatrixDiagonalPartitioned.h>`
+| :download:`GooseFEM/MatrixDiagonalPartitioned.hpp <../../include/GooseFEM/MatrixDiagonalPartitioned.hpp>`
Matrix
======
Matrix definition.
-.. todo::
+.. note::
+
+ A solver has to be chosen, see :ref:`linear_solver`.
+
+Matrix::nelem()
+---------------
+
+Return the number of elements.
+
+Matrix::nne()
+-------------
+
+Return the number of nodes-per-element.
+
+Matrix::nnode()
+---------------
+
+Return the number of nodes.
+
+Matrix::ndim()
+--------------
- Complete.
+Return the number of dimensions.
+
+Matrix::ndof()
+--------------
+
+Return the number of DOFs.
+
+Matrix::dofs()
+--------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+Matrix::assemble(...)
+---------------------
+
+Assemble matrix from element matrices stored as "elemmat".
+
+Matrix::solve(...)
+------------------
+
+Solve linear system.
MatrixPartitioned
=================
Partitioned matrix definition.
-.. todo::
+.. note::
+
+ A solver has to be chosen, see :ref:`linear_solver`.
+
+MatrixPartitioned::nelem()
+--------------------------
+
+Return the number of elements.
+
+MatrixPartitioned::nne()
+------------------------
+
+Return the number of nodes-per-element.
+
+MatrixPartitioned::nnode()
+--------------------------
+
+Return the number of nodes.
+
+MatrixPartitioned::ndim()
+-------------------------
+
+Return the number of dimensions.
+
+MatrixPartitioned::ndof()
+-------------------------
+
+Return the number of DOFs.
+
+MatrixPartitioned::nnu()
+------------------------
+
+Return the number of unknown DOFs.
+
+MatrixPartitioned::nnp()
+------------------------
+
+Return the number of prescribed DOFs.
+
+MatrixPartitioned::dofs()
+-------------------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+MatrixPartitioned::iiu()
+------------------------
+
+Return the unknown DOF-numbers per node [nnu].
- Complete.
+MatrixPartitioned::iip()
+------------------------
+
+Return the prescribed DOF-numbers per node [nnp].
+
+MatrixPartitioned::assemble(...)
+--------------------------------
+
+Assemble matrix from element matrices stored as "elemmat".
+
+MatrixPartitioned::solve(...)
+-----------------------------
+
+Solve linear system.
+
+MatrixPartitioned::solve_u(...)
+-------------------------------
+
+Solve linear system.
+
+MatrixPartitioned::reaction(...)
+--------------------------------
+
+Compute reaction forces (part of "b" that corresponds to "x_p").
+
+MatrixPartitioned::reaction_p(...)
+----------------------------------
+
+Compute reaction forces (part of "b" that corresponds to "x_p").
MatrixPartitionedTyings
=======================
Partitioned matrix definition with nodal tyings.
-.. todo::
+.. note::
+
+ A solver has to be chosen, see :ref:`linear_solver`.
+
+MatrixPartitionedTyings::nelem()
+--------------------------------
+
+Return the number of elements.
+
+MatrixPartitionedTyings::nne()
+------------------------------
+
+Return the number of nodes-per-element.
+
+MatrixPartitionedTyings::nnode()
+--------------------------------
+
+Return the number of nodes.
+
+MatrixPartitionedTyings::ndim()
+-------------------------------
+
+Return the number of dimensions.
+
+MatrixPartitionedTyings::ndof()
+-------------------------------
+
+Return the number of DOFs.
+
+MatrixPartitionedTyings::nnu()
+------------------------------
+
+Return the number of unknown DOFs.
+
+MatrixPartitionedTyings::nnp()
+------------------------------
+
+Return the number of prescribed DOFs.
+
+MatrixPartitionedTyings::nni()
+------------------------------
+
+Return the number of independent DOFs.
+
+MatrixPartitionedTyings::nnd()
+------------------------------
+
+Return the number of dependent DOFs.
+
+MatrixPartitionedTyings::dofs()
+-------------------------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+MatrixPartitionedTyings::iiu()
+------------------------------
+
+Return the unknown DOF-numbers per node [nnu].
+
+MatrixPartitionedTyings::iip()
+------------------------------
+
+Return the prescribed DOF-numbers per node [nnp].
- Complete.
+MatrixPartitionedTyings::iii()
+------------------------------
+
+Return the independent DOF-numbers per node [nni].
+
+MatrixPartitionedTyings::iid()
+------------------------------
+
+Return the dependent DOF-numbers per node [nnd].
+
+MatrixPartitionedTyings::assemble(...)
+--------------------------------------
+
+Assemble matrix from element matrices stored as "elemmat".
+
+MatrixPartitionedTyings::solve(...)
+-----------------------------------
+
+Solve linear system.
+
+MatrixPartitionedTyings::solve_u(...)
+-------------------------------------
+
+Solve linear system.
MatrixDiagonal
==============
Diagonal matrix definition.
-.. todo::
+MatrixDiagonal::nelem()
+-----------------------
+
+Return the number of elements.
+
+MatrixDiagonal::nne()
+---------------------
+
+Return the number of nodes-per-element.
+
+MatrixDiagonal::nnode()
+-----------------------
+
+Return the number of nodes.
+
+MatrixDiagonal::ndim()
+----------------------
+
+Return the number of dimensions.
+
+MatrixDiagonal::ndof()
+----------------------
+
+Return the number of DOFs.
- Complete.
+MatrixDiagonal::dofs()
+----------------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+MatrixDiagonal::assemble(...)
+-----------------------------
+
+Assemble matrix from element matrices stored as "elemmat".
+
+MatrixDiagonal::dot(...)
+------------------------
+
+Dot-product:
+
+.. math::
+
+ b_i = A_{ij} x_j
+
+MatrixDiagonal::solve(...)
+--------------------------
+
+Solve linear system.
+
+MatrixDiagonal::AsDiagonal(...)
+-------------------------------
+
+Return matrix as diagonal matrix (column)
MatrixDiagonalPartitioned
=========================
Diagonal and partitioned matrix definition.
-.. todo::
+MatrixDiagonalPartitioned::nelem()
+----------------------------------
+
+Return the number of elements.
+
+MatrixDiagonalPartitioned::nne()
+--------------------------------
+
+Return the number of nodes-per-element.
+
+MatrixDiagonalPartitioned::nnode()
+----------------------------------
+
+Return the number of nodes.
+
+MatrixDiagonalPartitioned::ndim()
+---------------------------------
+
+Return the number of dimensions.
+
+MatrixDiagonalPartitioned::ndof()
+---------------------------------
+
+Return the number of DOFs.
+
+MatrixDiagonalPartitioned::nnu()
+--------------------------------
+
+Return the number of unknown DOFs.
+
+MatrixDiagonalPartitioned::nnp()
+--------------------------------
+
+Return the number of prescribed DOFs.
+
+MatrixDiagonalPartitioned::dofs()
+---------------------------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+MatrixDiagonalPartitioned::iiu()
+--------------------------------
+
+Return the unknown DOF-numbers per node [nnu].
+
+MatrixDiagonalPartitioned::iip()
+--------------------------------
+
+Return the prescribed DOF-numbers per node [nnp].
+
+MatrixDiagonalPartitioned::assemble(...)
+----------------------------------------
+
+Assemble matrix from element matrices stored as "elemmat".
+
+MatrixDiagonalPartitioned::dot(...)
+-----------------------------------
+
+Dot-product:
+
+.. math::
+
+ b_i = A_{ij} x_j
+
+MatrixDiagonalPartitioned::dot_u(...)
+-------------------------------------
+
+Dot-product:
+
+.. math::
+
+ b_i = A_{ij} x_j
+
+MatrixDiagonalPartitioned::dot_p(...)
+-------------------------------------
+
+Dot-product:
+
+.. math::
+
+ b_i = A_{ij} x_j
+
+MatrixDiagonalPartitioned::solve(...)
+-------------------------------------
+
+Solve linear system.
+
+MatrixDiagonalPartitioned::solve_u(...)
+---------------------------------------
+
+Solve linear system.
+
+MatrixDiagonalPartitioned::reaction(...)
+----------------------------------------
+
+Compute reaction forces (part of "b" that corresponds to "x_p").
+
+MatrixDiagonalPartitioned::reaction_p(...)
+------------------------------------------
+
+Compute reaction forces (part of "b" that corresponds to "x_p").
+
+MatrixDiagonalPartitioned::AsDiagonal(...)
+------------------------------------------
+
+Return matrix as diagonal matrix (column)
- Complete.
+.. _linear_solver:
Linear solver
=============
The classes ``GooseFEM:::MatrixPartitioned`` and ``GooseFEM:::MatrixPartitionedTyings`` make use of a library to solver the linear system (stored as a sparse matrix). In particular the Eigen library and its plug-ins are used. To use the library's default solver:
.. code-block:: cpp
#include <Eigen/Eigen>
#include <GooseFEM/GooseFEM.h>
int main()
{
...
GooseFEM::MatrixPartitioned<> K(...);
...
return 0;
}
The default solver can, however, be quite slow. Therefore Eigen has quite some `plug-ins <http://eigen.tuxfamily.org/dox/group__TopicSparseSystems.html>`_ for the solver. GooseFEM allows the use of Eigen's Sparse Solver Concept to use such plug-ins. For example, to use SuiteSparse:
.. code-block:: cpp
#include <Eigen/Eigen>
#include <Eigen/CholmodSupport>
#include <GooseFEM/GooseFEM.h>
int main()
{
...
GooseFEM::MatrixPartitioned<Eigen::CholmodSupernodalLLT<Eigen::SparseMatrix<double>>> K(...);
...
return 0;
}
.. todo::
1. `Download SuiteSparse <http://faculty.cse.tamu.edu/davis/suitesparse.html>`_.
2. Extract the downloaded ``SuiteSparse-X.X.X.tar.gz```.
3. Compile the library by:
.. code-block:: bash
cd /path/to/SuiteSparse
make
.. code-block:: bash
clang++ -I/path/to/include/eigen3 -I/path/to/lapack/include -L/path/to/lapack/lib -I/path/to/openblas/include -L/path/to/openblas/lib -lopenblas -I/path/to/SuiteSparse/include -L/path/to/SuiteSparse/lib -lumfpack -lamd -lcholmod -lsuitesparseconfig -lm -std=c++14 -Wall -Wextra -pedantic -march=native -O3 -o example example.cpp
diff --git a/docs/details/Mesh.rst b/docs/details/Mesh.rst
index eeb2954..6d8450f 100644
--- a/docs/details/Mesh.rst
+++ b/docs/details/Mesh.rst
@@ -1,100 +1,101 @@
+.. _Mesh:
****
Mesh
****
| :download:`GooseFEM/Mesh.h <../../include/GooseFEM/Mesh.h>`
| :download:`GooseFEM/Mesh.hpp <../../include/GooseFEM/Mesh.hpp>`
Mesh::dofs
----------
Get a sequential list of DOF-numbers for each vector-component of each node. For example for 3 nodes in 2 dimensions the output is
.. math::
\begin{bmatrix}
0 & 1 \\
2 & 3 \\
4 & 5
\end{bmatrix}
Mesh::Renumber
--------------
Renumber (DOF) indices to lowest possible indices. For example:
.. math::
\begin{bmatrix}
0 & 1 \\
5 & 4
\end{bmatrix}
is renumbered to
.. math::
\begin{bmatrix}
0 & 1 \\
3 & 2
\end{bmatrix}
Or, in pseudo-code, the result of this function is that:
.. code-block:: python
dofs = renumber(dofs)
sort(unique(dofs[:])) == range(max(dofs+1))
.. tip::
One can use the wrapper function "GooseFEM::reorder" or the class "Mesh::Reorder" to get more advanced features.
Mesh::Reorder
-------------
Reorder (DOF) indices such to the lowest possible indices, such that some items are at the beginning or the end. For example:
.. math::
\mathrm{dofs} =
\begin{bmatrix}
0 & 1 \\
2 & 3 \\
4 & 5
\end{bmatrix}
with
.. math::
\mathrm{idx} =
\begin{bmatrix}
0 & 1
\end{bmatrix}
Implies that ``dofs`` is renumbered such that 0 becomes the one-before-last index (:math:`0 \rightarrow 4`), and the 1 becomes the last index (:math:`1 \rightarrow 5`). The remaining items are renumbered to the lowest index while keeping the same order. The result:
.. math::
\begin{bmatrix}
4 & 5 \\
0 & 1 \\
2 & 3
\end{bmatrix}
.. tip::
One can use the wrapper function "GooseFEM::reorder" or the class "Mesh::Reorder" to get more advanced features.
Mesh::coordination
------------------
Get the number of elements connected to each node.
Mesh::elem2node
---------------
Get the element numbers (columns) that are connected to each node (rows).
diff --git a/docs/details/MeshHex8.rst b/docs/details/MeshHex8.rst
index 7f124df..f390cad 100644
--- a/docs/details/MeshHex8.rst
+++ b/docs/details/MeshHex8.rst
@@ -1,69 +1,216 @@
+.. _MeshHex8:
**********
Mesh::Hex8
**********
| :download:`GooseFEM/MeshHex8.h <../../include/GooseFEM/MeshHex8.h>`
| :download:`GooseFEM/MeshHex8.hpp <../../include/GooseFEM/MeshHex8.hpp>`
Naming convention
=================
The following naming convention is used:
* **Front**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq y \leq L_y`, :math:`z = 0`.
* **Back**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq y \leq L_y`, :math:`z = L_z`.
* **Bottom**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq z \leq L_z`, :math:`y = 0`.
* **Top**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`0 \leq z \leq L_z`, :math:`y = L_y`.
* **Left**: all nodes whose coordinates :math:`0 \leq y \leq L_y`, :math:`0 \leq z \leq L_z`, :math:`x = 0`.
* **Right**: all nodes whose coordinates :math:`0 \leq y \leq L_y`, :math:`0 \leq z \leq L_z`, :math:`x = L_x`.
The edges and corners follow from the intersections, i.e.
* **FrontBottomEdge**: all nodes whose coordinates :math:`0 \leq x \leq L_x`, :math:`y = 0`, :math:`z = 0`.
* ...
* **FrontBottomLeftCorner**: the node whose coordinate :math:`x = 0`, :math:`y = 0`, :math:`z = 0`.
* ...
.. image:: figures/MeshHex8/naming_convention.svg
:width: 350px
:align: center
Mesh::Hex8::Regular
===================
Regular mesh.
-.. todo::
+.. seealso::
- Describe, illustrate
+ | :download:`Python/ParaView - example <figures/MeshHex8/Regular/paraview.py>`
+ | :download:`Python/ParaView - nodesets <figures/MeshHex8/Regular/paraview_nodesets.py>`
-.. todo::
+Mesh::Hex8::Regular::nelem()
+----------------------------
- More methods and classes
+Return number of elements.
-.. todo::
+Mesh::Hex8::Regular::nnode()
+----------------------------
- figures/MeshHex8/Regular/example...
+Return number of nodes.
-.. todo::
+Mesh::Hex8::Regular::nne()
+--------------------------
- figures/MeshHex8/Regular/nodes...
+Return number of nodes-per-element (= 3).
+Mesh::Hex8::Regular::ndim()
+---------------------------
+
+Return number of dimensions (= 2).
+
+Mesh::Hex8::Regular::getElementType()
+-------------------------------------
+
+Return element-type. For example used in the :ref:`ParaView` module.
+
+Mesh::Hex8::Regular::coor()
+---------------------------
+
+Return nodal coordinates [nnode, ndim].
+
+Mesh::Hex8::Regular::conn()
+---------------------------
+
+Return connectivity [nelem, nne].
+
+Mesh::Hex8::Regular::nodesXXXEdge()
+-----------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge.
+
+Mesh::Hex8::Regular::nodesXXXOpenEdge()
+---------------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge, excluding the corners.
+
+Mesh::Hex8::Regular::nodesXXXCorner()
+-------------------------------------
+
+Node number of one of the corners (e.g. "BottomLeft").
+
+Mesh::Hex8::Regular::nodesPeriodic()
+------------------------------------
+
+Periodic node pairs. Each row contains on pair of (independent, dependent) node numbers. The output shape is thus [n_pairs, 2].
+
+Mesh::Hex8::Regular::nodesOrigin()
+----------------------------------
+
+Bottom-left node, used as reference for periodicity.
+
+Mesh::Hex8::Regular::dofs()
+---------------------------
+
+DOF-numbers for each component of each node (sequential). The output shape is thus [nnode, ndim].
+
+Mesh::Hex8::Regular::dofsPeriodic()
+-----------------------------------
+
+DOF-numbers for each component of each node, for the case that the periodicity if fully eliminated. The output shape is thus [nnode, ndim].
+
+Mesh::Hex8::Regular::elementMatrix()
+------------------------------------
+
+Return element numbers as matrix [nely, nelx].
Mesh::Hex8::FineLayer
=====================
-Mesh with a middle plane that is fine the middle, and becomes course away from this plane.
+Mesh with a fine layer in the middle, and that becomes course away from this plane (see image below). Note coursening can only be done if the number of elements in x- and y-direction is dividable by 3, and that it is only optimal if the number of elements in x- and y-direction is a factor of 3. Note that the number of elements in the vertical direction is specified as the number of times the unit element (the number of times "h" the height should be), and that this number is only a target: the algorithm chooses in accordance with the applied coursing.
+
+.. seealso::
+
+ | :download:`Python/ParaView - example <figures/MeshHex8/FineLayer/paraview.py>`
+ | :download:`Python/ParaView - nodesets <figures/MeshHex8/FineLayer/paraview_nodesets.py>`
+
+Mesh::Hex8::FineLayer::nelem()
+------------------------------
+
+Return number of elements.
+
+Mesh::Hex8::FineLayer::nnode()
+------------------------------
+
+Return number of nodes.
+
+Mesh::Hex8::FineLayer::nne()
+----------------------------
+
+Return number of nodes-per-element (= 3).
+
+Mesh::Hex8::FineLayer::ndim()
+-----------------------------
+
+Return number of dimensions (= 2).
+
+Mesh::Hex8::FineLayer::nelx()
+-----------------------------
+
+Number of elements in horizontal direction (along the weak layer) (matches input).
+
+Mesh::Hex8::FineLayer::nely()
+-----------------------------
+
+Actual number of elements unit elements in vertical direction (actual number of times "h" the mesh is heigh).
+
+Mesh::Hex8::FineLayer::h()
+--------------------------
+
+Unit edge size (matches input).
+
+Mesh::Hex8::FineLayer::getElementType()
+---------------------------------------
+
+Return element-type. For example used in the :ref:`ParaView` module.
+
+Mesh::Hex8::FineLayer::coor()
+-----------------------------
+
+Return nodal coordinates [nnode, ndim].
+
+Mesh::Hex8::FineLayer::conn()
+-----------------------------
+
+Return connectivity [nelem, nne].
+
+Mesh::Hex8::FineLayer::nodesXXXEdge()
+-------------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", "Right", "Front", or "Back" edge.
+
+Mesh::Hex8::FineLayer::nodesXXXOpenEdge()
+-----------------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", "Right", "Front", or "Back" edge, excluding the corners.
+
+Mesh::Hex8::FineLayer::nodesXXXCorner()
+---------------------------------------
+
+Node number of one of the corners (e.g. "FrontBottomLeft").
+
+Mesh::Hex8::FineLayer::nodesPeriodic()
+--------------------------------------
+
+Periodic node pairs. Each row contains on pair of (independent, dependent) node numbers. The output shape is thus [n_pairs, 2].
+
+Mesh::Hex8::FineLayer::nodesOrigin()
+------------------------------------
+
+Bottom-left node, used as reference for periodicity.
-.. todo::
+Mesh::Hex8::FineLayer::dofs()
+-----------------------------
- Describe, illustrate
+DOF-numbers for each component of each node (sequential). The output shape is thus [nnode, ndim].
-.. todo::
+Mesh::Hex8::FineLayer::dofsPeriodic()
+-------------------------------------
- figures/MeshHex8/FineLayer/example...
+DOF-numbers for each component of each node, for the case that the periodicity if fully eliminated. The output shape is thus [nnode, ndim].
-.. todo::
+Mesh::Hex8::FineLayer::elementsMiddleLayer()
+--------------------------------------------
- figures/MeshHex8/FineLayer/nodes...
+Element numbers of the middle, fine, layer
diff --git a/docs/details/MeshQuad4.rst b/docs/details/MeshQuad4.rst
index a3e5989..0ab51eb 100644
--- a/docs/details/MeshQuad4.rst
+++ b/docs/details/MeshQuad4.rst
@@ -1,96 +1,289 @@
+.. _MeshQuad4:
***********
Mesh::Quad4
***********
| :download:`GooseFEM/MeshQuad4.h <../../include/GooseFEM/MeshQuad4.h>`
| :download:`GooseFEM/MeshQuad4.hpp <../../include/GooseFEM/MeshQuad4.hpp>`
Naming convention
=================
-.. todo::
-
- Finish
-
.. image:: figures/MeshQuad4/naming_convention.svg
:width: 350px
:align: center
Mesh::Quad4::Regular
====================
Regular mesh.
-.. todo::
+.. seealso::
+
+ | :download:`Python - example <figures/MeshQuad4/Regular/example.py>`
+ | :download:`Python/ParaView - example <figures/MeshQuad4/Regular/paraview.py>`
+ | :download:`Python/ParaView - nodesets <figures/MeshQuad4/Regular/paraview_nodesets.py>`
+
+Mesh::Quad4::Regular::nelem()
+-----------------------------
+
+Return number of elements.
+
+Mesh::Quad4::Regular::nnode()
+-----------------------------
+
+Return number of nodes.
+
+Mesh::Quad4::Regular::nne()
+---------------------------
+
+Return number of nodes-per-element (= 3).
+
+Mesh::Quad4::Regular::ndim()
+----------------------------
+
+Return number of dimensions (= 2).
+
+Mesh::Quad4::Regular::getElementType()
+--------------------------------------
+
+Return element-type. For example used in the :ref:`ParaView` module.
+
+Mesh::Quad4::Regular::coor()
+----------------------------
+
+Return nodal coordinates [nnode, ndim].
+
+Mesh::Quad4::Regular::conn()
+----------------------------
+
+Return connectivity [nelem, nne].
+
+Mesh::Quad4::Regular::nodesXXXEdge()
+------------------------------------
- Describe, illustrate
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge.
-.. todo::
+Mesh::Quad4::Regular::nodesXXXOpenEdge()
+----------------------------------------
- figures/MeshQuad4/Regular/example...
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge, excluding the corners.
-.. todo::
+Mesh::Quad4::Regular::nodesXXXCorner()
+--------------------------------------
- figures/MeshQuad4/Regular/example2...
+Node number of one of the corners (e.g. "BottomLeft").
-.. todo::
+Mesh::Quad4::Regular::nodesPeriodic()
+-------------------------------------
- figures/MeshQuad4/Regular/nodes...
+Periodic node pairs. Each row contains on pair of (independent, dependent) node numbers. The output shape is thus [n_pairs, 2].
+
+Mesh::Quad4::Regular::nodesOrigin()
+-----------------------------------
+
+Bottom-left node, used as reference for periodicity.
+
+Mesh::Quad4::Regular::dofs()
+----------------------------
+
+DOF-numbers for each component of each node (sequential). The output shape is thus [nnode, ndim].
+
+Mesh::Quad4::Regular::dofsPeriodic()
+------------------------------------
+
+DOF-numbers for each component of each node, for the case that the periodicity if fully eliminated. The output shape is thus [nnode, ndim].
+
+Mesh::Quad4::Regular::elementMatrix()
+-------------------------------------
+
+Return element numbers as matrix [nely, nelx].
Mesh::Quad4::FineLayer
======================
-Mesh with a middle plane that is fine the middle, and becomes course away from this plane.
+Mesh with a fine layer in the middle, and that becomes course away from this plane (see image below). Note coursening can only be done if the number of elements in horizontal direction is dividable by 3, and that it is only optimal if the number of elements in horizontal direction is a factor of 3. Note that the number of elements in the vertical direction is specified as the number of times the unit element (the number of times "h" the height should be), and that this number is only a target: the algorithm chooses in accordance with the applied coursing.
+
+.. image:: figures/MeshQuad4/FineLayer/behaviour.svg
+ :width: 800px
+ :align: center
+
+.. seealso::
+
+ | :download:`Python - example <figures/MeshQuad4/FineLayer/example.py>`
+ | :download:`Python/ParaView - example <figures/MeshQuad4/FineLayer/paraview.py>`
+ | :download:`Python/ParaView - nodesets <figures/MeshQuad4/FineLayer/paraview_nodesets.py>`
+ | :download:`Python - behaviour 'nx' <figures/MeshQuad4/FineLayer/behaviour.py>`
+ | :download:`Python - element numbers <figures/MeshQuad4/FineLayer/element-numbers.py>`
+
+Mesh::Quad4::FineLayer::nelem()
+-------------------------------
+
+Return number of elements.
+
+Mesh::Quad4::FineLayer::nnode()
+-------------------------------
+
+Return number of nodes.
+
+Mesh::Quad4::FineLayer::nne()
+-----------------------------
+
+Return number of nodes-per-element (= 3).
-.. todo::
+Mesh::Quad4::FineLayer::ndim()
+------------------------------
- Describe, illustrate
+Return number of dimensions (= 2).
-.. todo::
+Mesh::Quad4::FineLayer::nelx()
+------------------------------
- figures/MeshQuad4/FineLayer/behaviour...
+Number of elements in horizontal direction (along the weak layer) (matches input).
-.. todo::
+Mesh::Quad4::FineLayer::nely()
+------------------------------
- figures/MeshQuad4/FineLayer/element-numbers...
+Actual number of elements unit elements in vertical direction (actual number of times "h" the mesh is heigh).
-.. todo::
+Mesh::Quad4::FineLayer::h()
+---------------------------
- figures/MeshQuad4/FineLayer/example...
+Unit edge size (matches input).
-.. todo::
+Mesh::Quad4::FineLayer::getElementType()
+----------------------------------------
- figures/MeshQuad4/FineLayer/example2...
+Return element-type. For example used in the :ref:`ParaView` module.
-.. todo::
+Mesh::Quad4::FineLayer::coor()
+------------------------------
- figures/MeshQuad4/FineLayer/nodes...
+Return nodal coordinates [nnode, ndim].
+Mesh::Quad4::FineLayer::conn()
+------------------------------
+Return connectivity [nelem, nne].
+
+Mesh::Quad4::FineLayer::nodesXXXEdge()
+--------------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge.
+
+Mesh::Quad4::FineLayer::nodesXXXOpenEdge()
+------------------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge, excluding the corners.
+
+Mesh::Quad4::FineLayer::nodesXXXCorner()
+----------------------------------------
+
+Node number of one of the corners (e.g. "BottomLeft").
+
+Mesh::Quad4::FineLayer::nodesPeriodic()
+---------------------------------------
+
+Periodic node pairs. Each row contains on pair of (independent, dependent) node numbers. The output shape is thus [n_pairs, 2].
+
+Mesh::Quad4::FineLayer::nodesOrigin()
+-------------------------------------
+
+Bottom-left node, used as reference for periodicity.
+
+Mesh::Quad4::FineLayer::dofs()
+------------------------------
+
+DOF-numbers for each component of each node (sequential). The output shape is thus [nnode, ndim].
+
+Mesh::Quad4::FineLayer::dofsPeriodic()
+--------------------------------------
+
+DOF-numbers for each component of each node, for the case that the periodicity if fully eliminated. The output shape is thus [nnode, ndim].
+
+Mesh::Quad4::FineLayer::elementsMiddleLayer()
+---------------------------------------------
+
+Element numbers of the middle, fine, layer
Mesh::Quad4::Map::RefineRegular
===============================
-Refine mesh.
+Refine a "Regular" mesh.
+
+Mesh::Quad4::Map::RefineRegular::getCoarseMesh()
+------------------------------------------------
+
+Return course mesh as "Mesh::Quad4::Regular".
-.. todo::
+Mesh::Quad4::Map::RefineRegular::getFineMesh()
+----------------------------------------------
- Describe, illustrate
+Return fine mesh as "Mesh::Quad4::Regular".
+
+Mesh::Quad4::Map::RefineRegular::getMap()
+-----------------------------------------
+
+Elements of the fine mesh per element of the coarse mesh (rows).
+
+Mesh::Quad4::Map::RefineRegular::mapToCoarse(...)
+-------------------------------------------------
+
+Map field to the course mesh:
+
+* Scalar per element.
+* Scalar per integration point.
+* Tensor per integration point.
+
+Mesh::Quad4::Map::RefineRegular::mapToFine(...)
+-----------------------------------------------
+
+Map field to the fine mesh:
+
+* Scalar per element.
+* Scalar per integration point.
+* Tensor per integration point.
Mesh::Quad4::Map::FineLayer2Regular
===================================
Map "Regular" mesh to "FineLayer" mesh.
-.. todo::
+.. image:: figures/MeshQuad4/Map/FineLayer2Regular/map.svg
+ :width: 350px
+ :align: center
+
+.. seealso::
+
+ | :download:`Python - map <figures/MeshQuad4/Map/FineLayer2Regular/map.py>`
+ | :download:`Python - element numbers <figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.py>`
+
+Mesh::Quad4::Map::FineLayer2Regular::getCoarseMesh()
+----------------------------------------------------
+
+Return course mesh as "Mesh::Quad4::Regular".
+
+Mesh::Quad4::Map::FineLayer2Regular::getFineMesh()
+--------------------------------------------------
+
+Return fine mesh as "Mesh::Quad4::Regular".
+
+Mesh::Quad4::Map::FineLayer2Regular::getMap()
+---------------------------------------------
+
+Elements of the fine mesh per element of the coarse mesh (rows).
- Describe, illustrate
+Mesh::Quad4::Map::FineLayer2Regular::getMapFraction()
+-----------------------------------------------------
-.. todo::
+Get the fraction of overlap for the output of "getMap()".
- figures/MeshQuad4/FineLayer2Regular/element-numbers...
+Mesh::Quad4::Map::FineLayer2Regular::mapToRegular(...)
+------------------------------------------------------
-.. todo::
+Map field to the course mesh:
- figures/MeshQuad4/FineLayer2Regular/map...
+* Scalar per element.
+* Scalar per integration point.
+* Tensor per integration point.
diff --git a/docs/details/MeshTri3.rst b/docs/details/MeshTri3.rst
index c5f8f02..14d199e 100644
--- a/docs/details/MeshTri3.rst
+++ b/docs/details/MeshTri3.rst
@@ -1,46 +1,106 @@
+.. _MeshTri3:
**********
Mesh::Tri3
**********
| :download:`GooseFEM/MeshTri3.h <../../include/GooseFEM/MeshTri3.h>`
| :download:`GooseFEM/MeshTri3.hpp <../../include/GooseFEM/MeshTri3.hpp>`
+Naming convention
+=================
+
+.. image:: figures/MeshTri3/naming_convention.svg
+ :width: 350px
+ :align: center
+
Mesh::Tri3::Regular
--------------------
+===================
Regular mesh.
-.. todo::
+.. seealso::
+
+ | :download:`Python - example <figures/MeshTri3/Regular/example.py>`
+ | :download:`Python/ParaView - example <figures/MeshTri3/Regular/paraview.py>`
+ | :download:`Python/ParaView - nodesets <figures/MeshTri3/Regular/paraview_nodesets.py>`
- Describe, illustrate
+Mesh::Tri3::Regular::nelem()
+----------------------------
-.. todo::
+Return number of elements.
- figures/MeshTri3/Regular/example...
+Mesh::Tri3::Regular::nnode()
+----------------------------
-.. todo::
+Return number of nodes.
- figures/MeshTri3/Regular/example2...
+Mesh::Tri3::Regular::nne()
+--------------------------
-.. todo::
+Return number of nodes-per-element (= 3).
- figures/MeshTri3/Regular/nodes...
+Mesh::Tri3::Regular::ndim()
+---------------------------
-Mesh::Tri3::getOrientation
---------------------------
+Return number of dimensions (= 2).
-Get the orientation of all triangles.
+Mesh::Tri3::Regular::getElementType()
+-------------------------------------
-.. todo::
+Return element-type. For example used in the :ref:`ParaView` module.
- Describe
+Mesh::Tri3::Regular::coor()
+---------------------------
-Mesh::Tri3::setOrientation
---------------------------
+Return nodal coordinates [nnode, ndim].
+
+Mesh::Tri3::Regular::conn()
+---------------------------
+
+Return connectivity [nelem, nne].
+
+Mesh::Tri3::Regular::nodesXXXEdge()
+-----------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge.
+
+Mesh::Tri3::Regular::nodesXXXOpenEdge()
+---------------------------------------
+
+Node numbers along the "Bottom", "Top", "Left", or "Right" edge, excluding the corners.
+
+Mesh::Tri3::Regular::nodesXXXCorner()
+-------------------------------------
+
+Node number of one of the corners (e.g. "BottomLeft").
+
+Mesh::Tri3::Regular::nodesPeriodic()
+------------------------------------
+
+Periodic node pairs. Each row contains on pair of (independent, dependent) node numbers. The output shape is thus [n_pairs, 2].
+
+Mesh::Tri3::Regular::nodesOrigin()
+----------------------------------
+
+Bottom-left node, used as reference for periodicity.
+
+Mesh::Tri3::Regular::dofs()
+---------------------------
+
+DOF-numbers for each component of each node (sequential). The output shape is thus [nnode, ndim].
+
+Mesh::Tri3::Regular::dofsPeriodic()
+-----------------------------------
+
+DOF-numbers for each component of each node, for the case that the periodicity if fully eliminated. The output shape is thus [nnode, ndim].
+
+Mesh::Tri3::getOrientation(...)
+===============================
-Modify the orientation of all triangles.
+Get the orientation (-1 or +1) of all the elements.
-.. todo::
+Mesh::Tri3::setOrientation(...)
+===============================
- Describe
+Set the orientation (-1 or +1) of all the elements.
diff --git a/docs/details/ParaView.rst b/docs/details/ParaView.rst
index 24137bc..89b0dbb 100644
--- a/docs/details/ParaView.rst
+++ b/docs/details/ParaView.rst
@@ -1,48 +1,47 @@
+.. _ParaView:
********
ParaView
********
-.. seealso::
-
- | :download:`GooseFEM/ParaView.h <../../include/GooseFEM/ParaView.h>`
- | :download:`GooseFEM/ParaView.hpp <../../include/GooseFEM/ParaView.hpp>`
+| :download:`GooseFEM/ParaView.h <../../include/GooseFEM/ParaView.h>`
+| :download:`GooseFEM/ParaView.hpp <../../include/GooseFEM/ParaView.hpp>`
.. note::
This header relies on HDF5 and HighFive as dependencies. If you wish to use ParaView support without making use of HDF5 and HighFive, you have to define ``GOOSEFEM_NO_HIGHFIVE`` before including ``ParaView.h`` for the first time:
.. code-block:: cpp
#define GOOSEFEM_NO_HIGHFIVE
#include <GooseFEM/ParaView.h>
In this case the library does not automatically read the shapes of the datasets. Instead you'll have to provide them as ``std::vector<size_t>``.
HDF5
----
TimeSeries
^^^^^^^^^^
A TimeSeries is constructed from a number of Increments. The consecutive Increments are added to the TimeSeries using push_back. The order in which this is done will define the order of the TimeSeries. Each Increment is constructed from a mesh (using Connectivity and Coordinates) and a number of nodal or cell Attributes.
Consider this example
:download:`figures/ParaView/HDF5/main.cpp <figures/ParaView/HDF5/main.cpp>`
.. literalinclude:: figures/ParaView/HDF5/main.cpp
:language: cpp
.. tip::
A displacement vector in must be always 3-d in ParaView, even when the mesh is in 2-d. Use the ``GooseFEM::ParaView::HDF5::as3d(...)`` function to convert a matrix of 2-d displacements to a matrix of 3-d displacements.
.. note::
The Python interface avoids the HDF5 and HighFive dependencies. One therefore has to provide the datasets' shapes. Consider the following Python example:
:download:`figures/ParaView/HDF5/main.py <figures/ParaView/HDF5/main.py>`
.. literalinclude:: figures/ParaView/HDF5/main.py
:language: python
diff --git a/docs/details/Tyings.rst b/docs/details/Tyings.rst
index 3a6763c..3861cfe 100644
--- a/docs/details/Tyings.rst
+++ b/docs/details/Tyings.rst
@@ -1,22 +1,121 @@
+.. _Tyings:
******
Tyings
******
+| :download:`GooseFEM/TyingsPeriodic.h <../../include/GooseFEM/TyingsPeriodic.h>`
+| :download:`GooseFEM/TyingsPeriodic.hpp <../../include/GooseFEM/TyingsPeriodic.hpp>`
+
Tyings::Periodic
================
-Periodic nodal tyings.
+Periodic nodal tyings: partition the system (renumber the DOFs) in the following order [iii, iid]: first the independent DOFs and the the dependent DOFs. If, in addition, independent DOFs are prescribed the partitioning is [iiu, iip, iid], where iii = [iiu, iip]: first the unknown and then the prescribed DOFs.
+
+Tyings::Periodic::nnd()
+-----------------------
+
+Return the dependent DOF-numbers.
+
+Tyings::Periodic::nni()
+-----------------------
+
+Return the independent DOF-numbers.
+
+Tyings::Periodic::nnu()
+-----------------------
+
+Return the unknown DOF-numbers.
+
+Tyings::Periodic::nnp()
+-----------------------
+
+Return the prescribed DOF-numbers.
+
+Tyings::Periodic::dofs()
+------------------------
+
+Renumbered DOFs per node [nnode, ndim].
+
+Tyings::Periodic::control()
+---------------------------
+
+Control DOF, that should be fixed [ndim].
+
+Tyings::Periodic::iid()
+-----------------------
+
+Return the dependent DOFs.
+
+Tyings::Periodic::iii()
+-----------------------
+
+Return the independent DOFs.
+
+Tyings::Periodic::iiu()
+-----------------------
+
+Return the unknown DOFs.
+
+Tyings::Periodic::iip()
+-----------------------
-.. todo::
+Return the prescribed DOFs.
- Complete.
+Tyings::Periodic::Cdi()
+-----------------------
+
+Return the tying matrix, such that
+
+.. math::
+
+ u_d = C_{di} u_i
+
+In addition, the tying matrix in terms of the partitioned system can be obtained:
+
+.. math::
+
+ u_d = [C_{du}, C_{dp}]^T [u_u, u_p] = C_{du} u_u + C_{dp} u_p
+
+Tyings::Periodic::Cdu()
+-----------------------
+
+Return the tying matrix, such that:
+
+.. math::
+
+ u_d = [C_{du}, C_{dp}]^T [u_u, u_p] = C_{du} u_u + C_{dp} u_p
+
+Tyings::Periodic::Cdp()
+-----------------------
+
+Return the tying matrix, such that:
+
+.. math::
+
+ u_d = [C_{du}, C_{dp}]^T [u_u, u_p] = C_{du} u_u + C_{dp} u_p
Tyings::Control
===============
-Control nodes and degrees-of-freedom.
+Add virtual control nodes to the system.
+
+Tyings::Control::coor()
+-----------------------
+
+Nodal coordinates, including the virtual control nodes [nnode, ndim].
+
+Tyings::Control::dofs()
+-----------------------
+
+DOFs, including the virtual control nodes [nnode, ndim].
+
+Tyings::Control::controlDofs()
+------------------------------
+
+Virtual control DOFs [ndim, ndim].
-.. todo::
+Tyings::Control::controlNodes()
+-------------------------------
- Complete.
+Virtual control nodes [ndim].
diff --git a/docs/details/Vector.rst b/docs/details/Vector.rst
index 1f98a06..a6e0f97 100644
--- a/docs/details/Vector.rst
+++ b/docs/details/Vector.rst
@@ -1,49 +1,384 @@
-
-.. _vector:
+.. _Vector:
******
Vector
******
+| :download:`GooseFEM/Vector.h <../../include/GooseFEM/Vector.h>`
+| :download:`GooseFEM/Vector.hpp <../../include/GooseFEM/Vector.hpp>`
+| :download:`GooseFEM/VectorPartitioned.h <../../include/GooseFEM/VectorPartitioned.h>`
+| :download:`GooseFEM/VectorPartitioned.hpp <../../include/GooseFEM/VectorPartitioned.hpp>`
+| :download:`GooseFEM/VectorPartitionedTyings.h <../../include/GooseFEM/VectorPartitionedTyings.h>`
+| :download:`GooseFEM/VectorPartitionedTyings.hpp <../../include/GooseFEM/VectorPartitionedTyings.hpp>`
+
Vector
======
-Vector definition.
+Vector definition allowing transforming between "dofval", "nodevec", and "elemvec" representations. See :ref:`conventions_vector`.
+
+Vector::nelem()
+---------------
+
+Return the number of elements.
+
+Vector::nne()
+-------------
+
+Return the number of nodes-per-element.
+
+Vector::nnode()
+---------------
+
+Return the number of nodes.
+
+Vector::ndim()
+--------------
+
+Return the number of dimensions.
+
+Vector::ndof()
+--------------
+
+Return the number of DOFs.
+
+Vector::dofs()
+--------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+Vector::copy(...)
+-----------------
+
+Copy "nodevec" to "nodevec".
+
+Vector::asDofs(...)
+-------------------
+
+Convert "nodevec" or "elemvec" to "dofval".
-.. todo::
+.. warning::
- Describe
+ Verify that you don't need "assembleDofs(...)"
-.. todo::
+Vector::asNode(...)
+-------------------
- details/figures/Vector/mesh...
+Convert "dofval" or "elemvec" to "nodevec".
-.. todo::
+.. warning::
- details/figures/Vector/mesh_dofs-a...
+ Verify that you don't need "assembleNode(...)"
-.. todo::
+Vector::asElement(...)
+----------------------
- details/figures/Vector/mesh_dofs-b...
+Convert "dofval" or "nodevec" to "elemvec".
-.. todo::
+Vector::assembleDofs(...)
+-------------------------
- Complete.
+Convert "nodevec" or "elemvec" to "dofval".
+
+.. warning::
+
+ Verify that you don't need "asDofs(...)"
+
+Vector::assembleNode(...)
+-------------------------
+
+Convert "dofval" or "elemvec" to "nodevec".
+
+.. warning::
+
+ Verify that you don't need "asNode(...)"
VectorPartitioned
=================
-Partitioned vector definition.
+Partitioned vector definition allowing transforming between "dofval", "nodevec", and "elemvec" representations. See :ref:`conventions_vector`. The partitioning is such that the DOFs are ordered as "[iiu, iip]" with "iiu" the unknown DOFs and "iip" the prescribed DOFs.
+
+VectorPartitioned::nelem()
+--------------------------
+
+Return the number of elements.
+
+VectorPartitioned::nne()
+------------------------
+
+Return the number of nodes-per-element.
+
+VectorPartitioned::nnode()
+--------------------------
+
+Return the number of nodes.
+
+VectorPartitioned::ndim()
+-------------------------
+
+Return the number of dimensions.
+
+VectorPartitioned::ndof()
+-------------------------
+
+Return the number of DOFs.
+
+VectorPartitioned::nnu()
+------------------------
+
+Return the number of unknown DOFs.
+
+VectorPartitioned::nnp()
+------------------------
+
+Return the number of prescribed DOFs.
+
+VectorPartitioned::dofs()
+-------------------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+VectorPartitioned::iiu()
+------------------------
+
+Return the unknown DOF-numbers per node [nnu].
+
+VectorPartitioned::iip()
+------------------------
+
+Return the prescribed DOF-numbers per node [nnp].
+
+VectorPartitioned::copy(...)
+----------------------------
+
+Copy "nodevec" to "nodevec".
+
+VectorPartitioned::copy_u(...)
+------------------------------
+
+Copy the unknown DOFs from a "nodevec" to the unknown DOFs from another "nodevec".
+
+VectorPartitioned::copy_p(...)
+------------------------------
+
+Copy the prescribed DOFs from a "nodevec" to the prescribed DOFs from another "nodevec".
+
+VectorPartitioned::asDofs(...)
+------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval".
+
+.. warning::
+
+ Verify that you don't need "assembleDofs(...)"
+
+VectorPartitioned::asDofs_u(...)
+--------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval" and extract the unknown DOFs "iiu".
+
+.. warning::
+
+ Verify that you don't need "assembleDofs(...)"
+
+VectorPartitioned::asDofs_p(...)
+--------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval" and extract the prescribed DOFs "iip".
+
+.. warning::
+
+ Verify that you don't need "assembleDofs(...)"
+
+VectorPartitioned::asNode(...)
+------------------------------
+
+Convert "dofval" or "elemvec" to "nodevec".
+
+.. warning::
+
+ Verify that you don't need "assembleNode(...)"
+
+VectorPartitioned::asElement(...)
+---------------------------------
+
+Convert "dofval" or "nodevec" to "elemvec".
+
+VectorPartitioned::assembleDofs(...)
+------------------------------------
-.. todo::
+Convert "nodevec" or "elemvec" to "dofval".
- Complete.
+.. warning::
+
+ Verify that you don't need "asDofs(...)"
+
+VectorPartitioned::assembleDofs_u(...)
+--------------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval" and extract the unknown DOFs "iiu".
+
+.. warning::
+
+ Verify that you don't need "asDofs(...)"
+
+VectorPartitioned::assembleDofs_p(...)
+--------------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval" and extract the prescribed DOFs "iip".
+
+.. warning::
+
+ Verify that you don't need "asDofs(...)"
+
+VectorPartitioned::assembleNode(...)
+------------------------------------
+
+Convert "dofval" or "elemvec" to "nodevec".
+
+.. warning::
+
+ Verify that you don't need "asNode(...)"
VectorPartitionedTyings
=======================
-Partitioned vector definition with nodal tyings.
+Partitioned vector definition with nodal tyings allowing transforming between "dofval", "nodevec", and "elemvec" representations. See :ref:`conventions_vector`. The partitioning is such that the DOFs are ordered as "[iiu, iip, iid]" with "iiu" the unknown DOFs and "iip" the prescribed DOFs and "iid" the dependent DOFs.
+
+VectorPartitionedTyings::nelem()
+--------------------------------
+
+Return the number of elements.
+
+VectorPartitionedTyings::nne()
+------------------------------
+
+Return the number of nodes-per-element.
+
+VectorPartitionedTyings::nnode()
+--------------------------------
+
+Return the number of nodes.
+
+VectorPartitionedTyings::ndim()
+-------------------------------
+
+Return the number of dimensions.
+
+VectorPartitionedTyings::ndof()
+-------------------------------
+
+Return the number of DOFs.
+
+VectorPartitionedTyings::nnu()
+------------------------------
+
+Return the number of unknown DOFs.
+
+VectorPartitionedTyings::nnp()
+------------------------------
+
+Return the number of prescribed DOFs.
+
+VectorPartitionedTyings::nni()
+------------------------------
+
+Return the number of independent DOFs.
+
+VectorPartitionedTyings::nnd()
+------------------------------
+
+Return the number of dependent DOFs.
+
+VectorPartitionedTyings::dofs()
+-------------------------------
+
+Return the DOF-numbers per node [nnode, ndim].
+
+VectorPartitionedTyings::iiu()
+------------------------------
+
+Return the unknown DOF-numbers per node [nnu].
+
+VectorPartitionedTyings::iip()
+------------------------------
+
+Return the prescribed DOF-numbers per node [nnp].
+
+VectorPartitionedTyings::iii()
+------------------------------
+
+Return the independent DOF-numbers per node [nni].
+
+VectorPartitionedTyings::iid()
+------------------------------
+
+Return the dependent DOF-numbers per node [nnd].
+
+VectorPartitionedTyings::copy(...)
+----------------------------------
+
+Copy "nodevec" to "nodevec".
+
+VectorPartitionedTyings::copy_u(...)
+------------------------------------
+
+Copy the unknown DOFs from a "nodevec" to the unknown DOFs from another "nodevec".
+
+VectorPartitionedTyings::copy_p(...)
+------------------------------------
+
+Copy the prescribed DOFs from a "nodevec" to the prescribed DOFs from another "nodevec".
+
+VectorPartitionedTyings::asDofs(...)
+------------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval".
+
+.. warning::
+
+ Verify that you don't need "assembleDofs(...)"
+
+VectorPartitionedTyings::asDofs_i(...)
+--------------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval" and extract the independent DOFs "iii". Choose to apply the tyings:
+
+.. math::
+
+ u_i = C_{di}^T u_d
+
+.. warning::
+
+ Verify that you don't need "assembleDofs(...)"
+
+VectorPartitionedTyings::asNode(...)
+------------------------------------
+
+Convert "dofval" or "elemvec" to "nodevec".
+
+.. warning::
+
+ Verify that you don't need "assembleNode(...)"
+
+VectorPartitionedTyings::asElement(...)
+---------------------------------------
+
+Convert "dofval" or "nodevec" to "elemvec".
+
+VectorPartitionedTyings::assembleDofs(...)
+------------------------------------------
+
+Convert "nodevec" or "elemvec" to "dofval".
+
+.. warning::
+
+ Verify that you don't need "asDofs(...)"
+
+VectorPartitionedTyings::assembleNode(...)
+------------------------------------------
+
+Convert "dofval" or "elemvec" to "nodevec".
-.. todo::
+.. warning::
- Complete.
+ Verify that you don't need "asNode(...)"
diff --git a/docs/details/figures/MeshHex8/FineLayer/example.py b/docs/details/figures/MeshHex8/FineLayer/paraview.py
similarity index 72%
rename from docs/details/figures/MeshHex8/FineLayer/example.py
rename to docs/details/figures/MeshHex8/FineLayer/paraview.py
index 80be274..57574bb 100644
--- a/docs/details/figures/MeshHex8/FineLayer/example.py
+++ b/docs/details/figures/MeshHex8/FineLayer/paraview.py
@@ -1,34 +1,36 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Hex8.FineLayer(9,17,27)
# filename of the HDF5-file
-fname = 'MeshHex8-FineLayer.hdf5'
+fname = 'paraview.hdf5'
# define element set
elementsMiddleLayer = np.zeros((mesh.nelem()),dtype='int')
elementsMiddleLayer[mesh.elementsMiddleLayer()] = 1
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data['coor'] = mesh.coor()
data['conn'] = mesh.conn()
data['elementsMiddleLayer'] = elementsMiddleLayer
# write XDMF-file with metadata
-
xdmf = pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Hexahedron, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
)
-xdmf.push_back(pv.Attribute(fname, "/elementsMiddleLayer", "elementsMiddleLayer", pv.AttributeType.Cell, elementsMiddleLayer.shape))
+xdmf.push_back(pv.Attribute(
+ fname,
+ "/elementsMiddleLayer",
+ "elementsMiddleLayer",
+ pv.AttributeType.Cell,
+ elementsMiddleLayer.shape))
xdmf.write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshHex8/FineLayer/nodes.py b/docs/details/figures/MeshHex8/FineLayer/paraview_nodesets.py
similarity index 98%
rename from docs/details/figures/MeshHex8/FineLayer/nodes.py
rename to docs/details/figures/MeshHex8/FineLayer/paraview_nodesets.py
index 0664db4..c073d37 100644
--- a/docs/details/figures/MeshHex8/FineLayer/nodes.py
+++ b/docs/details/figures/MeshHex8/FineLayer/paraview_nodesets.py
@@ -1,130 +1,127 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Hex8.FineLayer(9,17,27)
# initialize all node sets
nodesets = dict(
nodesFront = np.zeros((mesh.nnode()),dtype='int'),
nodesBack = np.zeros((mesh.nnode()),dtype='int'),
nodesLeft = np.zeros((mesh.nnode()),dtype='int'),
nodesRight = np.zeros((mesh.nnode()),dtype='int'),
nodesBottom = np.zeros((mesh.nnode()),dtype='int'),
nodesTop = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontFace = np.zeros((mesh.nnode()),dtype='int'),
nodesBackFace = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftFace = np.zeros((mesh.nnode()),dtype='int'),
nodesRightFace = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomFace = np.zeros((mesh.nnode()),dtype='int'),
nodesTopFace = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopRightCorner = np.zeros((mesh.nnode()),dtype='int'),
)
# define node-sets
nodesets['nodesFront' ][mesh.nodesFront() ] = 1
nodesets['nodesBack' ][mesh.nodesBack() ] = 1
nodesets['nodesLeft' ][mesh.nodesLeft() ] = 1
nodesets['nodesRight' ][mesh.nodesRight() ] = 1
nodesets['nodesBottom' ][mesh.nodesBottom() ] = 1
nodesets['nodesTop' ][mesh.nodesTop() ] = 1
nodesets['nodesFrontFace' ][mesh.nodesFrontFace() ] = 1
nodesets['nodesBackFace' ][mesh.nodesBackFace() ] = 1
nodesets['nodesLeftFace' ][mesh.nodesLeftFace() ] = 1
nodesets['nodesRightFace' ][mesh.nodesRightFace() ] = 1
nodesets['nodesBottomFace' ][mesh.nodesBottomFace() ] = 1
nodesets['nodesTopFace' ][mesh.nodesTopFace() ] = 1
nodesets['nodesFrontBottomEdge' ][mesh.nodesFrontBottomEdge() ] = 1
nodesets['nodesFrontTopEdge' ][mesh.nodesFrontTopEdge() ] = 1
nodesets['nodesFrontLeftEdge' ][mesh.nodesFrontLeftEdge() ] = 1
nodesets['nodesFrontRightEdge' ][mesh.nodesFrontRightEdge() ] = 1
nodesets['nodesBackBottomEdge' ][mesh.nodesBackBottomEdge() ] = 1
nodesets['nodesBackTopEdge' ][mesh.nodesBackTopEdge() ] = 1
nodesets['nodesBackLeftEdge' ][mesh.nodesBackLeftEdge() ] = 1
nodesets['nodesBackRightEdge' ][mesh.nodesBackRightEdge() ] = 1
nodesets['nodesBottomLeftEdge' ][mesh.nodesBottomLeftEdge() ] = 1
nodesets['nodesBottomRightEdge' ][mesh.nodesBottomRightEdge() ] = 1
nodesets['nodesTopLeftEdge' ][mesh.nodesTopLeftEdge() ] = 1
nodesets['nodesTopRightEdge' ][mesh.nodesTopRightEdge() ] = 1
nodesets['nodesFrontBottomOpenEdge' ][mesh.nodesFrontBottomOpenEdge() ] = 1
nodesets['nodesFrontTopOpenEdge' ][mesh.nodesFrontTopOpenEdge() ] = 1
nodesets['nodesFrontLeftOpenEdge' ][mesh.nodesFrontLeftOpenEdge() ] = 1
nodesets['nodesFrontRightOpenEdge' ][mesh.nodesFrontRightOpenEdge() ] = 1
nodesets['nodesBackBottomOpenEdge' ][mesh.nodesBackBottomOpenEdge() ] = 1
nodesets['nodesBackTopOpenEdge' ][mesh.nodesBackTopOpenEdge() ] = 1
nodesets['nodesBackLeftOpenEdge' ][mesh.nodesBackLeftOpenEdge() ] = 1
nodesets['nodesBackRightOpenEdge' ][mesh.nodesBackRightOpenEdge() ] = 1
nodesets['nodesBottomLeftOpenEdge' ][mesh.nodesBottomLeftOpenEdge() ] = 1
nodesets['nodesBottomRightOpenEdge' ][mesh.nodesBottomRightOpenEdge() ] = 1
nodesets['nodesTopLeftOpenEdge' ][mesh.nodesTopLeftOpenEdge() ] = 1
nodesets['nodesTopRightOpenEdge' ][mesh.nodesTopRightOpenEdge() ] = 1
nodesets['nodesFrontBottomLeftCorner' ][mesh.nodesFrontBottomLeftCorner() ] = 1
nodesets['nodesFrontBottomRightCorner'][mesh.nodesFrontBottomRightCorner()] = 1
nodesets['nodesFrontTopLeftCorner' ][mesh.nodesFrontTopLeftCorner() ] = 1
nodesets['nodesFrontTopRightCorner' ][mesh.nodesFrontTopRightCorner() ] = 1
nodesets['nodesBackBottomLeftCorner' ][mesh.nodesBackBottomLeftCorner() ] = 1
nodesets['nodesBackBottomRightCorner' ][mesh.nodesBackBottomRightCorner() ] = 1
nodesets['nodesBackTopLeftCorner' ][mesh.nodesBackTopLeftCorner() ] = 1
nodesets['nodesBackTopRightCorner' ][mesh.nodesBackTopRightCorner() ] = 1
# add DOF-numbers after eliminating periodicity
nodesets['dofsPeriodic'] = mesh.dofsPeriodic()[:,0]
# filename of the HDF5-file
-fname = 'MeshHex8-FineLayer-nodes.hdf5'
+fname = 'paraview_nodesets.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data.file['coor'] = mesh.coor()
data.file['conn'] = mesh.conn()
for key, value in nodesets.items():
data[key] = value
# write XDMF-file with metadata
-
xdmf = pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Hexahedron, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
)
for key, value in nodesets.items():
xdmf.push_back(pv.Attribute(fname, "/"+key, key, pv.AttributeType.Node, value.shape))
xdmf.write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshHex8/Regular/example.py b/docs/details/figures/MeshHex8/Regular/paraview.py
similarity index 79%
rename from docs/details/figures/MeshHex8/Regular/example.py
rename to docs/details/figures/MeshHex8/Regular/paraview.py
index 9ecd659..ba7313d 100644
--- a/docs/details/figures/MeshHex8/Regular/example.py
+++ b/docs/details/figures/MeshHex8/Regular/paraview.py
@@ -1,25 +1,22 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Hex8.Regular(6,8,12)
# filename of the HDF5-file
-fname = 'MeshHex8-Regular.hdf5'
+fname = 'paraview.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data['coor'] = mesh.coor()
data['conn'] = mesh.conn()
# write XDMF-file with metadata
-
pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Hexahedron, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
).write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshHex8/Regular/nodes.py b/docs/details/figures/MeshHex8/Regular/paraview_nodesets.py
similarity index 98%
rename from docs/details/figures/MeshHex8/Regular/nodes.py
rename to docs/details/figures/MeshHex8/Regular/paraview_nodesets.py
index 81b78b2..2d039a3 100644
--- a/docs/details/figures/MeshHex8/Regular/nodes.py
+++ b/docs/details/figures/MeshHex8/Regular/paraview_nodesets.py
@@ -1,130 +1,127 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Hex8.Regular(6,8,12)
# initialize all node sets
nodesets = dict(
nodesFront = np.zeros((mesh.nnode()),dtype='int'),
nodesBack = np.zeros((mesh.nnode()),dtype='int'),
nodesLeft = np.zeros((mesh.nnode()),dtype='int'),
nodesRight = np.zeros((mesh.nnode()),dtype='int'),
nodesBottom = np.zeros((mesh.nnode()),dtype='int'),
nodesTop = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontFace = np.zeros((mesh.nnode()),dtype='int'),
nodesBackFace = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftFace = np.zeros((mesh.nnode()),dtype='int'),
nodesRightFace = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomFace = np.zeros((mesh.nnode()),dtype='int'),
nodesTopFace = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBackRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontBottomRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesFrontTopRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackBottomRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBackTopRightCorner = np.zeros((mesh.nnode()),dtype='int'),
)
# define node-sets
nodesets['nodesFront' ][mesh.nodesFront() ] = 1
nodesets['nodesBack' ][mesh.nodesBack() ] = 1
nodesets['nodesLeft' ][mesh.nodesLeft() ] = 1
nodesets['nodesRight' ][mesh.nodesRight() ] = 1
nodesets['nodesBottom' ][mesh.nodesBottom() ] = 1
nodesets['nodesTop' ][mesh.nodesTop() ] = 1
nodesets['nodesFrontFace' ][mesh.nodesFrontFace() ] = 1
nodesets['nodesBackFace' ][mesh.nodesBackFace() ] = 1
nodesets['nodesLeftFace' ][mesh.nodesLeftFace() ] = 1
nodesets['nodesRightFace' ][mesh.nodesRightFace() ] = 1
nodesets['nodesBottomFace' ][mesh.nodesBottomFace() ] = 1
nodesets['nodesTopFace' ][mesh.nodesTopFace() ] = 1
nodesets['nodesFrontBottomEdge' ][mesh.nodesFrontBottomEdge() ] = 1
nodesets['nodesFrontTopEdge' ][mesh.nodesFrontTopEdge() ] = 1
nodesets['nodesFrontLeftEdge' ][mesh.nodesFrontLeftEdge() ] = 1
nodesets['nodesFrontRightEdge' ][mesh.nodesFrontRightEdge() ] = 1
nodesets['nodesBackBottomEdge' ][mesh.nodesBackBottomEdge() ] = 1
nodesets['nodesBackTopEdge' ][mesh.nodesBackTopEdge() ] = 1
nodesets['nodesBackLeftEdge' ][mesh.nodesBackLeftEdge() ] = 1
nodesets['nodesBackRightEdge' ][mesh.nodesBackRightEdge() ] = 1
nodesets['nodesBottomLeftEdge' ][mesh.nodesBottomLeftEdge() ] = 1
nodesets['nodesBottomRightEdge' ][mesh.nodesBottomRightEdge() ] = 1
nodesets['nodesTopLeftEdge' ][mesh.nodesTopLeftEdge() ] = 1
nodesets['nodesTopRightEdge' ][mesh.nodesTopRightEdge() ] = 1
nodesets['nodesFrontBottomOpenEdge' ][mesh.nodesFrontBottomOpenEdge() ] = 1
nodesets['nodesFrontTopOpenEdge' ][mesh.nodesFrontTopOpenEdge() ] = 1
nodesets['nodesFrontLeftOpenEdge' ][mesh.nodesFrontLeftOpenEdge() ] = 1
nodesets['nodesFrontRightOpenEdge' ][mesh.nodesFrontRightOpenEdge() ] = 1
nodesets['nodesBackBottomOpenEdge' ][mesh.nodesBackBottomOpenEdge() ] = 1
nodesets['nodesBackTopOpenEdge' ][mesh.nodesBackTopOpenEdge() ] = 1
nodesets['nodesBackLeftOpenEdge' ][mesh.nodesBackLeftOpenEdge() ] = 1
nodesets['nodesBackRightOpenEdge' ][mesh.nodesBackRightOpenEdge() ] = 1
nodesets['nodesBottomLeftOpenEdge' ][mesh.nodesBottomLeftOpenEdge() ] = 1
nodesets['nodesBottomRightOpenEdge' ][mesh.nodesBottomRightOpenEdge() ] = 1
nodesets['nodesTopLeftOpenEdge' ][mesh.nodesTopLeftOpenEdge() ] = 1
nodesets['nodesTopRightOpenEdge' ][mesh.nodesTopRightOpenEdge() ] = 1
nodesets['nodesFrontBottomLeftCorner' ][mesh.nodesFrontBottomLeftCorner() ] = 1
nodesets['nodesFrontBottomRightCorner'][mesh.nodesFrontBottomRightCorner()] = 1
nodesets['nodesFrontTopLeftCorner' ][mesh.nodesFrontTopLeftCorner() ] = 1
nodesets['nodesFrontTopRightCorner' ][mesh.nodesFrontTopRightCorner() ] = 1
nodesets['nodesBackBottomLeftCorner' ][mesh.nodesBackBottomLeftCorner() ] = 1
nodesets['nodesBackBottomRightCorner' ][mesh.nodesBackBottomRightCorner() ] = 1
nodesets['nodesBackTopLeftCorner' ][mesh.nodesBackTopLeftCorner() ] = 1
nodesets['nodesBackTopRightCorner' ][mesh.nodesBackTopRightCorner() ] = 1
# add DOF-numbers after eliminating periodicity
nodesets['dofsPeriodic'] = mesh.dofsPeriodic()[:,0]
# filename of the HDF5-file
-fname = 'MeshHex8-Regular-nodes.hdf5'
+fname = 'paraview_nodesets.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data.file['coor'] = mesh.coor()
data.file['conn'] = mesh.conn()
for key, value in nodesets.items():
data[key] = value
# write XDMF-file with metadata
-
xdmf = pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Hexahedron, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
)
for key, value in nodesets.items():
xdmf.push_back(pv.Attribute(fname, "/"+key, key, pv.AttributeType.Node, value.shape))
xdmf.write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshQuad4/FineLayer/behaviour.py b/docs/details/figures/MeshQuad4/FineLayer/behaviour.py
index d1e4b62..581ea48 100644
--- a/docs/details/figures/MeshQuad4/FineLayer/behaviour.py
+++ b/docs/details/figures/MeshQuad4/FineLayer/behaviour.py
@@ -1,77 +1,74 @@
import GooseFEM as gf
import matplotlib.pyplot as plt
import GooseMPL as gplt
import numpy as np
plt.style.use(['goose'])
# --------------------------------------------------------------------------------------------------
fig, axes = plt.subplots(figsize=(18,6), ncols=3)
# --------------------------------------------------------------------------------------------------
-mesh = gf.Mesh.Quad4.FineLayer(6*9, 51)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Quad4.FineLayer(6*9, 51)
+coor = mesh.coor()
+conn = mesh.conn()
-print(mesh.nelem())
+cindex = np.arange(mesh.nelem())
# --------------------------------------------------------------------------------------------------
ax = axes[0]
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet', axis=ax)
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
-ax.set_title(r'$n_x = 6 \times 9$')
+ax.set_title(r'$n_x = 6 \times 9; n_{elem} = %d$' % mesh.nelem())
# --------------------------------------------------------------------------------------------------
-mesh = gf.Mesh.Quad4.FineLayer(6*9+3, 51)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Quad4.FineLayer(6*9+3, 51)
+coor = mesh.coor()
+conn = mesh.conn()
-print(mesh.nelem())
+cindex = np.arange(mesh.nelem())
# --------------------------------------------------------------------------------------------------
ax = axes[1]
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet', axis=ax)
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
-ax.set_title(r'$n_x = 6 \times 9 + 3$')
+ax.set_title(r'$n_x = 6 \times 9 + 3; n_{elem} = %d$' % mesh.nelem())
# --------------------------------------------------------------------------------------------------
-mesh = gf.Mesh.Quad4.FineLayer(6*9+1, 51)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Quad4.FineLayer(6*9+1, 51)
+coor = mesh.coor()
+conn = mesh.conn()
-print(mesh.nelem())
+cindex = np.arange(mesh.nelem())
# --------------------------------------------------------------------------------------------------
ax = axes[2]
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet', axis=ax)
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
-ax.set_title(r'$n_x = 6 \times 9 + 1$')
+ax.set_title(r'$n_x = 6 \times 9 + 1; n_{elem} = %d$' % mesh.nelem())
plt.savefig('behaviour.svg')
plt.show()
diff --git a/docs/details/figures/MeshQuad4/FineLayer/element-numbers.py b/docs/details/figures/MeshQuad4/FineLayer/element-numbers.py
index 62d8049..2e93989 100644
--- a/docs/details/figures/MeshQuad4/FineLayer/element-numbers.py
+++ b/docs/details/figures/MeshQuad4/FineLayer/element-numbers.py
@@ -1,32 +1,33 @@
import GooseFEM as gf
import matplotlib.pyplot as plt
import GooseMPL as gplt
import numpy as np
plt.style.use(['goose'])
# --------------------------------------------------------------------------------------------------
-mesh = gf.Mesh.Quad4.FineLayer(6, 18)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Quad4.FineLayer(6, 18)
+coor = mesh.coor()
+conn = mesh.conn()
+
+cindex = np.arange(mesh.nelem())
# --------------------------------------------------------------------------------------------------
-fig,ax = plt.subplots(figsize=(10,10))
+fig, ax = plt.subplots(figsize=(10,10))
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet')
for e in range(conn.shape[0]):
x = np.mean(coor[conn[e,:], 0])
y = np.mean(coor[conn[e,:], 1])
ax.text(x, y, str(e), ha='center', va='center')
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
plt.savefig('element_numbers.svg')
-plt.show()
+plt.close()
diff --git a/docs/details/figures/MeshQuad4/FineLayer/element-numbers.svg b/docs/details/figures/MeshQuad4/FineLayer/element-numbers.svg
deleted file mode 100644
index fe80d8d..0000000
--- a/docs/details/figures/MeshQuad4/FineLayer/element-numbers.svg
+++ /dev/null
@@ -1,1009 +0,0 @@
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- <defs>
- <style type="text/css">
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- </style>
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- <g id="figure_1">
- <g id="patch_1">
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-L 720 720
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-z
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- <path d="M 262.08 702.72
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diff --git a/docs/details/figures/MeshQuad4/FineLayer/example.py b/docs/details/figures/MeshQuad4/FineLayer/example.py
index ced43fd..849eb2c 100644
--- a/docs/details/figures/MeshQuad4/FineLayer/example.py
+++ b/docs/details/figures/MeshQuad4/FineLayer/example.py
@@ -1,44 +1,40 @@
+import numpy as np
import GooseFEM as gf
import matplotlib.pyplot as plt
import GooseMPL as gplt
-import numpy as np
plt.style.use(['goose'])
# --------------------------------------------------------------------------------------------------
-mesh = gf.Mesh.Quad4.FineLayer(6*9, 51)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Quad4.FineLayer(6*9, 51)
+coor = mesh.coor()
+conn = mesh.conn()
+
+cindex = np.arange(mesh.nelem())
+
+Left = mesh.nodesLeftEdge()
+Right = mesh.nodesRightEdge()
+Bottom = mesh.nodesBottomEdge()
+Top = mesh.nodesTopEdge()
# --------------------------------------------------------------------------------------------------
fig, ax = plt.subplots(figsize=(10,10))
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet')
ax.plot(coor[:,0], coor[:,1], marker='o', linestyle='none')
-lft = mesh.nodesLeftOpenEdge()
-rgt = mesh.nodesRightOpenEdge()
-bot = mesh.nodesBottomEdge()
-top = mesh.nodesTopEdge()
-
-ax.plot(coor[lft,0], coor[lft,1], marker='o', linestyle='none', color='g', label='nodesLeftOpenEdge')
-ax.plot(coor[rgt,0], coor[rgt,1], marker='o', linestyle='none', color='b', label='nodesRightOpenEdge')
-ax.plot(coor[bot,0], coor[bot,1], marker='o', linestyle='none', color='r', label='nodesBottomEdge')
-ax.plot(coor[top,0], coor[top,1], marker='o', linestyle='none', color='y', label='nodesTopEdge')
+ax.plot(coor[Left ,0], coor[Left ,1], marker='o', linestyle='none', color='g')
+ax.plot(coor[Right ,0], coor[Right ,1], marker='o', linestyle='none', color='b')
+ax.plot(coor[Bottom,0], coor[Bottom,1], marker='o', linestyle='none', color='r')
+ax.plot(coor[Top ,0], coor[Top ,1], marker='o', linestyle='none', color='y')
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
-ax.set_xlim([-1, 55])
-ax.set_ylim([-1, 58])
-
-ax.legend(ncol=2, loc='upper center')
-
plt.savefig('example.svg')
-plt.show()
+plt.close()
diff --git a/docs/details/figures/MeshQuad4/FineLayer/example.svg b/docs/details/figures/MeshQuad4/FineLayer/example.svg
deleted file mode 100644
index c8c8359..0000000
--- a/docs/details/figures/MeshQuad4/FineLayer/example.svg
+++ /dev/null
@@ -1,4547 +0,0 @@
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diff --git a/docs/details/figures/MeshQuad4/FineLayer/example2.py b/docs/details/figures/MeshQuad4/FineLayer/paraview.py
similarity index 71%
rename from docs/details/figures/MeshQuad4/FineLayer/example2.py
rename to docs/details/figures/MeshQuad4/FineLayer/paraview.py
index a8a3dcc..9534d6f 100644
--- a/docs/details/figures/MeshQuad4/FineLayer/example2.py
+++ b/docs/details/figures/MeshQuad4/FineLayer/paraview.py
@@ -1,34 +1,36 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Quad4.FineLayer(9,17)
# filename of the HDF5-file
-fname = 'MeshQuad4-FineLayer.hdf5'
+fname = 'paraview.hdf5'
# define element set
elementsMiddleLayer = np.zeros((mesh.nelem()),dtype='int')
elementsMiddleLayer[mesh.elementsMiddleLayer()] = 1
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data['coor'] = mesh.coor()
data['conn'] = mesh.conn()
data['elementsMiddleLayer'] = elementsMiddleLayer
# write XDMF-file with metadata
-
xdmf = pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Quadrilateral, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
)
-xdmf.push_back(pv.Attribute(fname, "/elementsMiddleLayer", "elementsMiddleLayer", pv.AttributeType.Cell, elementsMiddleLayer.shape))
+xdmf.push_back(pv.Attribute(
+ fname,
+ "/elementsMiddleLayer",
+ "elementsMiddleLayer",
+ pv.AttributeType.Cell,
+ elementsMiddleLayer.shape))
xdmf.write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshQuad4/FineLayer/nodes.py b/docs/details/figures/MeshQuad4/FineLayer/paraview_nodesets.py
similarity index 95%
rename from docs/details/figures/MeshQuad4/FineLayer/nodes.py
rename to docs/details/figures/MeshQuad4/FineLayer/paraview_nodesets.py
index 0f18200..de3c9ad 100644
--- a/docs/details/figures/MeshQuad4/FineLayer/nodes.py
+++ b/docs/details/figures/MeshQuad4/FineLayer/paraview_nodesets.py
@@ -1,66 +1,63 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Quad4.FineLayer(9,17)
# initialize all node sets
nodesets = dict(
nodesBottomEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesTopLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesTopRightCorner = np.zeros((mesh.nnode()),dtype='int'),
)
# define node-sets
nodesets['nodesBottomEdge' ][mesh.nodesBottomEdge() ] = 1
nodesets['nodesTopEdge' ][mesh.nodesTopEdge() ] = 1
nodesets['nodesLeftEdge' ][mesh.nodesLeftEdge() ] = 1
nodesets['nodesRightEdge' ][mesh.nodesRightEdge() ] = 1
nodesets['nodesBottomOpenEdge' ][mesh.nodesBottomOpenEdge() ] = 1
nodesets['nodesTopOpenEdge' ][mesh.nodesTopOpenEdge() ] = 1
nodesets['nodesLeftOpenEdge' ][mesh.nodesLeftOpenEdge() ] = 1
nodesets['nodesRightOpenEdge' ][mesh.nodesRightOpenEdge() ] = 1
nodesets['nodesBottomLeftCorner' ][mesh.nodesBottomLeftCorner() ] = 1
nodesets['nodesBottomRightCorner'][mesh.nodesBottomRightCorner()] = 1
nodesets['nodesTopLeftCorner' ][mesh.nodesTopLeftCorner() ] = 1
nodesets['nodesTopRightCorner' ][mesh.nodesTopRightCorner() ] = 1
# add DOF-numbers after eliminating periodicity
nodesets['dofsPeriodic'] = mesh.dofsPeriodic()[:,0]
# filename of the HDF5-file
-fname = 'MeshQuad4-FineLayer-nodes.hdf5'
+fname = 'paraview_nodesets.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data.file['coor'] = mesh.coor()
data.file['conn'] = mesh.conn()
for key, value in nodesets.items():
data[key] = value
# write XDMF-file with metadata
-
xdmf = pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Quadrilateral, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
)
for key, value in nodesets.items():
xdmf.push_back(pv.Attribute(fname, "/"+key, key, pv.AttributeType.Node, value.shape))
xdmf.write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.py b/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.py
index 6842569..043f0ac 100644
--- a/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.py
+++ b/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.py
@@ -1,57 +1,59 @@
import GooseFEM as gf
import matplotlib.pyplot as plt
import GooseMPL as gplt
import numpy as np
plt.style.use(['goose'])
# --------------------------------------------------------------------------------------------------
fig, axes = plt.subplots(figsize=(10,10), ncols=2)
# ---
ax = axes[0]
-mesh = gf.Mesh.Quad4.FineLayer(6, 18)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Quad4.FineLayer(6, 18)
+coor = mesh.coor()
+conn = mesh.conn()
+
+cindex = np.arange(mesh.nelem())
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet', axis=ax)
-for e in range(conn.shape[0]):
+for e in range(mesh.nelem()):
x = np.mean(coor[conn[e,:], 0])
y = np.mean(coor[conn[e,:], 1])
ax.text(x, y, str(e), ha='center', va='center')
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
# ---
ax = axes[1]
-new_mesh = gf.Mesh.Quad4.Regular(mesh.shape(0), mesh.shape(1))
+new_mesh = gf.Mesh.Quad4.Regular(mesh.nelx(), mesh.nely())
+
+coor = new_mesh.coor()
+conn = new_mesh.conn()
-coor = new_mesh.coor()
-conn = new_mesh.conn()
-cindex = np.arange(conn.shape[0])
+cindex = np.arange(new_mesh.nelem())
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet', axis=ax)
-for e in range(conn.shape[0]):
+for e in range(new_mesh.nelem()):
x = np.mean(coor[conn[e,:], 0])
y = np.mean(coor[conn[e,:], 1])
ax.text(x, y, str(e), ha='center', va='center')
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
# ---
plt.savefig('element-numbers.svg')
plt.show()
diff --git a/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.svg b/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.svg
deleted file mode 100644
index a0022d2..0000000
--- a/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/element-numbers.svg
+++ /dev/null
@@ -1,2698 +0,0 @@
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diff --git a/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/map.py b/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/map.py
index a391020..0386999 100644
--- a/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/map.py
+++ b/docs/details/figures/MeshQuad4/Map/FineLayer2Regular/map.py
@@ -1,50 +1,51 @@
import GooseFEM as gf
import matplotlib.pyplot as plt
import GooseMPL as gplt
import numpy as np
plt.style.use(['goose'])
# --------------------------------------------------------------------------------------------------
fig, axes = plt.subplots(figsize=(10,10), ncols=2)
# ---
ax = axes[0]
-mesh = gf.Mesh.Quad4.FineLayer(6*3, 18*2)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.random.random(conn.shape[0])
+mesh = gf.Mesh.Quad4.FineLayer(6*3, 18*2)
+coor = mesh.coor()
+conn = mesh.conn()
+
+cindex = np.random.random(mesh.nelem())
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet', axis=ax)
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
# ---
ax = axes[1]
mapping = gf.Mesh.Quad4.Map.FineLayer2Regular(mesh)
-new_mesh = mapping.getRegular()
+new_mesh = mapping.getRegularMesh()
-coor = new_mesh.coor()
-conn = new_mesh.conn()
+coor = new_mesh.coor()
+conn = new_mesh.conn()
-c = mapping.map(cindex)
+c = mapping.mapToRegular(cindex)
im = gplt.patch(coor=coor, conn=conn, cindex=c, cmap='jet', axis=ax)
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
# ---
plt.savefig('map.svg')
plt.show()
diff --git a/docs/details/figures/MeshQuad4/Regular/example.py b/docs/details/figures/MeshQuad4/Regular/example.py
index cdcee34..8e25228 100644
--- a/docs/details/figures/MeshQuad4/Regular/example.py
+++ b/docs/details/figures/MeshQuad4/Regular/example.py
@@ -1,44 +1,40 @@
+import numpy as np
import GooseFEM as gf
import matplotlib.pyplot as plt
import GooseMPL as gplt
-import numpy as np
plt.style.use(['goose'])
# --------------------------------------------------------------------------------------------------
-mesh = gf.Mesh.Quad4.Regular(21,11)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Quad4.Regular(5, 6)
+coor = mesh.coor()
+conn = mesh.conn()
+
+cindex = np.arange(mesh.nelem())
+
+Left = mesh.nodesLeftEdge()
+Right = mesh.nodesRightEdge()
+Bottom = mesh.nodesBottomEdge()
+Top = mesh.nodesTopEdge()
# --------------------------------------------------------------------------------------------------
fig, ax = plt.subplots(figsize=(10,10))
im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet')
ax.plot(coor[:,0], coor[:,1], marker='o', linestyle='none')
-lft = mesh.nodesLeftOpenEdge()
-rgt = mesh.nodesRightOpenEdge()
-bot = mesh.nodesBottomEdge()
-top = mesh.nodesTopEdge()
-
-ax.plot(coor[lft,0], coor[lft,1], marker='o', linestyle='none', color='g', label='nodesLeftOpenEdge')
-ax.plot(coor[rgt,0], coor[rgt,1], marker='o', linestyle='none', color='b', label='nodesRightOpenEdge')
-ax.plot(coor[bot,0], coor[bot,1], marker='o', linestyle='none', color='r', label='nodesBottomEdge')
-ax.plot(coor[top,0], coor[top,1], marker='o', linestyle='none', color='y', label='nodesTopEdge')
+ax.plot(coor[Left ,0], coor[Left ,1], marker='o', linestyle='none', color='g')
+ax.plot(coor[Right ,0], coor[Right ,1], marker='o', linestyle='none', color='b')
+ax.plot(coor[Bottom,0], coor[Bottom,1], marker='o', linestyle='none', color='r')
+ax.plot(coor[Top ,0], coor[Top ,1], marker='o', linestyle='none', color='y')
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
-ax.set_xlim([-1, 22])
-ax.set_ylim([-1, 14])
-
-ax.legend(ncol=2, loc='upper center')
-
plt.savefig('example.svg')
-plt.show()
+plt.close()
diff --git a/docs/details/figures/MeshQuad4/Regular/example.svg b/docs/details/figures/MeshQuad4/Regular/example.svg
deleted file mode 100644
index 5cdc3fa..0000000
--- a/docs/details/figures/MeshQuad4/Regular/example.svg
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diff --git a/docs/details/figures/MeshQuad4/Regular/example2.py b/docs/details/figures/MeshQuad4/Regular/paraview.py
similarity index 79%
rename from docs/details/figures/MeshQuad4/Regular/example2.py
rename to docs/details/figures/MeshQuad4/Regular/paraview.py
index 013ca73..752bd4c 100644
--- a/docs/details/figures/MeshQuad4/Regular/example2.py
+++ b/docs/details/figures/MeshQuad4/Regular/paraview.py
@@ -1,25 +1,22 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Quad4.Regular(9,11)
# filename of the HDF5-file
-fname = 'MeshQuad4-Regular.hdf5'
+fname = 'paraview.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data['coor'] = mesh.coor()
data['conn'] = mesh.conn()
# write XDMF-file with metadata
-
pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Quadrilateral, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
).write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshQuad4/Regular/nodes.py b/docs/details/figures/MeshQuad4/Regular/paraview_nodesets.py
similarity index 95%
rename from docs/details/figures/MeshQuad4/Regular/nodes.py
rename to docs/details/figures/MeshQuad4/Regular/paraview_nodesets.py
index 746bb34..4ccb477 100644
--- a/docs/details/figures/MeshQuad4/Regular/nodes.py
+++ b/docs/details/figures/MeshQuad4/Regular/paraview_nodesets.py
@@ -1,66 +1,63 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Quad4.Regular(9,11)
# initialize all node sets
nodesets = dict(
nodesBottomEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesTopLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesTopRightCorner = np.zeros((mesh.nnode()),dtype='int'),
)
# define node-sets
nodesets['nodesBottomEdge' ][mesh.nodesBottomEdge() ] = 1
nodesets['nodesTopEdge' ][mesh.nodesTopEdge() ] = 1
nodesets['nodesLeftEdge' ][mesh.nodesLeftEdge() ] = 1
nodesets['nodesRightEdge' ][mesh.nodesRightEdge() ] = 1
nodesets['nodesBottomOpenEdge' ][mesh.nodesBottomOpenEdge() ] = 1
nodesets['nodesTopOpenEdge' ][mesh.nodesTopOpenEdge() ] = 1
nodesets['nodesLeftOpenEdge' ][mesh.nodesLeftOpenEdge() ] = 1
nodesets['nodesRightOpenEdge' ][mesh.nodesRightOpenEdge() ] = 1
nodesets['nodesBottomLeftCorner' ][mesh.nodesBottomLeftCorner() ] = 1
nodesets['nodesBottomRightCorner'][mesh.nodesBottomRightCorner()] = 1
nodesets['nodesTopLeftCorner' ][mesh.nodesTopLeftCorner() ] = 1
nodesets['nodesTopRightCorner' ][mesh.nodesTopRightCorner() ] = 1
# add DOF-numbers after eliminating periodicity
nodesets['dofsPeriodic'] = mesh.dofsPeriodic()[:,0]
# filename of the HDF5-file
-fname = 'MeshQuad4-Regular-nodes.hdf5'
+fname = 'paraview_nodesets.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data.file['coor'] = mesh.coor()
data.file['conn'] = mesh.conn()
for key, value in nodesets.items():
data[key] = value
# write XDMF-file with metadata
-
xdmf = pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Quadrilateral, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
)
for key, value in nodesets.items():
xdmf.push_back(pv.Attribute(fname, "/"+key, key, pv.AttributeType.Node, value.shape))
xdmf.write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshTri3/Regular/example.py b/docs/details/figures/MeshTri3/Regular/example.py
index 7474094..c272f80 100644
--- a/docs/details/figures/MeshTri3/Regular/example.py
+++ b/docs/details/figures/MeshTri3/Regular/example.py
@@ -1,33 +1,40 @@
+import numpy as np
import GooseFEM as gf
import matplotlib.pyplot as plt
-import goosempl as gplt
-import numpy as np
+import GooseMPL as gplt
plt.style.use(['goose'])
# --------------------------------------------------------------------------------------------------
-mesh = gf.Mesh.Tri3.Regular(6*9,51)
-coor = mesh.coor()
-conn = mesh.conn()
-cindex = np.arange(conn.shape[0])
+mesh = gf.Mesh.Tri3.Regular(5, 6)
+coor = mesh.coor()
+conn = mesh.conn()
+
+cindex = np.arange(mesh.nelem())
+
+Left = mesh.nodesLeftEdge()
+Right = mesh.nodesRightEdge()
+Bottom = mesh.nodesBottomEdge()
+Top = mesh.nodesTopEdge()
# --------------------------------------------------------------------------------------------------
-fig,ax = plt.subplots(figsize=(10,10))
+fig, ax = plt.subplots(figsize=(10,10))
+
+im = gplt.patch(coor=coor, conn=conn, cindex=cindex, cmap='jet')
-im = gplt.patch(coor=coor,conn=conn,cindex=cindex,cmap='jet')
+ax.plot(coor[:,0], coor[:,1], marker='o', linestyle='none')
-ax.plot(coor[: ,0],coor[: ,1],marker='o',linestyle='none')
-ax.plot(coor[mesh.nodesLeft (),0],coor[mesh.nodesLeft (),1],marker='o',linestyle='none',color='g')
-ax.plot(coor[mesh.nodesRight (),0],coor[mesh.nodesRight (),1],marker='o',linestyle='none',color='b')
-ax.plot(coor[mesh.nodesBottom(),0],coor[mesh.nodesBottom(),1],marker='o',linestyle='none',color='r')
-ax.plot(coor[mesh.nodesTop (),0],coor[mesh.nodesTop (),1],marker='o',linestyle='none',color='y')
+ax.plot(coor[Left ,0], coor[Left ,1], marker='o', linestyle='none', color='g')
+ax.plot(coor[Right ,0], coor[Right ,1], marker='o', linestyle='none', color='b')
+ax.plot(coor[Bottom,0], coor[Bottom,1], marker='o', linestyle='none', color='r')
+ax.plot(coor[Top ,0], coor[Top ,1], marker='o', linestyle='none', color='y')
ax.set_aspect('equal')
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
plt.savefig('example.svg')
-plt.show()
+plt.close()
diff --git a/docs/details/figures/MeshTri3/Regular/example.svg b/docs/details/figures/MeshTri3/Regular/example.svg
deleted file mode 100644
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diff --git a/docs/details/figures/MeshTri3/Regular/example2.py b/docs/details/figures/MeshTri3/Regular/paraview.py
similarity index 79%
rename from docs/details/figures/MeshTri3/Regular/example2.py
rename to docs/details/figures/MeshTri3/Regular/paraview.py
index bf95ea8..06c7961 100644
--- a/docs/details/figures/MeshTri3/Regular/example2.py
+++ b/docs/details/figures/MeshTri3/Regular/paraview.py
@@ -1,25 +1,22 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Tri3.Regular(9,11)
# filename of the HDF5-file
-fname = 'MeshTri3-Regular.hdf5'
+fname = 'paraview.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data['coor'] = mesh.coor()
data['conn'] = mesh.conn()
# write XDMF-file with metadata
-
pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Triangle, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
).write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshTri3/Regular/nodes.py b/docs/details/figures/MeshTri3/Regular/paraview_nodesets.py
similarity index 95%
rename from docs/details/figures/MeshTri3/Regular/nodes.py
rename to docs/details/figures/MeshTri3/Regular/paraview_nodesets.py
index 5d2e99e..337879c 100644
--- a/docs/details/figures/MeshTri3/Regular/nodes.py
+++ b/docs/details/figures/MeshTri3/Regular/paraview_nodesets.py
@@ -1,66 +1,63 @@
import h5py, os
import numpy as np
import GooseFEM as gf
import GooseFEM.ParaView.HDF5 as pv
# create mesh object
mesh = gf.Mesh.Tri3.Regular(9,11)
# initialize all node sets
nodesets = dict(
nodesBottomEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesRightEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesTopOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesLeftOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesRightOpenEdge = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesBottomRightCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesTopLeftCorner = np.zeros((mesh.nnode()),dtype='int'),
nodesTopRightCorner = np.zeros((mesh.nnode()),dtype='int'),
)
# define node-sets
nodesets['nodesBottomEdge' ][mesh.nodesBottomEdge() ] = 1
nodesets['nodesTopEdge' ][mesh.nodesTopEdge() ] = 1
nodesets['nodesLeftEdge' ][mesh.nodesLeftEdge() ] = 1
nodesets['nodesRightEdge' ][mesh.nodesRightEdge() ] = 1
nodesets['nodesBottomOpenEdge' ][mesh.nodesBottomOpenEdge() ] = 1
nodesets['nodesTopOpenEdge' ][mesh.nodesTopOpenEdge() ] = 1
nodesets['nodesLeftOpenEdge' ][mesh.nodesLeftOpenEdge() ] = 1
nodesets['nodesRightOpenEdge' ][mesh.nodesRightOpenEdge() ] = 1
nodesets['nodesBottomLeftCorner' ][mesh.nodesBottomLeftCorner() ] = 1
nodesets['nodesBottomRightCorner'][mesh.nodesBottomRightCorner()] = 1
nodesets['nodesTopLeftCorner' ][mesh.nodesTopLeftCorner() ] = 1
nodesets['nodesTopRightCorner' ][mesh.nodesTopRightCorner() ] = 1
# add DOF-numbers after eliminating periodicity
nodesets['dofsPeriodic'] = mesh.dofsPeriodic()[:,0]
# filename of the HDF5-file
-fname = 'MeshTri3-Regular-nodes.hdf5'
+fname = 'paraview_nodesets.hdf5'
# write HDF-file containing the data
-
with h5py.File(fname, 'w') as data:
-
data.file['coor'] = mesh.coor()
data.file['conn'] = mesh.conn()
for key, value in nodesets.items():
data[key] = value
# write XDMF-file with metadata
-
xdmf = pv.Mesh(
- pv.Connectivity(fname, "/conn", pv.ElementType.Triangle, mesh.conn().shape),
+ pv.Connectivity(fname, "/conn", mesh.getElementType(), mesh.conn().shape),
pv.Coordinates(fname, "/coor", mesh.coor().shape),
)
for key, value in nodesets.items():
xdmf.push_back(pv.Attribute(fname, "/"+key, key, pv.AttributeType.Node, value.shape))
xdmf.write(os.path.splitext(fname)[0] + '.xdmf')
diff --git a/docs/details/figures/MeshTri3/naming_convention.svg b/docs/details/figures/MeshTri3/naming_convention.svg
new file mode 100644
index 0000000..e4a5726
--- /dev/null
+++ b/docs/details/figures/MeshTri3/naming_convention.svg
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diff --git a/docs/details/macros.rst b/docs/details/macros.rst
index 9a1c55a..3ee52c0 100644
--- a/docs/details/macros.rst
+++ b/docs/details/macros.rst
@@ -1,17 +1,18 @@
+.. _macros:
******
Macros
******
GOOSEFEM_ENABLE_ASSERT
======================
To enable assertions use
.. code-block:: cpp
#define GOOSEFEM_ENABLE_ASSERT
.. note::
Assertions are always turned on in the Python API.
diff --git a/docs/examples/dynamics_inertia-damping.rst b/docs/examples/dynamics_inertia-damping.rst
index 3c6c61a..258f661 100644
--- a/docs/examples/dynamics_inertia-damping.rst
+++ b/docs/examples/dynamics_inertia-damping.rst
@@ -1,77 +1,77 @@
*****************
Inertia + damping
*****************
Velocity Verlet
===============
.. code-block:: cpp
// position, velocity, acceleration (and history: last increment)
xt::xtensor<double,2> u = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> v = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> a = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> v_n = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> a_n = xt::zeros<double>({nnode, ndim});
// residual force
xt::xtensor<double,2> fr = xt::zeros<double>({nnode, ndim});
// compute mass matrix
// (often assumed constant & diagonal, remove either assumption if needed)
GooseFEM::MatrixDiagonal M(...);
...
// time increments
for ( ... )
{
// store history
xt::noalias(v_n) = v;
xt::noalias(a_n) = a;
// new displacement
xt::noalias(u) = u + dt * v + 0.5 * std::pow(dt,2.) * a;
// update residual force (and mass matrix if needed)
...
// estimate 1: new velocity
xt::noalias(v) = v_n + dt * a_n;
// estimate 1: new residual force (and mass matrix if needed)
...
// estimate 1: new acceleration
M.solve(fr, a);
// estimate 2: new velocity
xt::noalias(v) = v_n + .5 * dt * ( a_n + a );
// estimate 2: new residual force (and mass matrix if needed)
...
// estimate 2: new acceleration
M.solve(fr, a);
// new velocity
xt::noalias(v) = v_n + .5 * dt * ( a_n + a );
// new residual force (and mass matrix if needed)
...
// new acceleration
M.solve(fr, a);
}
Example
=======
.. todo::
Compile, run, and view instructions
-| :download:`main.cpp <Dynamics/Elastic-VelocityVerlet/main.cpp>`
-| :download:`CMakeLists.txt <Dynamics/Elastic-VelocityVerlet/CMakeLists.txt>`
-| :download:`plot.py <Dynamics/Elastic-VelocityVerlet/plot.py>`
+| :download:`main.cpp <dynamics/Elastic-VelocityVerlet/main.cpp>`
+| :download:`CMakeLists.txt <dynamics/Elastic-VelocityVerlet/CMakeLists.txt>`
+| :download:`plot.py <dynamics/Elastic-VelocityVerlet/plot.py>`
diff --git a/docs/examples/dynamics_inertia.rst b/docs/examples/dynamics_inertia.rst
index 6d11659..e2d0ce4 100644
--- a/docs/examples/dynamics_inertia.rst
+++ b/docs/examples/dynamics_inertia.rst
@@ -1,65 +1,65 @@
*******
Inertia
*******
Verlet
======
.. code-block:: cpp
// position, velocity, acceleration (and history: last increment)
xt::xtensor<double,2> u = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> v = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> a = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> v_n = xt::zeros<double>({nnode, ndim});
xt::xtensor<double,2> a_n = xt::zeros<double>({nnode, ndim});
// residual force
xt::xtensor<double,2> fr = xt::zeros<double>({nnode, ndim});
// compute mass matrix
// (often assumed constant & diagonal, remove either assumption if needed)
GooseFEM::MatrixDiagonal M(...);
...
// time increments
for ( ... )
{
// store history
xt::noalias(v_n) = v;
xt::noalias(a_n) = a;
// new displacement
xt::noalias(u) = u + dt * v + 0.5 * std::pow(dt,2.) * a;
// new residual force (and mass matrix if needed)
...
// new acceleration
M.solve(fr, a);
// new velocity
xt::noalias(v) = v_n + .5 * dt * ( a_n + a );
}
Example
=======
.. todo::
Compile, run, and view instructions:
.. code-block:: bash
mkdir build
cd build
make
./main
python3 plot.py
-| :download:`main.cpp <Dynamics/Elastic-Verlet/main.cpp>`
-| :download:`CMakeLists.txt <Dynamics/Elastic-Verlet/CMakeLists.txt>`
-| :download:`plot.py <Dynamics/Elastic-Verlet/plot.py>`
+| :download:`main.cpp <dynamics/Elastic-Verlet/main.cpp>`
+| :download:`CMakeLists.txt <dynamics/Elastic-Verlet/CMakeLists.txt>`
+| :download:`plot.py <dynamics/Elastic-Verlet/plot.py>`
diff --git a/docs/examples/statics/FixedDisplacements_LinearElastic/example/main.py b/docs/examples/statics/FixedDisplacements_LinearElastic/example/main.py
index 249cdc9..de064fa 100644
--- a/docs/examples/statics/FixedDisplacements_LinearElastic/example/main.py
+++ b/docs/examples/statics/FixedDisplacements_LinearElastic/example/main.py
@@ -1,163 +1,164 @@
import GooseFEM
import GMatElastic
import numpy as np
# mesh
# ----
# define mesh
mesh = GooseFEM.Mesh.Quad4.Regular(5,5)
# mesh dimensions
nelem = mesh.nelem()
nne = mesh.nne()
ndim = mesh.ndim()
# mesh definitions
coor = mesh.coor()
conn = mesh.conn()
dofs = mesh.dofs()
# node sets
nodesLeft = mesh.nodesLeftEdge()
nodesRight = mesh.nodesRightEdge()
nodesTop = mesh.nodesTopEdge()
nodesBottom = mesh.nodesBottomEdge()
# fixed displacements DOFs
# ------------------------
iip = np.concatenate((
dofs[nodesRight , 0],
dofs[nodesTop , 1],
dofs[nodesLeft , 0],
dofs[nodesBottom, 1]
))
# simulation variables
# --------------------
# vector definition
vector = GooseFEM.VectorPartitioned(conn, dofs, iip)
# allocate system matrix
K = GooseFEM.MatrixPartitioned(conn, dofs, iip)
# nodal quantities
disp = np.zeros(coor.shape)
fint = np.zeros(coor.shape)
fext = np.zeros(coor.shape)
fres = np.zeros(coor.shape)
# element vectors
ue = np.empty((nelem, nne, ndim))
fe = np.empty((nelem, nne, ndim))
Ke = np.empty((nelem, nne*ndim, nne*ndim))
# element/material definition
# ---------------------------
# element definition
elem = GooseFEM.Element.Quad4.QuadraturePlanar(vector.AsElement(coor))
nip = elem.nip()
# material definition
mat = GMatElastic.Cartesian3d.Matrix(nelem, nip, 1., 1.)
# integration point tensors
d = 3
Eps = np.empty((nelem, nip, d, d ))
Sig = np.empty((nelem, nip, d, d ))
C = np.empty((nelem, nip, d, d, d, d))
# solve
# -----
# strain
ue = vector.AsElement(disp)
Eps = elem.SymGradN_vector(ue)
# stress & tangent
(Sig, C) = mat.Tangent(Eps)
# internal force
fe = elem.Int_gradN_dot_tensor2_dV(Sig)
fint = vector.AssembleNode(fe)
# stiffness matrix
Ke = elem.Int_gradN_dot_tensor4_dot_gradNT_dV(C)
K.assemble(Ke)
# set fixed displacements
disp[nodesRight , 0] = +0.1
disp[nodesTop , 1] = -0.1
disp[nodesLeft , 0] = 0.0
disp[nodesBottom, 1] = 0.0
# residual
fres = fext - fint
# solve
disp = K.Solve(fres, disp)
# post-process
# ------------
# compute strain and stress
ue = vector.AsElement(disp)
Eps = elem.SymGradN_vector(ue)
Sig = mat.Stress(Eps)
# internal force
fe = elem.Int_gradN_dot_tensor2_dV(Sig)
fint = vector.AssembleNode(fe)
# apply reaction force
fext = vector.Copy_p(fint, fext)
# residual
fres = fext - fint
# print residual
print(np.sum(np.abs(fres)) / np.sum(np.abs(fext)))
# average stress per node
dV = elem.DV(2)
Sig = np.average(Sig, weights=dV, axis=1)
# plot
# ----
import matplotlib.pyplot as plt
import GooseMPL as gplt
plt.style.use(['goose', 'goose-latex'])
# extract dimension
nelem = conn.shape[0]
# tensor products
ddot22 = lambda A2,B2: np.einsum('eij ,eji->e ',A2,B2)
ddot42 = lambda A4,B2: np.einsum('eijkl,elk->eij ',A4,B2)
dyad22 = lambda A2,B2: np.einsum('eij ,ekl->eijkl',A2,B2)
# identity tensor (single tensor)
i = np.eye(3)
# identity tensors (grid)
I = np.einsum('ij ,e' , i ,np.ones([nelem]))
I4 = np.einsum('ijkl,e->eijkl',np.einsum('il,jk',i,i),np.ones([nelem]))
I4rt = np.einsum('ijkl,e->eijkl',np.einsum('ik,jl',i,i),np.ones([nelem]))
I4s = (I4+I4rt)/2.
II = dyad22(I,I)
I4d = I4s-II/3.
# compute equivalent stress
Sigd = ddot42(I4d, Sig)
sigeq = np.sqrt(3./2.*ddot22(Sigd,Sigd))
# plot
fig, ax = plt.subplots()
gplt.patch(coor=coor+disp, conn=conn, cindex=sigeq, cmap='jet', axis=ax, clim=(0,0.1))
gplt.patch(coor=coor, conn=conn, linestyle='--', axis=ax)
-plt.show()
+plt.savefig('main.pdf')
+plt.close()
diff --git a/docs/examples/statics/FixedDisplacements_LinearElastic/example/plot.py b/docs/examples/statics/FixedDisplacements_LinearElastic/example/plot.py
index 0bf1209..a5b511a 100644
--- a/docs/examples/statics/FixedDisplacements_LinearElastic/example/plot.py
+++ b/docs/examples/statics/FixedDisplacements_LinearElastic/example/plot.py
@@ -1,51 +1,49 @@
import h5py
import matplotlib.pyplot as plt
import GooseMPL as gplt
import numpy as np
plt.style.use(['goose', 'goose-latex'])
# open file
file = h5py.File('main.h5', 'r')
# read fields
coor = file['/coor'][...]
conn = file['/conn'][...]
disp = file['/disp'][...]
Sig = file['/Sig' ][...]
# extract dimension
nelem = conn.shape[0]
# tensor products
ddot22 = lambda A2,B2: np.einsum('eij ,eji->e ',A2,B2)
ddot42 = lambda A4,B2: np.einsum('eijkl,elk->eij ',A4,B2)
dyad22 = lambda A2,B2: np.einsum('eij ,ekl->eijkl',A2,B2)
# identity tensor (single tensor)
i = np.eye(3)
# identity tensors (grid)
I = np.einsum('ij ,e' , i ,np.ones([nelem]))
I4 = np.einsum('ijkl,e->eijkl',np.einsum('il,jk',i,i),np.ones([nelem]))
I4rt = np.einsum('ijkl,e->eijkl',np.einsum('ik,jl',i,i),np.ones([nelem]))
I4s = (I4+I4rt)/2.
II = dyad22(I,I)
I4d = I4s-II/3.
# compute equivalent stress
Sigd = ddot42(I4d, Sig)
sigeq = np.sqrt(3./2.*ddot22(Sigd,Sigd))
# plot
fig, ax = plt.subplots()
-
gplt.patch(coor=coor+disp, conn=conn, cindex=sigeq, cmap='jet', axis=ax, clim=(0,0.1))
-
gplt.patch(coor=coor, conn=conn, linestyle='--', axis=ax)
-
-plt.show()
+plt.savefig('plot.pdf')
+plt.close()
diff --git a/docs/examples/statics_linear.rst b/docs/examples/statics_linear.rst
index 81d5ca4..cc3170a 100644
--- a/docs/examples/statics_linear.rst
+++ b/docs/examples/statics_linear.rst
@@ -1,266 +1,311 @@
**************
Linear elastic
**************
-Consider a uniform linear elastic bar that is extended by a uniform fixed displacement on both sides. This problem can be modelled and discretised using symmetry as show below. In this example we will furthermore assume that the bar is sufficiently thick in the out-of-plane direction that it can be modelled using two-dimensional plane strain.
+Consider a uniform linear elastic bar that is extended by a uniform fixed displacement on both sides. This problem can be modelled and discretised using symmetry as show below. In this example we will furthermore assume that the bar is sufficiently thick in the out-of-plane direction to be modelled using two-dimensional plane strain.
.. image:: statics/FixedDisplacements_LinearElastic/problem-sketch.svg
:width: 300px
:align: center
|
Below an example is described line-by-line. The full example can be downloaded:
| :download:`main.cpp <statics/FixedDisplacements_LinearElastic/example/main.cpp>`
| :download:`CMakeLists.txt <statics/FixedDisplacements_LinearElastic/example/CMakeLists.txt>`
| :download:`plot.py <statics/FixedDisplacements_LinearElastic/example/plot.py>`
.. todo::
Compile and run instructions.
.. note::
- This example is also available using the Python interface (:download:`main.py <statics/FixedDisplacements_LinearElastic/example/main.py>`). Note that compared to the C++ API, the Python API requires more data-allocation, in particular in the functions "AsElement" and "AssembleNode". See :ref:`conventions_allocation`.
+ This example is also available using the Python interface (:download:`main.py <statics/FixedDisplacements_LinearElastic/example/main.py>`). Compared to the C++ API, the Python API requires more data-allocation, in particular for the functions "AsElement" and "AssembleNode". See: :ref:`conventions_allocation`.
Include library
===============
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 1-4
:emphasize-lines: 1-2
The first step is to include the header-only library. Note that for this example we also make use of a material model (`GMatElastic <https://www.github.com/tdegeus/GMatElastic>`_) and a library to write (and read) HDF5 files (`HighFive <https://www.github.com/BlueBrain/HighFive>`_).
Define mesh
===========
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 11-28
:emphasize-lines: 2
A mesh is defined using GooseFEM. As observed the "mesh" is a class that has methods to extract the relevant information such as the nodal coordinates ("coor"), the connectivity ("conn"), the degrees-of-freedom per node ("dofs") and several node-sets that will be used to impose the sketched boundary conditions ("nodesLeft", "nodesRight", "nodesTop", "nodesBottom").
Note that:
* The connectivity ("conn") contains information of which nodes, in which order, belong to which element.
* The degrees-of-freedom per node ("dofs") contains information of how a nodal vector (a vector stored per node) can be transformed to a list of degrees-of-freedom as used in the linear system (although this can be mostly done automatically as we will see below).
.. seealso::
- :ref:`conventions_terminology`
+ * :ref:`conventions_terminology`
+ * Details: :ref:`MeshQuad4`
Define partitioning
===================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 33-38
We will reorder such that degrees-of-freedom are ordered such that
.. math::
\texttt{u} =
\begin{bmatrix}
\texttt{u}_u \\
\texttt{u}_p
\end{bmatrix}
where the subscript :math:`u` and :math:`p` respectively denote *Unknown* and *Prescribed* degrees-of-freedom. To achieve this we start by collecting all prescribed degrees-of-freedom in "iip".
(Avoid) Book-keeping
====================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 44
:emphasize-lines: 1
To switch between the three of GooseFEM's data-representations, an instance of the "Vector" class is used. This instance, "vector", will enable us to switch between a vector field (e.g. the displacement)
1. collected per node,
2. collected per degree-of-freedom, or
3. collected per element.
.. note::
The "Vector" class collects most, if not all, the burden of book-keeping. It is thus here that "conn", "dofs", and "iip" are used. In particular,
- * "nodevec" :math:`\leftrightarrow` "dofval" using "dofs" and "iip",
- * "nodevec" :math:`\leftrightarrow` "elemvec" using "conn".
+ * 'nodevec' :math:`\leftrightarrow` 'dofval' using "dofs" and "iip",
+ * 'nodevec' :math:`\leftrightarrow` 'elemvec' using "conn".
By contrast, most of GooseFEM's other methods receive the relevant representation, and consequently require no problem specific knowledge. They thus do not have to supplied with "conn", "dofs", or "iip".
.. seealso::
* :ref:`conventions_vector`
* :ref:`conventions_storage`
+ * Details: :ref:`Vector`
System matrix
=============
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 47
:emphasize-lines: 1
We now also allocate the system/stiffness system (stored as sparse matrix). Like vector, it can accept and return different vector representations, in addition to the ability to assemble from element system matrices.
+.. note::
+
+ Here, the default solver is used (which is the default template, hence the "<>"). To use other solvers see: :ref:`linear_solver`.
+
.. seealso::
* :ref:`conventions_matrix`
- * :ref:`sparse`
+ * Details: :ref:`Matrix`
Allocate nodal vectors
======================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 50-53
* "disp": nodal displacements
* "fint": nodal internal forces
* "fext": nodal external forces
* "fres": nodal residual forces
Allocate element vectors
========================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 56-58
* "ue": displacement
* "fe": force
* "Ke": tangent matrix
.. warning::
- Upsizing (e.g. from "disp" to "ue") can be done uniquely, but downsizing (e.g. from "fe" to "fint") can be done in more than one way, see :ref:`conventions_vector_conversion`. We will get back to this point below.
+ Upsizing (e.g. "disp" :math:`\rightarrow` "ue") can be done uniquely, but downsizing (e.g. "fe" :math:`\rightarrow` "fint") can be done in more than one way, see :ref:`conventions_vector_conversion`. We will get back to this point below.
Element definition
==================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 64-65
-At this moment the interpolation and quadrature is allocated. The shape functions and integration points (that can be customised) are stored in this class. As observed, no further information is needed that the number of elements and the nodal coordinates per element. Both are contained in the output of "vector.AsElement(coor)", which is an "elemvec" of shape "[nelem, nne, ndim]". This illustrates that problem specific book-keeping is isolated to the main program, using "Vector" as tool.
+At this moment the interpolation and quadrature is allocated. The shape functions and integration points (that can be customised) are stored in this class. As observed, no further information is needed than the number of elements and the nodal coordinates per element. Both are contained in the output of "vector.AsElement(coor)", which is an 'elemvec' of shape "[nelem, nne, ndim]". This illustrates that problem specific book-keeping is isolated to the main program, using "Vector" as tool.
.. note::
The shape functions are computed when constructing this class, they are not recomputed when evaluating them. One can recompute them if the nodal coordinates change using ".update_x(...)", however, this is only relevant in a large deformation setting.
+.. seealso::
+
+ * :ref:`conventions_vector`
+ * :ref:`conventions_storage`
+ * Details: :ref:`Vector`
+ * Details: :ref:`ElementQuad4`
+
Material definition
===================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 68
We now define a uniform linear elastic material, using an external library that is tuned to GooseFEM. This material library will translate a strain tensor per integration point to a stress tensor per integration point and a stiffness tensor per integration point.
.. seealso::
Material libraries tuned to GooseFEM include:
* `GMatElastic <https:://www.github.com/tdegeus/GMatElastic>`__
* `GMatElastoPlastic <https:://www.github.com/tdegeus/GMatElastoPlastic>`__
* `GMatElastoPlasticFiniteStrainSimo <https:://www.github.com/tdegeus/GMatElastoPlasticFiniteStrainSimo>`__
* `GMatElastoPlasticQPot <https:://www.github.com/tdegeus/GMatElastoPlasticQPot>`__
* `GMatElastoPlasticQPot3d <https:://www.github.com/tdegeus/GMatElastoPlasticQPot3d>`__
* `GMatNonLinearElastic <https:://www.github.com/tdegeus/GMatNonLinearElastic>`__
+ But other libraries can also be easily used with (simple) wrappers.
+
Integration point tensors
=========================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 71-74
These strain, stress, and stiffness tensors per integration point are now allocated. Note that these tensors are 3-d while our problem was 2-d. This is thanks to the plane strain assumption, and the element definition that ignores all third-dimension components.
Compute strain
==============
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 80-81
-The strain per integration point is now computed using the current nodal displacements (stored as "elemvec" in "ue") and the gradient of the shape functions.
+The strain per integration point is now computed using the current nodal displacements (stored as 'elemvec' in "ue") and the gradient of the shape functions.
+
+.. note::
+
+ "ue" is the output of "vector.asElement(disp, ue)". Using this syntax re-allocation of "ue" is avoided. If this optimisation is irrelevant for you problem (or if you are using the Python interface), please use the same function, but starting with a capital:
+
+ .. code-block:: cpp
+
+ ue = vector.AsElement(disp);
+
+ Note that this allows the one-liner
+
+ .. code-block:: cpp
+
+ Eps = elem.SymGradN_vector(vector.AElement(disp));
Compute stress and tangent
==========================
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 84
The stress and stiffness tensors are now computed for each integration point (completely independently) using the external material model.
+.. note::
+
+ "Sig" and "C" are the output variables that were preallocated in the main.
+
Assemble system
===============
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 86-92
-The stress stored per integration point ("Sig") is now converted to nodal internal force vectors stored per element ("fe"). Using "vector" this "elemvec" representation is then converted of a "nodevec" representation in "fint". Likewise, the stiffness tensor stored for integration point ("C") are converted to system matrices stored per element ("elemmat") and finally assembled to the global stiffness matrix.
+The stress stored per integration point ("Sig") is now converted to nodal internal force vectors stored per element ("fe"). Using "vector" this 'elemvec' representation is then converted of a 'nodevec' representation in "fint". Likewise, the stiffness tensor stored for integration point ("C") are converted to system matrices stored per element ('elemmat') and finally assembled to the global stiffness matrix.
.. warning::
- Please note that downsizing ("fe" to "fint" and "Ke" to "K") can be done in two ways, and that "assemble..." is the right function here as it adds entries that occur more than once. In contrast "as..." be false here.
+ Please note that downsizing ("fe" :math:`\rightarrow` "fint" and "Ke" :math:`\rightarrow` "K") can be done in two ways, and that "assemble..." is the right function here as it adds entries that occur more than once. In contrast "as..." would not result in what we want here.
+
+.. note::
+
+ Once more, "fe", "fint", and "Ke" are output variables. Less efficient, but shorter, is:
+
+ .. code-block:: cpp
+
+ // internal force
+ fint = vector.AssembleNode(elem.Int_gradN_dot_tensor2_dV(Sig));
+
+ // stiffness matrix
+ K.assemble(elem.Int_gradN_dot_tensor4_dot_gradNT_dV(C));
Solve
=====
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 94-104
-We now prescribe the displacement of the Prescribed degrees-of-freedom directly of "disp" and compute the residual force. This is follows by partitioning and solving, all done internally in the "MatrixPartitioned" class.
+We now prescribe the displacement of the Prescribed degrees-of-freedom directly in the nodal displacements "disp" and compute the residual force. This is follows by partitioning and solving, all done internally in the "MatrixPartitioned" class.
Post-process
============
Strain and stress
-----------------
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 110-112
The strain and stress per integration point are recomputed for post-processing.
Residual force
--------------
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 114-125
-We now convince ourselves that the solution is indeed in mechanical equilibrium.
+We convince ourselves that the solution is indeed in mechanical equilibrium.
Store & plot
------------
.. literalinclude:: statics/FixedDisplacements_LinearElastic/example/main.cpp
:language: cpp
:lines: 127-136
Finally we store some fields for plotting using :download:`plot.py <statics/FixedDisplacements_LinearElastic/example/plot.py>`.
Manual partitioning
===================
-To verify how partitioning and solving is done internally using the "Vector" and "MatrixPartitioned" classes, the same example is provided where partitioning is done manually:
+To verify how partitioning and solving is done internally using the "MatrixPartitioned" class, the same example is provided where partitioning is done manually:
-:download:`main.cpp <statics/FixedDisplacements_LinearElastic/manual_partition/main.cpp>`
-:download:`CMakeLists.txt <statics/FixedDisplacements_LinearElastic/manual_partition/CMakeLists.txt>`
-:download:`plot.py <statics/FixedDisplacements_LinearElastic/manual_partition/plot.py>`
-:download:`main.py <statics/FixedDisplacements_LinearElastic/manual_partition/main.py>`
+| :download:`main.cpp <statics/FixedDisplacements_LinearElastic/manual_partition/main.cpp>`
+| :download:`CMakeLists.txt <statics/FixedDisplacements_LinearElastic/manual_partition/CMakeLists.txt>`
+| :download:`plot.py <statics/FixedDisplacements_LinearElastic/manual_partition/plot.py>`
+| :download:`main.py <statics/FixedDisplacements_LinearElastic/manual_partition/main.py>`
diff --git a/docs/introduction.rst b/docs/introduction.rst
index 4f4f9f7..ac0d47e 100644
--- a/docs/introduction.rst
+++ b/docs/introduction.rst
@@ -1,27 +1,25 @@
************
Introduction
************
Overview
--------
This header-only module provides C++ classes (including Python wrappers) to write simulations using the Finite Element Method.
.. note::
This library is free to use under the `GPLv3 license <https://github.com/tdegeus/GooseFEM/blob/master/LICENSE>`_. Any additions are very much appreciated, in terms of suggested functionality, code, documentation, testimonials, word of mouth advertisement, .... Bugs or feature requests can be filed on `GitHub <http://github.com/tdegeus/GooseFEM>`_. As always, the code comes with no guarantee. None of the developers can be held responsible for possible mistakes.
Hallmark feature
----------------
-The hallmark feature of GooseFEM is that data is not stored in GooseFEM's classes but in multi-dimensional arrays with certain storage conventions. Consequently one is entirely free to mix and match routines, from GooseFEM or even from somewhere else.
-
-This design choice also has resulted in a very simple library: As very little problem specific information is needed all classes are transparent single functionality classes.
+The hallmark feature of GooseFEM is that data is not stored in GooseFEM's classes but only in multi-dimensional arrays with certain :ref:`storage conventions <conventions_storage>`. Consequently one is entirely free to mix and match routines, from GooseFEM or even from somewhere else. Consequently the readability of the end-user's code and of the library remains high: Only the main function combines different ingredients, there is no dependence between GooseFEM's classes.
Documentation
-------------
This document should be considered as a quick-start guide. A lot effort has been spent on the readability of the code itself (in particular the ``*.h`` files should be instructive). One is highly encouraged to answer more advanced questions that arise from this guide directly using the code. Download buttons to the relevant files are included throughout this reader.
-A compact reader covering the basic theory is available `here <https://github.com/tdegeus/GooseFEM/docs/theory/readme.pdf>`_.
+A compact reader covering the basic theory is available as :download:`PDF <theory/readme.pdf>`.
diff --git a/include/GooseFEM/Element.hpp b/include/GooseFEM/Element.hpp
index dcd5a44..f786978 100644
--- a/include/GooseFEM/Element.hpp
+++ b/include/GooseFEM/Element.hpp
@@ -1,111 +1,111 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENT_HPP
#define GOOSEFEM_ELEMENT_HPP
// -------------------------------------------------------------------------------------------------
#include "Element.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> asElementVector(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<double,2>& nodevec)
{
- size_t nelem = conn.shape()[0];
- size_t nne = conn.shape()[1];
- size_t ndim = nodevec.shape()[1];
+ size_t nelem = conn.shape(0);
+ size_t nne = conn.shape(1);
+ size_t ndim = nodevec.shape(1);
xt::xtensor<double,3> elemvec = xt::empty<double>({nelem, nne, ndim});
#pragma omp parallel for
for (size_t e = 0 ; e < nelem ; ++e)
for (size_t m = 0 ; m < nne ; ++m)
for (size_t i = 0 ; i < ndim ; ++i)
elemvec(e,m,i) = nodevec(conn(e,m),i);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> assembleNodeVector(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<double,3>& elemvec)
{
- size_t nelem = conn.shape()[0];
- size_t nne = conn.shape()[1];
- size_t ndim = elemvec.shape()[2];
+ size_t nelem = conn.shape(0);
+ size_t nne = conn.shape(1);
+ size_t ndim = elemvec.shape(2);
size_t nnode = xt::amax(conn)[0]+1;
- GOOSEFEM_ASSERT(elemvec.shape()[0] == nelem);
- GOOSEFEM_ASSERT(elemvec.shape()[1] == nne);
+ GOOSEFEM_ASSERT(elemvec.shape(0) == nelem);
+ GOOSEFEM_ASSERT(elemvec.shape(1) == nne);
xt::xtensor<double,2> nodevec = xt::zeros<double>({nnode, ndim});
for (size_t e = 0 ; e < nelem ; ++e)
for (size_t m = 0 ; m < nne ; ++m)
for (size_t i = 0 ; i < ndim ; ++i)
nodevec(conn(e,m),i) += elemvec(e,m,i);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
template<class E>
inline bool isSequential(const E& dofs)
{
size_t ndof = xt::amax(dofs)[0] + 1;
xt::xtensor<int,1> exists = xt::zeros<int>({ndof});
for (auto& i: dofs)
exists[i]++;
for (auto& i: dofs)
- if ( exists[i] == 0 )
+ if (exists[i] == 0)
return false;
return true;
}
// -------------------------------------------------------------------------------------------------
inline bool isDiagonal(const xt::xtensor<double,3>& elemmat)
{
- GOOSEFEM_ASSERT(elemmat.shape()[1] == elemmat.shape()[2]);
+ GOOSEFEM_ASSERT(elemmat.shape(1) == elemmat.shape(2));
- size_t nelem = elemmat.shape()[0];
- size_t N = elemmat.shape()[1];
+ size_t nelem = elemmat.shape(0);
+ size_t N = elemmat.shape(1);
double eps = std::numeric_limits<double>::epsilon();
#pragma omp parallel for
for (size_t e = 0 ; e < nelem ; ++e)
for (size_t i = 0 ; i < N ; ++i)
for (size_t j = 0 ; j < N ; ++j)
- if ( i != j )
- if ( std::abs(elemmat(e,i,j)) > eps )
+ if (i != j)
+ if (std::abs(elemmat(e,i,j)) > eps)
return false;
return true;
}
// -------------------------------------------------------------------------------------------------
}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/ElementHex8.h b/include/GooseFEM/ElementHex8.h
index 2abce84..11e42ce 100644
--- a/include/GooseFEM/ElementHex8.h
+++ b/include/GooseFEM/ElementHex8.h
@@ -1,191 +1,191 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTHEX8_H
#define GOOSEFEM_ELEMENTHEX8_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Hex8 {
// -------------------------------------------------------------------------------------------------
inline double inv(
const xt::xtensor_fixed<double, xt::xshape<3,3>>& A,
xt::xtensor_fixed<double, xt::xshape<3,3>>& Ainv);
// -------------------------------------------------------------------------------------------------
namespace Gauss {
inline size_t nip(); // number of integration points
inline xt::xtensor<double,2> xi(); // integration point coordinates (local coordinates)
inline xt::xtensor<double,1> w(); // integration point weights
}
// -------------------------------------------------------------------------------------------------
namespace Nodal {
inline size_t nip(); // number of integration points
inline xt::xtensor<double,2> xi(); // integration point coordinates (local coordinates)
inline xt::xtensor<double,1> w(); // integration point weights
}
// -------------------------------------------------------------------------------------------------
class Quadrature
{
public:
// Fixed dimensions:
// ndim = 3 - number of dimensions
// nne = 8 - number of nodes per element
//
// Naming convention:
// "elemmat" - matrices stored per element - [nelem, nne*ndim, nne*ndim]
// "elemvec" - nodal vectors stored per element - [nelem, nne, ndim]
// "qtensor" - integration point tensor - [nelem, nip, ndim, ndim]
// "qscalar" - integration point scalar - [nelem, nip]
// Constructor: integration point coordinates and weights are optional (default: Gauss)
Quadrature() = default;
Quadrature(
const xt::xtensor<double,3>& x);
Quadrature(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w);
// Update the nodal positions (shape of "x" should match the earlier definition)
void update_x(const xt::xtensor<double,3>& x);
// Return dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t ndim() const; // number of dimension
size_t nip() const; // number of integration points
// Return shape function gradients
- xt::xtensor<double,4> gradN() const;
+ xt::xtensor<double,4> GradN() const;
// Return integration volume
void dV(xt::xtensor<double,2>& qscalar) const;
void dV(xt::xtensor<double,4>& qtensor) const; // same volume for all tensor components
void dV(xt::xarray<double>& qtensor) const; // same volume for all tensor components
// Dyadic product (and its transpose and symmetric part)
// qtensor(i,j) += dNdx(m,i) * elemvec(m,j)
void gradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
void gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
void symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
// Integral of the scalar product
// elemmat(m*ndim+i,n*ndim+i) += N(m) * qscalar * N(n) * dV
void int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar,
xt::xtensor<double,3>& elemmat) const; // overwritten
// Integral of the dot product
// elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV
void int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor,
xt::xtensor<double,3>& elemvec) const; // overwritten
// Integral of the dot product
// elemmat(m*2+j, n*2+k) += dNdx(m,i) * qtensor(i,j,k,l) * dNdx(n,l) * dV
void int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor,
xt::xtensor<double,3>& elemmat) const; // overwritten
// Auto-allocation of the functions above
xt::xtensor<double,2> DV() const;
xt::xarray<double> DV(
size_t rank) const;
xt::xtensor<double,4> GradN_vector(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,4> GradN_vector_T(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,4> SymGradN_vector(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,3> Int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar) const;
xt::xtensor<double,3> Int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor) const;
xt::xtensor<double,3> Int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor) const;
private:
// Compute "vol" and "dNdx" based on current "x"
void compute_dN();
private:
// Dimensions (flexible)
size_t m_nelem; // number of elements
size_t m_nip; // number of integration points
// Dimensions (fixed for this element type)
static const size_t m_nne=8; // number of nodes per element
static const size_t m_ndim=3; // number of dimensions
// Data arrays
xt::xtensor<double,3> m_x; // nodal positions stored per element [nelem, nne, ndim]
xt::xtensor<double,1> m_w; // weight of each integration point [nip]
xt::xtensor<double,2> m_xi; // local coordinate of each integration point [nip, ndim]
xt::xtensor<double,2> m_N; // shape functions [nip, nne]
xt::xtensor<double,3> m_dNxi; // shape function grad. w.r.t. local coor. [nip, nne, ndim]
xt::xtensor<double,4> m_dNx; // shape function grad. w.r.t. global coor. [nelem, nip, nne, ndim]
xt::xtensor<double,2> m_vol; // integration point volume [nelem, nip]
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#include "ElementHex8.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/ElementHex8.hpp b/include/GooseFEM/ElementHex8.hpp
index dbbbb51..143f851 100644
--- a/include/GooseFEM/ElementHex8.hpp
+++ b/include/GooseFEM/ElementHex8.hpp
@@ -1,707 +1,707 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTHEX8_HPP
#define GOOSEFEM_ELEMENTHEX8_HPP
// -------------------------------------------------------------------------------------------------
#include "ElementHex8.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Hex8 {
// =================================================================================================
inline double inv(
const xt::xtensor_fixed<double, xt::xshape<3,3>>& A,
xt::xtensor_fixed<double, xt::xshape<3,3>>& Ainv)
{
// compute determinant
double det = ( A(0,0) * A(1,1) * A(2,2) +
A(0,1) * A(1,2) * A(2,0) +
A(0,2) * A(1,0) * A(2,1) ) -
( A(0,2) * A(1,1) * A(2,0) +
A(0,1) * A(1,0) * A(2,2) +
A(0,0) * A(1,2) * A(2,1) );
// compute inverse
Ainv(0,0) = (A(1,1)*A(2,2)-A(1,2)*A(2,1)) / det;
Ainv(0,1) = (A(0,2)*A(2,1)-A(0,1)*A(2,2)) / det;
Ainv(0,2) = (A(0,1)*A(1,2)-A(0,2)*A(1,1)) / det;
Ainv(1,0) = (A(1,2)*A(2,0)-A(1,0)*A(2,2)) / det;
Ainv(1,1) = (A(0,0)*A(2,2)-A(0,2)*A(2,0)) / det;
Ainv(1,2) = (A(0,2)*A(1,0)-A(0,0)*A(1,2)) / det;
Ainv(2,0) = (A(1,0)*A(2,1)-A(1,1)*A(2,0)) / det;
Ainv(2,1) = (A(0,1)*A(2,0)-A(0,0)*A(2,1)) / det;
Ainv(2,2) = (A(0,0)*A(1,1)-A(0,1)*A(1,0)) / det;
return det;
}
// =================================================================================================
namespace Gauss {
// -------------------------------------------------------------------------------------------------
inline size_t nip()
{
return 8;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> xi()
{
size_t nip = 8;
size_t ndim = 3;
xt::xtensor<double,2> xi = xt::empty<double>({nip,ndim});
xi(0,0) = -1./std::sqrt(3.); xi(0,1) = -1./std::sqrt(3.); xi(0,2) = -1./std::sqrt(3.);
xi(1,0) = +1./std::sqrt(3.); xi(1,1) = -1./std::sqrt(3.); xi(1,2) = -1./std::sqrt(3.);
xi(2,0) = +1./std::sqrt(3.); xi(2,1) = +1./std::sqrt(3.); xi(2,2) = -1./std::sqrt(3.);
xi(3,0) = -1./std::sqrt(3.); xi(3,1) = +1./std::sqrt(3.); xi(3,2) = -1./std::sqrt(3.);
xi(4,0) = -1./std::sqrt(3.); xi(4,1) = -1./std::sqrt(3.); xi(4,2) = +1./std::sqrt(3.);
xi(5,0) = +1./std::sqrt(3.); xi(5,1) = -1./std::sqrt(3.); xi(5,2) = +1./std::sqrt(3.);
xi(6,0) = +1./std::sqrt(3.); xi(6,1) = +1./std::sqrt(3.); xi(6,2) = +1./std::sqrt(3.);
xi(7,0) = -1./std::sqrt(3.); xi(7,1) = +1./std::sqrt(3.); xi(7,2) = +1./std::sqrt(3.);
return xi;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> w()
{
size_t nip = 8;
xt::xtensor<double,1> w = xt::empty<double>({nip});
w(0) = 1.;
w(1) = 1.;
w(2) = 1.;
w(3) = 1.;
w(4) = 1.;
w(5) = 1.;
w(6) = 1.;
w(7) = 1.;
return w;
}
// -------------------------------------------------------------------------------------------------
}
// =================================================================================================
namespace Nodal {
// -------------------------------------------------------------------------------------------------
inline size_t nip()
{
return 8;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> xi()
{
size_t nip = 8;
size_t ndim = 3;
xt::xtensor<double,2> xi = xt::empty<double>({nip,ndim});
xi(0,0) = -1.; xi(0,1) = -1.; xi(0,2) = -1.;
xi(1,0) = +1.; xi(1,1) = -1.; xi(1,2) = -1.;
xi(2,0) = +1.; xi(2,1) = +1.; xi(2,2) = -1.;
xi(3,0) = -1.; xi(3,1) = +1.; xi(3,2) = -1.;
xi(4,0) = -1.; xi(4,1) = -1.; xi(4,2) = +1.;
xi(5,0) = +1.; xi(5,1) = -1.; xi(5,2) = +1.;
xi(6,0) = +1.; xi(6,1) = +1.; xi(6,2) = +1.;
xi(7,0) = -1.; xi(7,1) = +1.; xi(7,2) = +1.;
return xi;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> w()
{
size_t nip = 8;
xt::xtensor<double,1> w = xt::empty<double>({nip});
w(0) = 1.;
w(1) = 1.;
w(2) = 1.;
w(3) = 1.;
w(4) = 1.;
w(5) = 1.;
w(6) = 1.;
w(7) = 1.;
return w;
}
// -------------------------------------------------------------------------------------------------
}
// =================================================================================================
inline Quadrature::Quadrature(const xt::xtensor<double,3>& x) :
Quadrature(x, Gauss::xi(), Gauss::w()) {}
// -------------------------------------------------------------------------------------------------
inline Quadrature::Quadrature(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w) :
m_x(x), m_w(w), m_xi(xi)
{
- GOOSEFEM_ASSERT(m_x.shape()[1] == m_nne);
- GOOSEFEM_ASSERT(m_x.shape()[2] == m_ndim);
+ GOOSEFEM_ASSERT(m_x.shape(1) == m_nne);
+ GOOSEFEM_ASSERT(m_x.shape(2) == m_ndim);
- m_nelem = m_x.shape()[0];
+ m_nelem = m_x.shape(0);
m_nip = m_w.size();
- GOOSEFEM_ASSERT(m_xi.shape()[0] == m_nip);
- GOOSEFEM_ASSERT(m_xi.shape()[1] == m_ndim);
+ GOOSEFEM_ASSERT(m_xi.shape(0) == m_nip);
+ GOOSEFEM_ASSERT(m_xi.shape(1) == m_ndim);
GOOSEFEM_ASSERT(m_w.size() == m_nip);
- m_N = xt::empty<double>({ m_nip, m_nne });
- m_dNxi = xt::empty<double>({ m_nip, m_nne, m_ndim});
- m_dNx = xt::empty<double>({m_nelem, m_nip, m_nne, m_ndim});
- m_vol = xt::empty<double>({m_nelem, m_nip });
+ m_N = xt::empty<double>({m_nip, m_nne});
+ m_dNxi = xt::empty<double>({m_nip, m_nne, m_ndim});
+ m_dNx = xt::empty<double>({m_nelem, m_nip, m_nne, m_ndim});
+ m_vol = xt::empty<double>({m_nelem, m_nip});
// shape functions
for (size_t q = 0 ; q < m_nip ; ++q)
{
m_N(q,0) = .125 * (1.-m_xi(q,0)) * (1.-m_xi(q,1)) * (1.-m_xi(q,2));
m_N(q,1) = .125 * (1.+m_xi(q,0)) * (1.-m_xi(q,1)) * (1.-m_xi(q,2));
m_N(q,2) = .125 * (1.+m_xi(q,0)) * (1.+m_xi(q,1)) * (1.-m_xi(q,2));
m_N(q,3) = .125 * (1.-m_xi(q,0)) * (1.+m_xi(q,1)) * (1.-m_xi(q,2));
m_N(q,4) = .125 * (1.-m_xi(q,0)) * (1.-m_xi(q,1)) * (1.+m_xi(q,2));
m_N(q,5) = .125 * (1.+m_xi(q,0)) * (1.-m_xi(q,1)) * (1.+m_xi(q,2));
m_N(q,6) = .125 * (1.+m_xi(q,0)) * (1.+m_xi(q,1)) * (1.+m_xi(q,2));
m_N(q,7) = .125 * (1.-m_xi(q,0)) * (1.+m_xi(q,1)) * (1.+m_xi(q,2));
}
// shape function gradients in local coordinates
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - dN / dxi_0
m_dNxi(q,0,0) = -.125*(1.-m_xi(q,1))*(1.-m_xi(q,2));
m_dNxi(q,1,0) = +.125*(1.-m_xi(q,1))*(1.-m_xi(q,2));
m_dNxi(q,2,0) = +.125*(1.+m_xi(q,1))*(1.-m_xi(q,2));
m_dNxi(q,3,0) = -.125*(1.+m_xi(q,1))*(1.-m_xi(q,2));
m_dNxi(q,4,0) = -.125*(1.-m_xi(q,1))*(1.+m_xi(q,2));
m_dNxi(q,5,0) = +.125*(1.-m_xi(q,1))*(1.+m_xi(q,2));
m_dNxi(q,6,0) = +.125*(1.+m_xi(q,1))*(1.+m_xi(q,2));
m_dNxi(q,7,0) = -.125*(1.+m_xi(q,1))*(1.+m_xi(q,2));
// - dN / dxi_1
m_dNxi(q,0,1) = -.125*(1.-m_xi(q,0))*(1.-m_xi(q,2));
m_dNxi(q,1,1) = -.125*(1.+m_xi(q,0))*(1.-m_xi(q,2));
m_dNxi(q,2,1) = +.125*(1.+m_xi(q,0))*(1.-m_xi(q,2));
m_dNxi(q,3,1) = +.125*(1.-m_xi(q,0))*(1.-m_xi(q,2));
m_dNxi(q,4,1) = -.125*(1.-m_xi(q,0))*(1.+m_xi(q,2));
m_dNxi(q,5,1) = -.125*(1.+m_xi(q,0))*(1.+m_xi(q,2));
m_dNxi(q,6,1) = +.125*(1.+m_xi(q,0))*(1.+m_xi(q,2));
m_dNxi(q,7,1) = +.125*(1.-m_xi(q,0))*(1.+m_xi(q,2));
// - dN / dxi_2
m_dNxi(q,0,2) = -.125*(1.-m_xi(q,0))*(1.-m_xi(q,1));
m_dNxi(q,1,2) = -.125*(1.+m_xi(q,0))*(1.-m_xi(q,1));
m_dNxi(q,2,2) = -.125*(1.+m_xi(q,0))*(1.+m_xi(q,1));
m_dNxi(q,3,2) = -.125*(1.-m_xi(q,0))*(1.+m_xi(q,1));
m_dNxi(q,4,2) = +.125*(1.-m_xi(q,0))*(1.-m_xi(q,1));
m_dNxi(q,5,2) = +.125*(1.+m_xi(q,0))*(1.-m_xi(q,1));
m_dNxi(q,6,2) = +.125*(1.+m_xi(q,0))*(1.+m_xi(q,1));
m_dNxi(q,7,2) = +.125*(1.-m_xi(q,0))*(1.+m_xi(q,1));
}
// compute the shape function gradients, based on "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::nip() const
{
return m_nip;
}
// -------------------------------------------------------------------------------------------------
-inline xt::xtensor<double,4> Quadrature::gradN() const
+inline xt::xtensor<double,4> Quadrature::GradN() const
{
return m_dNx;
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::dV(xt::xtensor<double,2>& qscalar) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
qscalar(e,q) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::dV(xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
qtensor(e,q,i,j) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::dV(xt::xarray<double>& qtensor) const
{
- GOOSEFEM_ASSERT(qtensor.shape()[0] == m_nelem);
- GOOSEFEM_ASSERT(qtensor.shape()[1] == m_nip);
+ GOOSEFEM_ASSERT(qtensor.shape(0) == m_nelem);
+ GOOSEFEM_ASSERT(qtensor.shape(1) == m_nip);
xt::dynamic_shape<ptrdiff_t> strides = {
static_cast<ptrdiff_t>(m_vol.strides()[0]),
static_cast<ptrdiff_t>(m_vol.strides()[1])};
for (size_t i = 2; i < qtensor.shape().size(); ++i)
strides.push_back(0);
qtensor = xt::strided_view(m_vol, qtensor.shape(), std::move(strides), 0ul, xt::layout_type::dynamic);
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::update_x(const xt::xtensor<double,3>& x)
{
GOOSEFEM_ASSERT(x.shape() == m_x.shape());
xt::noalias(m_x) = x;
// update the shape function gradients for the new "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::compute_dN()
{
#pragma omp parallel
{
// allocate local variables
xt::xtensor_fixed<double, xt::xshape<3,3>> J, Jinv;
// loop over all elements (in parallel)
#pragma omp for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias nodal positions
auto x = xt::adapt(&m_x(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over integration points
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNxi = xt::adapt(&m_dNxi( q,0,0), xt::xshape<m_nne,m_ndim>());
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne,m_ndim>());
// - zero-initialize
J.fill(0.0);
// - Jacobian
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
J(i,j) += dNxi(m,i) * x(m,j);
// - determinant and inverse of the Jacobian
double Jdet = inv(J, Jinv);
// - shape function gradients wrt global coordinates (loops partly unrolled for efficiency)
// dNx(m,i) += Jinv(i,j) * dNxi(m,j);
for (size_t m = 0 ; m < m_nne ; ++m)
{
dNx(m,0) = Jinv(0,0) * dNxi(m,0) + Jinv(0,1) * dNxi(m,1) + Jinv(0,2) * dNxi(m,2);
dNx(m,1) = Jinv(1,0) * dNxi(m,0) + Jinv(1,1) * dNxi(m,1) + Jinv(1,2) * dNxi(m,2);
dNx(m,2) = Jinv(2,0) * dNxi(m,0) + Jinv(2,1) * dNxi(m,1) + Jinv(2,2) * dNxi(m,2);
}
// - integration point volume
m_vol(e,q) = m_w(q) * Jdet;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::gradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
// zero-initialize
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
// - evaluate dyadic product
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
gradu(i,j) += dNx(m,i) * u(m,j);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
// zero-initialize
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
// - evaluate transpose of dyadic product
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
gradu(j,i) += dNx(m,i) * u(m,j);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
// zero-initialize
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto eps = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
// - evaluate symmetrized dyadic product
for (size_t m = 0 ; m < m_nne ; ++m ){
for (size_t i = 0 ; i < m_ndim ; ++i ){
for (size_t j = 0 ; j < m_ndim ; ++j ){
eps(i,j) += dNx(m,i) * u(m,j) / 2.;
eps(j,i) += dNx(m,i) * u(m,j) / 2.;
}
}
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize: matrix of matrices
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. mass matrix)
auto M = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto N = xt::adapt(&m_N(q,0), xt::xshape<m_nne>());
auto& vol = m_vol (e,q);
auto& rho = qscalar(e,q);
// - evaluate scalar product, for all dimensions, and assemble
// M(m*ndim+i,n*ndim+i) += N(m) * scalar * N(n) * dV
for (size_t m = 0 ; m < m_nne ; ++m ){
for (size_t n = 0 ; n < m_nne ; ++n ){
M(m*m_ndim+0, n*m_ndim+0) += N(m) * rho * N(n) * vol;
M(m*m_ndim+1, n*m_ndim+1) += N(m) * rho * N(n) * vol;
M(m*m_ndim+2, n*m_ndim+2) += N(m) * rho * N(n) * vol;
}
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
// zero-initialize output: matrix of vectors
elemvec.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto f = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto sig = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
auto& vol = m_vol(e,q);
// - evaluate dot product, and assemble
for (size_t m = 0 ; m < m_nne ; ++m)
{
f(m,0) += ( dNx(m,0) * sig(0,0) + dNx(m,1) * sig(1,0) + dNx(m,2) * sig(2,0) ) * vol;
f(m,1) += ( dNx(m,0) * sig(0,1) + dNx(m,1) * sig(1,1) + dNx(m,2) * sig(2,1) ) * vol;
f(m,2) += ( dNx(m,0) * sig(0,2) + dNx(m,1) * sig(1,2) + dNx(m,2) * sig(2,2) ) * vol;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim, m_ndim, m_ndim}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize output: matrix of vector
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto K = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx(e,q,0,0), xt::xshape<m_nne,m_ndim>());
auto C = xt::adapt(&qtensor(e,q,0,0,0,0), xt::xshape<m_ndim,m_ndim,m_ndim,m_ndim>());
auto& vol = m_vol(e,q);
// - evaluate dot product, and assemble
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t n = 0 ; n < m_nne ; ++n)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
for (size_t k = 0 ; k < m_ndim ; ++k)
for (size_t l = 0 ; l < m_ndim ; ++l)
K(m*m_ndim+j, n*m_ndim+k) += dNx(m,i) * C(i,j,k,l) * dNx(n,l) * vol;
}
}
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Quadrature::DV() const
{
xt::xtensor<double,2> out = xt::empty<double>({m_nelem, m_nip});
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xarray<double> Quadrature::DV(size_t rank) const
{
std::vector<size_t> shape = {m_nelem, m_nip};
for (size_t i = 0; i < rank; ++i)
shape.push_back(static_cast<size_t>(m_ndim));
xt::xarray<double> out = xt::empty<double>(shape);
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> Quadrature::GradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_ndim, m_ndim});
this->gradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> Quadrature::GradN_vector_T(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_ndim, m_ndim});
this->gradN_vector_T(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> Quadrature::SymGradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_ndim, m_ndim});
this->symGradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Quadrature::Int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_nne*m_ndim, m_nne*m_ndim});
this->int_N_scalar_NT_dV(qscalar, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Quadrature::Int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->int_gradN_dot_tensor2_dV(qtensor, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Quadrature::Int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_ndim*m_nne, m_ndim*m_nne});
this->int_gradN_dot_tensor4_dot_gradNT_dV(qtensor, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/ElementQuad4.h b/include/GooseFEM/ElementQuad4.h
index 057fb0c..b3fbbfb 100644
--- a/include/GooseFEM/ElementQuad4.h
+++ b/include/GooseFEM/ElementQuad4.h
@@ -1,198 +1,198 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTQUAD4_H
#define GOOSEFEM_ELEMENTQUAD4_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// -------------------------------------------------------------------------------------------------
inline double inv(
const xt::xtensor_fixed<double, xt::xshape<2,2>>& A,
xt::xtensor_fixed<double, xt::xshape<2,2>>& Ainv);
// -------------------------------------------------------------------------------------------------
namespace Gauss {
inline size_t nip(); // number of integration points
inline xt::xtensor<double,2> xi(); // integration point coordinates (local coordinates)
inline xt::xtensor<double,1> w(); // integration point weights
}
// -------------------------------------------------------------------------------------------------
namespace Nodal {
inline size_t nip(); // number of integration points
inline xt::xtensor<double,2> xi(); // integration point coordinates (local coordinates)
inline xt::xtensor<double,1> w(); // integration point weights
}
// -------------------------------------------------------------------------------------------------
namespace MidPoint {
inline size_t nip(); // number of integration points
inline xt::xtensor<double,2> xi(); // integration point coordinates (local coordinates)
inline xt::xtensor<double,1> w(); // integration point weights
}
// -------------------------------------------------------------------------------------------------
class Quadrature
{
public:
// Fixed dimensions:
// ndim = 2 - number of dimensions
// nne = 4 - number of nodes per element
//
// Naming convention:
// "elemmat" - matrices stored per element - [nelem, nne*ndim, nne*ndim]
// "elemvec" - nodal vectors stored per element - [nelem, nne, ndim]
// "qtensor" - integration point tensor - [nelem, nip, ndim, ndim]
// "qscalar" - integration point scalar - [nelem, nip]
// Constructor: integration point coordinates and weights are optional (default: Gauss)
Quadrature() = default;
Quadrature(
const xt::xtensor<double,3>& x);
Quadrature(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w);
// Update the nodal positions (shape of "x" should match the earlier definition)
void update_x(const xt::xtensor<double,3>& x);
// Return dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t ndim() const; // number of dimension
size_t nip() const; // number of integration points
// Return shape function gradients
- xt::xtensor<double,4> gradN() const;
+ xt::xtensor<double,4> GradN() const;
// Return integration volume
void dV(xt::xtensor<double,2>& qscalar) const;
void dV(xt::xtensor<double,4>& qtensor) const; // same volume for all tensor components
void dV(xt::xarray<double>& qtensor) const; // same volume for all tensor components
// Dyadic product (and its transpose and symmetric part)
// qtensor(i,j) += dNdx(m,i) * elemvec(m,j)
void gradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
void gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
void symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
// Integral of the scalar product
// elemmat(m*ndim+i,n*ndim+i) += N(m) * qscalar * N(n) * dV
void int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar,
xt::xtensor<double,3>& elemmat) const; // overwritten
// Integral of the dot product
// elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV
void int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor,
xt::xtensor<double,3>& elemvec) const; // overwritten
// Integral of the dot product
// elemmat(m*2+j, n*2+k) += dNdx(m,i) * qtensor(i,j,k,l) * dNdx(n,l) * dV
void int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor,
xt::xtensor<double,3>& elemmat) const; // overwritten
// Auto-allocation of the functions above
xt::xtensor<double,2> DV() const;
xt::xarray<double> DV(
size_t rank) const;
xt::xtensor<double,4> GradN_vector(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,4> GradN_vector_T(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,4> SymGradN_vector(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,3> Int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar) const;
xt::xtensor<double,3> Int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor) const;
xt::xtensor<double,3> Int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor) const;
private:
// Compute "vol" and "dNdx" based on current "x"
void compute_dN();
private:
// Dimensions (flexible)
size_t m_nelem; // number of elements
size_t m_nip; // number of integration points
// Dimensions (fixed for this element type)
static const size_t m_nne=4; // number of nodes per element
static const size_t m_ndim=2; // number of dimensions
// Data arrays
xt::xtensor<double,3> m_x; // nodal positions stored per element [nelem, nne, ndim]
xt::xtensor<double,1> m_w; // weight of each integration point [nip]
xt::xtensor<double,2> m_xi; // local coordinate of each integration point [nip, ndim]
xt::xtensor<double,2> m_N; // shape functions [nip, nne]
xt::xtensor<double,3> m_dNxi; // shape function grad. w.r.t. local coor. [nip, nne, ndim]
xt::xtensor<double,4> m_dNx; // shape function grad. w.r.t. global coor. [nelem, nip, nne, ndim]
xt::xtensor<double,2> m_vol; // integration point volume [nelem, nip]
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#include "ElementQuad4.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/ElementQuad4.hpp b/include/GooseFEM/ElementQuad4.hpp
index ab35199..6b1225e 100644
--- a/include/GooseFEM/ElementQuad4.hpp
+++ b/include/GooseFEM/ElementQuad4.hpp
@@ -1,692 +1,692 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTQUAD4_HPP
#define GOOSEFEM_ELEMENTQUAD4_HPP
// -------------------------------------------------------------------------------------------------
#include "ElementQuad4.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// =================================================================================================
inline double inv(
const xt::xtensor_fixed<double, xt::xshape<2,2>>& A,
xt::xtensor_fixed<double, xt::xshape<2,2>>& Ainv)
{
// compute determinant
double det = A(0,0) * A(1,1) - A(0,1) * A(1,0);
// compute inverse
Ainv(0,0) = A(1,1) / det;
Ainv(0,1) = -1. * A(0,1) / det;
Ainv(1,0) = -1. * A(1,0) / det;
Ainv(1,1) = A(0,0) / det;
return det;
}
// =================================================================================================
namespace Gauss {
// -------------------------------------------------------------------------------------------------
inline size_t nip()
{
return 4;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> xi()
{
size_t nip = 4;
size_t ndim = 2;
xt::xtensor<double,2> xi = xt::empty<double>({nip,ndim});
xi(0,0) = -1./std::sqrt(3.); xi(0,1) = -1./std::sqrt(3.);
xi(1,0) = +1./std::sqrt(3.); xi(1,1) = -1./std::sqrt(3.);
xi(2,0) = +1./std::sqrt(3.); xi(2,1) = +1./std::sqrt(3.);
xi(3,0) = -1./std::sqrt(3.); xi(3,1) = +1./std::sqrt(3.);
return xi;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> w()
{
size_t nip = 4;
xt::xtensor<double,1> w = xt::empty<double>({nip});
w(0) = 1.;
w(1) = 1.;
w(2) = 1.;
w(3) = 1.;
return w;
}
// -------------------------------------------------------------------------------------------------
}
// =================================================================================================
namespace Nodal {
// -------------------------------------------------------------------------------------------------
inline size_t nip()
{
return 4;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> xi()
{
size_t nip = 4;
size_t ndim = 2;
xt::xtensor<double,2> xi = xt::empty<double>({nip,ndim});
xi(0,0) = -1.; xi(0,1) = -1.;
xi(1,0) = +1.; xi(1,1) = -1.;
xi(2,0) = +1.; xi(2,1) = +1.;
xi(3,0) = -1.; xi(3,1) = +1.;
return xi;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> w()
{
size_t nip = 4;
xt::xtensor<double,1> w = xt::empty<double>({nip});
w(0) = 1.;
w(1) = 1.;
w(2) = 1.;
w(3) = 1.;
return w;
}
// -------------------------------------------------------------------------------------------------
}
// =================================================================================================
namespace MidPoint {
// -------------------------------------------------------------------------------------------------
inline size_t nip()
{
return 1;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> xi()
{
size_t nip = 1;
size_t ndim = 2;
xt::xtensor<double,2> xi = xt::empty<double>({nip,ndim});
xi(0,0) = 0.; xi(0,1) = 0.;
return xi;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> w()
{
size_t nip = 1;
xt::xtensor<double,1> w = xt::empty<double>({nip});
w(0) = 1.;
return w;
}
// -------------------------------------------------------------------------------------------------
}
// =================================================================================================
inline Quadrature::Quadrature(const xt::xtensor<double,3>& x) :
Quadrature(x, Gauss::xi(), Gauss::w()) {}
// -------------------------------------------------------------------------------------------------
inline Quadrature::Quadrature(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w) :
m_x(x), m_w(w), m_xi(xi)
{
- GOOSEFEM_ASSERT(m_x.shape()[1] == m_nne);
- GOOSEFEM_ASSERT(m_x.shape()[2] == m_ndim);
+ GOOSEFEM_ASSERT(m_x.shape(1) == m_nne);
+ GOOSEFEM_ASSERT(m_x.shape(2) == m_ndim);
- m_nelem = m_x.shape()[0];
+ m_nelem = m_x.shape(0);
m_nip = m_w.size();
- GOOSEFEM_ASSERT(m_xi.shape()[0] == m_nip);
- GOOSEFEM_ASSERT(m_xi.shape()[1] == m_ndim);
+ GOOSEFEM_ASSERT(m_xi.shape(0) == m_nip);
+ GOOSEFEM_ASSERT(m_xi.shape(1) == m_ndim);
GOOSEFEM_ASSERT(m_w.size() == m_nip);
- m_N = xt::empty<double>({ m_nip, m_nne });
- m_dNxi = xt::empty<double>({ m_nip, m_nne, m_ndim});
- m_dNx = xt::empty<double>({m_nelem, m_nip, m_nne, m_ndim});
- m_vol = xt::empty<double>({m_nelem, m_nip });
+ m_N = xt::empty<double>({m_nip, m_nne});
+ m_dNxi = xt::empty<double>({m_nip, m_nne, m_ndim});
+ m_dNx = xt::empty<double>({m_nelem, m_nip, m_nne, m_ndim});
+ m_vol = xt::empty<double>({m_nelem, m_nip});
// shape functions
for (size_t q = 0 ; q < m_nip ; ++q)
{
m_N(q,0) = .25 * (1.-m_xi(q,0)) * (1.-m_xi(q,1));
m_N(q,1) = .25 * (1.+m_xi(q,0)) * (1.-m_xi(q,1));
m_N(q,2) = .25 * (1.+m_xi(q,0)) * (1.+m_xi(q,1));
m_N(q,3) = .25 * (1.-m_xi(q,0)) * (1.+m_xi(q,1));
}
// shape function gradients in local coordinates
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - dN / dxi_0
m_dNxi(q,0,0) = -.25*(1.-m_xi(q,1));
m_dNxi(q,1,0) = +.25*(1.-m_xi(q,1));
m_dNxi(q,2,0) = +.25*(1.+m_xi(q,1));
m_dNxi(q,3,0) = -.25*(1.+m_xi(q,1));
// - dN / dxi_1
m_dNxi(q,0,1) = -.25*(1.-m_xi(q,0));
m_dNxi(q,1,1) = -.25*(1.+m_xi(q,0));
m_dNxi(q,2,1) = +.25*(1.+m_xi(q,0));
m_dNxi(q,3,1) = +.25*(1.-m_xi(q,0));
}
// compute the shape function gradients, based on "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t Quadrature::nip() const
{
return m_nip;
}
// -------------------------------------------------------------------------------------------------
-inline xt::xtensor<double,4> Quadrature::gradN() const
+inline xt::xtensor<double,4> Quadrature::GradN() const
{
return m_dNx;
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::dV(xt::xtensor<double,2>& qscalar) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
qscalar(e,q) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::dV(xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
qtensor(e,q,i,j) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::dV(xt::xarray<double>& qtensor) const
{
- GOOSEFEM_ASSERT(qtensor.shape()[0] == m_nelem);
- GOOSEFEM_ASSERT(qtensor.shape()[1] == m_nip);
+ GOOSEFEM_ASSERT(qtensor.shape(0) == m_nelem);
+ GOOSEFEM_ASSERT(qtensor.shape(1) == m_nip);
xt::dynamic_shape<ptrdiff_t> strides = {
static_cast<ptrdiff_t>(m_vol.strides()[0]),
static_cast<ptrdiff_t>(m_vol.strides()[1])};
for (size_t i = 2; i < qtensor.shape().size(); ++i)
strides.push_back(0);
qtensor = xt::strided_view(m_vol, qtensor.shape(), std::move(strides), 0ul, xt::layout_type::dynamic);
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::update_x(const xt::xtensor<double,3>& x)
{
GOOSEFEM_ASSERT(x.shape() == m_x.shape());
xt::noalias(m_x) = x;
// update the shape function gradients for the new "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::compute_dN()
{
#pragma omp parallel
{
// allocate local variables
xt::xtensor_fixed<double, xt::xshape<2,2>> J, Jinv;
// loop over all elements (in parallel)
#pragma omp for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias nodal positions
auto x = xt::adapt(&m_x(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over integration points
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNxi = xt::adapt(&m_dNxi( q,0,0), xt::xshape<m_nne,m_ndim>());
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne,m_ndim>());
// - Jacobian (loops unrolled for efficiency)
// J(i,j) += dNxi(m,i) * x(m,j);
J(0,0) = dNxi(0,0)*x(0,0) + dNxi(1,0)*x(1,0) + dNxi(2,0)*x(2,0) + dNxi(3,0)*x(3,0);
J(0,1) = dNxi(0,0)*x(0,1) + dNxi(1,0)*x(1,1) + dNxi(2,0)*x(2,1) + dNxi(3,0)*x(3,1);
J(1,0) = dNxi(0,1)*x(0,0) + dNxi(1,1)*x(1,0) + dNxi(2,1)*x(2,0) + dNxi(3,1)*x(3,0);
J(1,1) = dNxi(0,1)*x(0,1) + dNxi(1,1)*x(1,1) + dNxi(2,1)*x(2,1) + dNxi(3,1)*x(3,1);
// - determinant and inverse of the Jacobian
double Jdet = inv(J, Jinv);
// - shape function gradients wrt global coordinates (loops partly unrolled for efficiency)
// dNx(m,i) += Jinv(i,j) * dNxi(m,j);
for (size_t m = 0 ; m < m_nne ; ++m)
{
dNx(m,0) = Jinv(0,0) * dNxi(m,0) + Jinv(0,1) * dNxi(m,1);
dNx(m,1) = Jinv(1,0) * dNxi(m,0) + Jinv(1,1) * dNxi(m,1);
}
// - integration point volume
m_vol(e,q) = m_w(q) * Jdet;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::gradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
// - evaluate dyadic product (loops unrolled for efficiency)
// gradu(i,j) += dNx(m,i) * u(m,j)
gradu(0,0) = dNx(0,0)*u(0,0) + dNx(1,0)*u(1,0) + dNx(2,0)*u(2,0) + dNx(3,0)*u(3,0);
gradu(0,1) = dNx(0,0)*u(0,1) + dNx(1,0)*u(1,1) + dNx(2,0)*u(2,1) + dNx(3,0)*u(3,1);
gradu(1,0) = dNx(0,1)*u(0,0) + dNx(1,1)*u(1,0) + dNx(2,1)*u(2,0) + dNx(3,1)*u(3,0);
gradu(1,1) = dNx(0,1)*u(0,1) + dNx(1,1)*u(1,1) + dNx(2,1)*u(2,1) + dNx(3,1)*u(3,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
// - evaluate transpose of dyadic product (loops unrolled for efficiency)
// gradu(j,i) += dNx(m,i) * u(m,j)
gradu(0,0) = dNx(0,0)*u(0,0) + dNx(1,0)*u(1,0) + dNx(2,0)*u(2,0) + dNx(3,0)*u(3,0);
gradu(1,0) = dNx(0,0)*u(0,1) + dNx(1,0)*u(1,1) + dNx(2,0)*u(2,1) + dNx(3,0)*u(3,1);
gradu(0,1) = dNx(0,1)*u(0,0) + dNx(1,1)*u(1,0) + dNx(2,1)*u(2,0) + dNx(3,1)*u(3,0);
gradu(1,1) = dNx(0,1)*u(0,1) + dNx(1,1)*u(1,1) + dNx(2,1)*u(2,1) + dNx(3,1)*u(3,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto eps = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
// - evaluate symmetrized dyadic product (loops unrolled for efficiency)
// gradu(i,j) += dNx(m,i) * u(m,j)
// eps (j,i) = 0.5 * ( gradu(i,j) + gradu(j,i) )
eps(0,0) = dNx(0,0)*u(0,0) + dNx(1,0)*u(1,0) + dNx(2,0)*u(2,0) + dNx(3,0)*u(3,0);
eps(1,1) = dNx(0,1)*u(0,1) + dNx(1,1)*u(1,1) + dNx(2,1)*u(2,1) + dNx(3,1)*u(3,1);
eps(0,1) = ( dNx(0,0)*u(0,1) + dNx(1,0)*u(1,1) + dNx(2,0)*u(2,1) + dNx(3,0)*u(3,1) +
dNx(0,1)*u(0,0) + dNx(1,1)*u(1,0) + dNx(2,1)*u(2,0) + dNx(3,1)*u(3,0) ) * 0.5;
eps(1,0) = eps(0,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize: matrix of matrices
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. mass matrix)
auto M = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto N = xt::adapt(&m_N(q,0), xt::xshape<m_nne>());
auto& vol = m_vol (e,q);
auto& rho = qscalar(e,q);
// - evaluate scalar product, for all dimensions, and assemble
// M(m*ndim+i,n*ndim+i) += N(m) * scalar * N(n) * dV
for (size_t m = 0 ; m < m_nne ; ++m ){
for (size_t n = 0 ; n < m_nne ; ++n ){
M(m*m_ndim+0, n*m_ndim+0) += N(m) * rho * N(n) * vol;
M(m*m_ndim+1, n*m_ndim+1) += N(m) * rho * N(n) * vol;
}
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim}));
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
// zero-initialize output: matrix of vectors
elemvec.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto f = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto sig = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_ndim,m_ndim>());
auto& vol = m_vol(e,q);
// - evaluate dot product, and assemble
for (size_t m = 0 ; m < m_nne ; ++m)
{
f(m,0) += ( dNx(m,0) * sig(0,0) + dNx(m,1) * sig(1,0) ) * vol;
f(m,1) += ( dNx(m,0) * sig(0,1) + dNx(m,1) * sig(1,1) ) * vol;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void Quadrature::int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_ndim, m_ndim, m_ndim, m_ndim}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize output: matrix of vector
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto K = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx(e,q,0,0), xt::xshape<m_nne,m_ndim>());
auto C = xt::adapt(&qtensor(e,q,0,0,0,0), xt::xshape<m_ndim,m_ndim,m_ndim,m_ndim>());
auto& vol = m_vol(e,q);
// - evaluate dot product, and assemble
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t n = 0 ; n < m_nne ; ++n)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
for (size_t k = 0 ; k < m_ndim ; ++k)
for (size_t l = 0 ; l < m_ndim ; ++l)
K(m*m_ndim+j, n*m_ndim+k) += dNx(m,i) * C(i,j,k,l) * dNx(n,l) * vol;
}
}
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Quadrature::DV() const
{
xt::xtensor<double,2> out = xt::empty<double>({m_nelem, m_nip});
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xarray<double> Quadrature::DV(size_t rank) const
{
std::vector<size_t> shape = {m_nelem, m_nip};
for (size_t i = 0; i < rank; ++i)
shape.push_back(static_cast<size_t>(m_ndim));
xt::xarray<double> out = xt::empty<double>(shape);
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> Quadrature::GradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_ndim, m_ndim});
this->gradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> Quadrature::GradN_vector_T(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_ndim, m_ndim});
this->gradN_vector_T(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> Quadrature::SymGradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_ndim, m_ndim});
this->symGradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Quadrature::Int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_nne*m_ndim, m_nne*m_ndim});
this->int_N_scalar_NT_dV(qscalar, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Quadrature::Int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->int_gradN_dot_tensor2_dV(qtensor, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Quadrature::Int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_ndim*m_nne, m_ndim*m_nne});
this->int_gradN_dot_tensor4_dot_gradNT_dV(qtensor, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/ElementQuad4Axisymmetric.hpp b/include/GooseFEM/ElementQuad4Axisymmetric.hpp
index 2bbcd8c..3e97c3e 100644
--- a/include/GooseFEM/ElementQuad4Axisymmetric.hpp
+++ b/include/GooseFEM/ElementQuad4Axisymmetric.hpp
@@ -1,583 +1,583 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTQUADAXISYMMETRIC_HPP
#define GOOSEFEM_ELEMENTQUADAXISYMMETRIC_HPP
// -------------------------------------------------------------------------------------------------
#include "ElementQuad4Axisymmetric.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// =================================================================================================
inline QuadratureAxisymmetric::QuadratureAxisymmetric(const xt::xtensor<double,3>& x) :
QuadratureAxisymmetric(x, Gauss::xi(), Gauss::w()) {}
// -------------------------------------------------------------------------------------------------
inline QuadratureAxisymmetric::QuadratureAxisymmetric(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w) :
m_x(x), m_w(w), m_xi(xi)
{
- GOOSEFEM_ASSERT(m_x.shape()[1] == m_nne);
- GOOSEFEM_ASSERT(m_x.shape()[2] == m_ndim);
+ GOOSEFEM_ASSERT(m_x.shape(1) == m_nne);
+ GOOSEFEM_ASSERT(m_x.shape(2) == m_ndim);
- m_nelem = m_x.shape()[0];
- m_nip = m_w.size();
+ m_nelem = m_x.shape(0);
+ m_nip = m_w.size();
- GOOSEFEM_ASSERT(m_xi.shape()[0] == m_nip);
- GOOSEFEM_ASSERT(m_xi.shape()[1] == m_ndim);
+ GOOSEFEM_ASSERT(m_xi.shape(0) == m_nip);
+ GOOSEFEM_ASSERT(m_xi.shape(1) == m_ndim);
GOOSEFEM_ASSERT(m_w.size() == m_nip);
- m_N = xt::empty<double>({ m_nip, m_nne });
- m_dNxi = xt::empty<double>({ m_nip, m_nne, m_ndim });
- m_B = xt::empty<double>({m_nelem, m_nip, m_nne, m_tdim, m_tdim, m_tdim});
- m_vol = xt::empty<double>({m_nelem, m_nip });
+ m_N = xt::empty<double>({m_nip, m_nne});
+ m_dNxi = xt::empty<double>({m_nip, m_nne, m_ndim});
+ m_B = xt::empty<double>({m_nelem, m_nip, m_nne, m_tdim, m_tdim, m_tdim});
+ m_vol = xt::empty<double>({m_nelem, m_nip});
// shape functions
for (size_t q = 0 ; q < m_nip ; ++q)
{
m_N(q,0) = .25 * (1.-m_xi(q,0)) * (1.-m_xi(q,1));
m_N(q,1) = .25 * (1.+m_xi(q,0)) * (1.-m_xi(q,1));
m_N(q,2) = .25 * (1.+m_xi(q,0)) * (1.+m_xi(q,1));
m_N(q,3) = .25 * (1.-m_xi(q,0)) * (1.+m_xi(q,1));
}
// shape function gradients in local coordinates
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - dN / dxi_0
m_dNxi(q,0,0) = -.25*(1.-m_xi(q,1));
m_dNxi(q,1,0) = +.25*(1.-m_xi(q,1));
m_dNxi(q,2,0) = +.25*(1.+m_xi(q,1));
m_dNxi(q,3,0) = -.25*(1.+m_xi(q,1));
// - dN / dxi_1
m_dNxi(q,0,1) = -.25*(1.-m_xi(q,0));
m_dNxi(q,1,1) = -.25*(1.+m_xi(q,0));
m_dNxi(q,2,1) = +.25*(1.+m_xi(q,0));
m_dNxi(q,3,1) = +.25*(1.-m_xi(q,0));
}
// compute the shape function gradients, based on "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadratureAxisymmetric::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadratureAxisymmetric::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadratureAxisymmetric::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadratureAxisymmetric::nip() const
{
return m_nip;
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::dV(xt::xtensor<double,2>& qscalar) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
qscalar(e,q) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::dV(xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
for (size_t i = 0 ; i < m_tdim ; ++i)
for (size_t j = 0 ; j < m_tdim ; ++j)
qtensor(e,q,i,j) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::dV(xt::xarray<double>& qtensor) const
{
- GOOSEFEM_ASSERT(qtensor.shape()[0] == m_nelem);
- GOOSEFEM_ASSERT(qtensor.shape()[1] == m_nip);
+ GOOSEFEM_ASSERT(qtensor.shape(0) == m_nelem);
+ GOOSEFEM_ASSERT(qtensor.shape(1) == m_nip);
xt::dynamic_shape<ptrdiff_t> strides = {
static_cast<ptrdiff_t>(m_vol.strides()[0]),
static_cast<ptrdiff_t>(m_vol.strides()[1])};
for (size_t i = 2; i < qtensor.shape().size(); ++i)
strides.push_back(0);
qtensor = xt::strided_view(m_vol, qtensor.shape(), std::move(strides), 0ul, xt::layout_type::dynamic);
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::update_x(const xt::xtensor<double,3>& x)
{
GOOSEFEM_ASSERT(x.shape() == m_x.shape());
xt::noalias(m_x) = x;
// update the shape function gradients for the new "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::compute_dN()
{
// zero-initialize full B-matrix (most component remain zero, and are not written)
m_B.fill(0.0);
#pragma omp parallel
{
// allocate local variables
xt::xtensor_fixed<double, xt::xshape<2,2>> J, Jinv;
// loop over all elements (in parallel)
#pragma omp for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias nodal positions
auto x = xt::adapt(&m_x(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over integration points
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNxi = xt::adapt(&m_dNxi( q,0,0 ), xt::xshape<m_nne,m_ndim>());
auto B = xt::adapt(&m_B (e,q,0,0,0,0), xt::xshape<m_nne,m_tdim,m_tdim,m_tdim>());
auto N = xt::adapt(&m_N ( q,0 ), xt::xshape<m_nne>());
// - Jacobian (loops unrolled for efficiency)
// J(i,j) += dNxi(m,i) * x(m,j);
J(0,0) = dNxi(0,0)*x(0,0) + dNxi(1,0)*x(1,0) + dNxi(2,0)*x(2,0) + dNxi(3,0)*x(3,0);
J(0,1) = dNxi(0,0)*x(0,1) + dNxi(1,0)*x(1,1) + dNxi(2,0)*x(2,1) + dNxi(3,0)*x(3,1);
J(1,0) = dNxi(0,1)*x(0,0) + dNxi(1,1)*x(1,0) + dNxi(2,1)*x(2,0) + dNxi(3,1)*x(3,0);
J(1,1) = dNxi(0,1)*x(0,1) + dNxi(1,1)*x(1,1) + dNxi(2,1)*x(2,1) + dNxi(3,1)*x(3,1);
// - determinant and inverse of the Jacobian
double Jdet = inv(J, Jinv);
// - get radius for computation of volume
double rq = N(0)*x(0,1) + N(1)*x(1,1) + N(2)*x(2,1) + N(3)*x(3,1);
// - compute the B matrix (loops partly unrolled for efficiency)
// N.B. "dNx(m,i) += Jinv(i,j) * dNxi(m,j);"
for (size_t m = 0; m < m_nne; ++m)
{
B(m,0,0,0) = Jinv(1,0) * dNxi(m,0) + Jinv(1,1) * dNxi(m,1); // B(m, r, r, r) = dNdx(m,1)
B(m,0,2,2) = Jinv(1,0) * dNxi(m,0) + Jinv(1,1) * dNxi(m,1); // B(m, r, z, z) = dNdx(m,1)
B(m,1,1,0) = 1./rq * N(m); // B(m, t, t, r)
B(m,2,0,0) = Jinv(0,0) * dNxi(m,0) + Jinv(0,1) * dNxi(m,1); // B(m, z, r, r) = dNdx(m,0)
B(m,2,2,2) = Jinv(0,0) * dNxi(m,0) + Jinv(0,1) * dNxi(m,1); // B(m, z, z, z) = dNdx(m,0)
}
// - integration point volume
m_vol(e, q) = m_w(q) * Jdet * 2. * M_PI * rq;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::gradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
// zero-initialize (zero components not written below)
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto B = xt::adapt(&m_B (e,q,0,0,0,0), xt::xshape<m_nne,m_tdim,m_tdim,m_tdim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0 ), xt::xshape<m_tdim,m_tdim>());
// - evaluate dyadic product (loops unrolled for efficiency)
// gradu(i,j) += B(m,i,j,k) * u(m,perm(k))
// (where perm(0) = 1, perm(2) = 0)
gradu(0,0) = B(0,0,0,0)*u(0,1) + B(1,0,0,0)*u(1,1) + B(2,0,0,0)*u(2,1) + B(3,0,0,0)*u(3,1);
gradu(1,1) = B(0,1,1,0)*u(0,1) + B(1,1,1,0)*u(1,1) + B(2,1,1,0)*u(2,1) + B(3,1,1,0)*u(3,1);
gradu(2,2) = B(0,2,2,2)*u(0,0) + B(1,2,2,2)*u(1,0) + B(2,2,2,2)*u(2,0) + B(3,2,2,2)*u(3,0);
gradu(0,2) = B(0,0,2,2)*u(0,0) + B(1,0,2,2)*u(1,0) + B(2,0,2,2)*u(2,0) + B(3,0,2,2)*u(3,0);
gradu(2,0) = B(0,2,0,0)*u(0,1) + B(1,2,0,0)*u(1,1) + B(2,2,0,0)*u(2,1) + B(3,2,0,0)*u(3,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
// zero-initialize (zero components not written below)
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto B = xt::adapt(&m_B (e,q,0,0,0,0), xt::xshape<m_nne,m_tdim,m_tdim,m_tdim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0 ), xt::xshape<m_tdim,m_tdim>());
// - evaluate transpose of dyadic product (loops unrolled for efficiency)
// gradu(j,i) += B(m,i,j,k) * u(m,perm(k))
// (where perm(0) = 1, perm(2) = 0)
gradu(0,0) = B(0,0,0,0)*u(0,1) + B(1,0,0,0)*u(1,1) + B(2,0,0,0)*u(2,1) + B(3,0,0,0)*u(3,1);
gradu(1,1) = B(0,1,1,0)*u(0,1) + B(1,1,1,0)*u(1,1) + B(2,1,1,0)*u(2,1) + B(3,1,1,0)*u(3,1);
gradu(2,2) = B(0,2,2,2)*u(0,0) + B(1,2,2,2)*u(1,0) + B(2,2,2,2)*u(2,0) + B(3,2,2,2)*u(3,0);
gradu(2,0) = B(0,0,2,2)*u(0,0) + B(1,0,2,2)*u(1,0) + B(2,0,2,2)*u(2,0) + B(3,0,2,2)*u(3,0);
gradu(0,2) = B(0,2,0,0)*u(0,1) + B(1,2,0,0)*u(1,1) + B(2,2,0,0)*u(2,1) + B(3,2,0,0)*u(3,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
// zero-initialize (zero components not written below)
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto B = xt::adapt(&m_B (e,q,0,0,0,0), xt::xshape<m_nne,m_tdim,m_tdim,m_tdim>());
auto eps = xt::adapt(&qtensor(e,q,0,0 ), xt::xshape<m_tdim,m_tdim>());
// - evaluate symmetrized dyadic product (loops unrolled for efficiency)
// gradu(j,i) += B(m,i,j,k) * u(m,perm(k))
// eps (j,i) = 0.5 * ( gradu(i,j) + gradu(j,i) )
// (where perm(0) = 1, perm(2) = 0)
eps(0,0) = B(0,0,0,0)*u(0,1) + B(1,0,0,0)*u(1,1) + B(2,0,0,0)*u(2,1) + B(3,0,0,0)*u(3,1);
eps(1,1) = B(0,1,1,0)*u(0,1) + B(1,1,1,0)*u(1,1) + B(2,1,1,0)*u(2,1) + B(3,1,1,0)*u(3,1);
eps(2,2) = B(0,2,2,2)*u(0,0) + B(1,2,2,2)*u(1,0) + B(2,2,2,2)*u(2,0) + B(3,2,2,2)*u(3,0);
eps(2,0) = ( B(0,0,2,2)*u(0,0) + B(1,0,2,2)*u(1,0) + B(2,0,2,2)*u(2,0) + B(3,0,2,2)*u(3,0) +
B(0,2,0,0)*u(0,1) + B(1,2,0,0)*u(1,1) + B(2,2,0,0)*u(2,1) + B(3,2,0,0)*u(3,1) ) * 0.5;
eps(0,2) = eps(2,0);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize: matrix of matrices
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. mass matrix)
auto M = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto N = xt::adapt(&m_N(q,0), xt::xshape<m_nne>());
auto& vol = m_vol (e,q);
auto& rho = qscalar(e,q);
// - evaluate scalar product, for all dimensions, and assemble
// M(m*ndim+i,n*ndim+i) += N(m) * scalar * N(n) * dV
for (size_t m = 0 ; m < m_nne ; ++m ){
for (size_t n = 0 ; n < m_nne ; ++n ){
M(m*m_ndim+0, n*m_ndim+0) += N(m) * rho * N(n) * vol;
M(m*m_ndim+1, n*m_ndim+1) += N(m) * rho * N(n) * vol;
}
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
// zero-initialize output: matrix of vectors
elemvec.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto f = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto B = xt::adapt(&m_B(e,q,0,0,0,0), xt::xshape<m_nne,m_tdim,m_tdim,m_tdim>());
auto sig = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_tdim,m_tdim>());
auto& vol = m_vol(e,q);
// - evaluate dot product, and assemble
// f(m,i) += B(m,i,j,perm(k)) * sig(i,j) * dV
// (where perm(0) = 1, perm(2) = 0)
for (size_t m = 0 ; m < m_nne ; ++m)
{
f(m,0) += ( B(m,2,2,2)*sig(2,2) + B(m,0,2,2)*sig(0,2) ) * vol;
f(m,1) += ( B(m,0,0,0)*sig(0,0) + B(m,1,1,0)*sig(1,1) + B(m,2,0,0)*sig(2,0) ) * vol;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadratureAxisymmetric::int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim, m_tdim, m_tdim}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize output: matrix of vector
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto K = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto B = xt::adapt(&m_B(e,q,0,0,0,0), xt::xshape<m_nne,m_tdim,m_tdim,m_tdim>());
auto C = xt::adapt(&qtensor(e,q,0,0,0,0), xt::xshape<m_tdim,m_tdim,m_tdim,m_tdim>());
auto& vol = m_vol(e,q);
// - compute product:
// K(m*m_ndim+perm(c), n*m_ndim+perm(f)) = B(m,a,b,c) * C(a,b,d,e) * B(n,e,d,f) * vol;
// (where perm(0) = 1, perm(2) = 0)
for (size_t m = 0 ; m < m_nne ; ++m)
{
for (size_t n = 0 ; n < m_nne ; ++n)
{
K(m*m_ndim+1, n*m_ndim+1) += B(m,0,0,0) * C(0,0,0,0) * B(n,0,0,0) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,0,0,0) * C(0,0,1,1) * B(n,1,1,0) * vol;
K(m*m_ndim+1, n*m_ndim+0) += B(m,0,0,0) * C(0,0,2,2) * B(n,2,2,2) * vol;
K(m*m_ndim+1, n*m_ndim+0) += B(m,0,0,0) * C(0,0,2,0) * B(n,0,2,2) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,0,0,0) * C(0,0,0,2) * B(n,2,0,0) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,1,1,0) * C(1,1,0,0) * B(n,0,0,0) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,1,1,0) * C(1,1,1,1) * B(n,1,1,0) * vol;
K(m*m_ndim+1, n*m_ndim+0) += B(m,1,1,0) * C(1,1,2,2) * B(n,2,2,2) * vol;
K(m*m_ndim+1, n*m_ndim+0) += B(m,1,1,0) * C(1,1,2,0) * B(n,0,2,2) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,1,1,0) * C(1,1,0,2) * B(n,2,0,0) * vol;
K(m*m_ndim+0, n*m_ndim+1) += B(m,2,2,2) * C(2,2,0,0) * B(n,0,0,0) * vol;
K(m*m_ndim+0, n*m_ndim+1) += B(m,2,2,2) * C(2,2,1,1) * B(n,1,1,0) * vol;
K(m*m_ndim+0, n*m_ndim+0) += B(m,2,2,2) * C(2,2,2,2) * B(n,2,2,2) * vol;
K(m*m_ndim+0, n*m_ndim+0) += B(m,2,2,2) * C(2,2,2,0) * B(n,0,2,2) * vol;
K(m*m_ndim+0, n*m_ndim+1) += B(m,2,2,2) * C(2,2,0,2) * B(n,2,0,0) * vol;
K(m*m_ndim+0, n*m_ndim+1) += B(m,0,2,2) * C(0,2,0,0) * B(n,0,0,0) * vol;
K(m*m_ndim+0, n*m_ndim+1) += B(m,0,2,2) * C(0,2,1,1) * B(n,1,1,0) * vol;
K(m*m_ndim+0, n*m_ndim+0) += B(m,0,2,2) * C(0,2,2,2) * B(n,2,2,2) * vol;
K(m*m_ndim+0, n*m_ndim+0) += B(m,0,2,2) * C(0,2,2,0) * B(n,0,2,2) * vol;
K(m*m_ndim+0, n*m_ndim+1) += B(m,0,2,2) * C(0,2,0,2) * B(n,2,0,0) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,2,0,0) * C(2,0,0,0) * B(n,0,0,0) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,2,0,0) * C(2,0,1,1) * B(n,1,1,0) * vol;
K(m*m_ndim+1, n*m_ndim+0) += B(m,2,0,0) * C(2,0,2,2) * B(n,2,2,2) * vol;
K(m*m_ndim+1, n*m_ndim+0) += B(m,2,0,0) * C(2,0,2,0) * B(n,0,2,2) * vol;
K(m*m_ndim+1, n*m_ndim+1) += B(m,2,0,0) * C(2,0,0,2) * B(n,2,0,0) * vol;
}
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> QuadratureAxisymmetric::DV() const
{
xt::xtensor<double,2> out = xt::empty<double>({m_nelem, m_nip});
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xarray<double> QuadratureAxisymmetric::DV(size_t rank) const
{
std::vector<size_t> shape = {m_nelem, m_nip};
for (size_t i = 0; i < rank; ++i)
shape.push_back(static_cast<size_t>(m_tdim));
xt::xarray<double> out = xt::empty<double>(shape);
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> QuadratureAxisymmetric::GradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_tdim, m_tdim});
this->gradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> QuadratureAxisymmetric::GradN_vector_T(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_tdim, m_tdim});
this->gradN_vector_T(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> QuadratureAxisymmetric::SymGradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_tdim, m_tdim});
this->symGradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> QuadratureAxisymmetric::Int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_nne*m_ndim, m_nne*m_ndim});
this->int_N_scalar_NT_dV(qscalar, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> QuadratureAxisymmetric::Int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->int_gradN_dot_tensor2_dV(qtensor, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> QuadratureAxisymmetric::Int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_ndim*m_nne, m_ndim*m_nne});
this->int_gradN_dot_tensor4_dot_gradNT_dV(qtensor, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/ElementQuad4Planar.h b/include/GooseFEM/ElementQuad4Planar.h
index 39feebd..4ae90a7 100644
--- a/include/GooseFEM/ElementQuad4Planar.h
+++ b/include/GooseFEM/ElementQuad4Planar.h
@@ -1,175 +1,175 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTQUAD4PLANAR_H
#define GOOSEFEM_ELEMENTQUAD4PLANAR_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// -------------------------------------------------------------------------------------------------
class QuadraturePlanar
{
public:
// Fixed dimensions:
// ndim = 2 - number of dimensions
// nne = 4 - number of nodes per element
// tdim = 3 - number of dimensions of tensors
//
// Naming convention:
// "elemmat" - matrices stored per element - [nelem, nne*ndim, nne*ndim]
// "elemvec" - nodal vectors stored per element - [nelem, nne, ndim]
// "qtensor" - integration point tensor - [nelem, nip, tdim, tdim]
// "qscalar" - integration point scalar - [nelem, nip]
// Constructor: integration point coordinates and weights are optional (default: Gauss)
QuadraturePlanar() = default;
QuadraturePlanar(
const xt::xtensor<double,3>& x,
double thick=1.);
QuadraturePlanar(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w,
double thick=1.);
// Update the nodal positions (shape of "x" should match the earlier definition)
void update_x(const xt::xtensor<double,3>& x);
// Return dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t ndim() const; // number of dimension
size_t nip() const; // number of integration points
// Return shape function gradients
- xt::xtensor<double,4> gradN() const;
+ xt::xtensor<double,4> GradN() const;
// Return integration volume
void dV(xt::xtensor<double,2>& qscalar) const;
void dV(xt::xtensor<double,4>& qtensor) const; // same volume for all tensor components
void dV(xt::xarray<double>& qtensor) const; // same volume for all tensor components
// Dyadic product (and its transpose and symmetric part)
// qtensor(i,j) += dNdx(m,i) * elemvec(m,j)
void gradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
void gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
void symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const; // overwritten
// Integral of the scalar product
// elemmat(m*ndim+i,n*ndim+i) += N(m) * qscalar * N(n) * dV
void int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar,
xt::xtensor<double,3>& elemmat) const; // overwritten
// Integral of the dot product
// elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV
void int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor,
xt::xtensor<double,3>& elemvec) const; // overwritten
// Integral of the dot product
// elemmat(m*2+j, n*2+k) += dNdx(m,i) * qtensor(i,j,k,l) * dNdx(n,l) * dV
void int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor,
xt::xtensor<double,3>& elemmat) const; // overwritten
// Auto-allocation of the functions above
xt::xtensor<double,2> DV() const;
xt::xarray<double> DV(
size_t rank) const;
xt::xtensor<double,4> GradN_vector(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,4> GradN_vector_T(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,4> SymGradN_vector(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,3> Int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar) const;
xt::xtensor<double,3> Int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor) const;
xt::xtensor<double,3> Int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor) const;
private:
// Compute "vol" and "dNdx" based on current "x"
void compute_dN();
private:
// Dimensions (flexible)
size_t m_nelem; // number of elements
size_t m_nip; // number of integration points
// Dimensions (fixed for this element type)
static const size_t m_nne=4; // number of nodes per element
static const size_t m_ndim=2; // number of dimensions
static const size_t m_tdim=3; // number of dimensions of tensors
// Data arrays
xt::xtensor<double,3> m_x; // nodal positions stored per element [nelem, nne, ndim]
xt::xtensor<double,1> m_w; // weight of each integration point [nip]
xt::xtensor<double,2> m_xi; // local coordinate of each integration point [nip, ndim]
xt::xtensor<double,2> m_N; // shape functions [nip, nne]
xt::xtensor<double,3> m_dNxi; // shape function grad. w.r.t. local coor. [nip, nne, ndim]
xt::xtensor<double,4> m_dNx; // shape function grad. w.r.t. global coor. [nelem, nip, nne, ndim]
xt::xtensor<double,2> m_vol; // integration point volume [nelem, nip]
// Thickness
double m_thick;
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#include "ElementQuad4Planar.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/ElementQuad4Planar.hpp b/include/GooseFEM/ElementQuad4Planar.hpp
index bf91aed..7ecfafe 100644
--- a/include/GooseFEM/ElementQuad4Planar.hpp
+++ b/include/GooseFEM/ElementQuad4Planar.hpp
@@ -1,543 +1,543 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTQUAD4PLANAR_HPP
#define GOOSEFEM_ELEMENTQUAD4PLANAR_HPP
// -------------------------------------------------------------------------------------------------
#include "ElementQuad4Planar.h"
// =================================================================================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// =================================================================================================
inline QuadraturePlanar::QuadraturePlanar(const xt::xtensor<double,3>& x, double thick) :
QuadraturePlanar(x, Gauss::xi(), Gauss::w(), thick) {}
// -------------------------------------------------------------------------------------------------
inline QuadraturePlanar::QuadraturePlanar(
const xt::xtensor<double,3>& x,
const xt::xtensor<double,2>& xi,
const xt::xtensor<double,1>& w,
double thick) :
m_x(x), m_w(w), m_xi(xi), m_thick(thick)
{
- GOOSEFEM_ASSERT(m_x.shape()[1] == m_nne);
- GOOSEFEM_ASSERT(m_x.shape()[2] == m_ndim);
+ GOOSEFEM_ASSERT(m_x.shape(1) == m_nne);
+ GOOSEFEM_ASSERT(m_x.shape(2) == m_ndim);
- m_nelem = m_x.shape()[0];
- m_nip = m_w.size();
+ m_nelem = m_x.shape(0);
+ m_nip = m_w.size();
- GOOSEFEM_ASSERT(m_xi.shape()[0] == m_nip);
- GOOSEFEM_ASSERT(m_xi.shape()[1] == m_ndim);
+ GOOSEFEM_ASSERT(m_xi.shape(0) == m_nip);
+ GOOSEFEM_ASSERT(m_xi.shape(1) == m_ndim);
GOOSEFEM_ASSERT(m_w.size() == m_nip);
- m_N = xt::empty<double>({ m_nip, m_nne });
- m_dNxi = xt::empty<double>({ m_nip, m_nne, m_ndim});
- m_dNx = xt::empty<double>({m_nelem, m_nip, m_nne, m_ndim});
- m_vol = xt::empty<double>({m_nelem, m_nip });
+ m_N = xt::empty<double>({m_nip, m_nne});
+ m_dNxi = xt::empty<double>({m_nip, m_nne, m_ndim});
+ m_dNx = xt::empty<double>({m_nelem, m_nip, m_nne, m_ndim});
+ m_vol = xt::empty<double>({m_nelem, m_nip});
// shape functions
for (size_t q = 0 ; q < m_nip ; ++q)
{
m_N(q,0) = .25 * (1.-m_xi(q,0)) * (1.-m_xi(q,1));
m_N(q,1) = .25 * (1.+m_xi(q,0)) * (1.-m_xi(q,1));
m_N(q,2) = .25 * (1.+m_xi(q,0)) * (1.+m_xi(q,1));
m_N(q,3) = .25 * (1.-m_xi(q,0)) * (1.+m_xi(q,1));
}
// shape function gradients in local coordinates
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - dN / dxi_0
m_dNxi(q,0,0) = -.25*(1.-m_xi(q,1));
m_dNxi(q,1,0) = +.25*(1.-m_xi(q,1));
m_dNxi(q,2,0) = +.25*(1.+m_xi(q,1));
m_dNxi(q,3,0) = -.25*(1.+m_xi(q,1));
// - dN / dxi_1
m_dNxi(q,0,1) = -.25*(1.-m_xi(q,0));
m_dNxi(q,1,1) = -.25*(1.+m_xi(q,0));
m_dNxi(q,2,1) = +.25*(1.+m_xi(q,0));
m_dNxi(q,3,1) = +.25*(1.-m_xi(q,0));
}
// compute the shape function gradients, based on "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadraturePlanar::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadraturePlanar::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadraturePlanar::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t QuadraturePlanar::nip() const
{
return m_nip;
}
// -------------------------------------------------------------------------------------------------
-inline xt::xtensor<double,4> QuadraturePlanar::gradN() const
+inline xt::xtensor<double,4> QuadraturePlanar::GradN() const
{
return m_dNx;
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::dV(xt::xtensor<double,2>& qscalar) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
qscalar(e,q) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::dV(xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t q = 0 ; q < m_nip ; ++q)
for (size_t i = 0 ; i < m_tdim ; ++i)
for (size_t j = 0 ; j < m_tdim ; ++j)
qtensor(e,q,i,j) = m_vol(e,q);
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::dV(xt::xarray<double>& qtensor) const
{
- GOOSEFEM_ASSERT(qtensor.shape()[0] == m_nelem);
- GOOSEFEM_ASSERT(qtensor.shape()[1] == m_nip);
+ GOOSEFEM_ASSERT(qtensor.shape(0) == m_nelem);
+ GOOSEFEM_ASSERT(qtensor.shape(1) == m_nip);
xt::dynamic_shape<ptrdiff_t> strides = {
static_cast<ptrdiff_t>(m_vol.strides()[0]),
static_cast<ptrdiff_t>(m_vol.strides()[1])};
for (size_t i = 2; i < qtensor.shape().size(); ++i)
strides.push_back(0);
qtensor = xt::strided_view(m_vol, qtensor.shape(), std::move(strides), 0ul, xt::layout_type::dynamic);
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::update_x(const xt::xtensor<double,3>& x)
{
GOOSEFEM_ASSERT(x.shape() == m_x.shape());
xt::noalias(m_x) = x;
// update the shape function gradients for the new "x"
compute_dN();
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::compute_dN()
{
#pragma omp parallel
{
// allocate local variables
xt::xtensor_fixed<double, xt::xshape<2,2>> J, Jinv;
// loop over all elements (in parallel)
#pragma omp for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias nodal positions
auto x = xt::adapt(&m_x(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over integration points
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNxi = xt::adapt(&m_dNxi( q,0,0), xt::xshape<m_nne,m_ndim>());
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne,m_ndim>());
// - Jacobian (loops unrolled for efficiency)
// J(i,j) += dNxi(m,i) * x(m,j);
J(0,0) = dNxi(0,0)*x(0,0) + dNxi(1,0)*x(1,0) + dNxi(2,0)*x(2,0) + dNxi(3,0)*x(3,0);
J(0,1) = dNxi(0,0)*x(0,1) + dNxi(1,0)*x(1,1) + dNxi(2,0)*x(2,1) + dNxi(3,0)*x(3,1);
J(1,0) = dNxi(0,1)*x(0,0) + dNxi(1,1)*x(1,0) + dNxi(2,1)*x(2,0) + dNxi(3,1)*x(3,0);
J(1,1) = dNxi(0,1)*x(0,1) + dNxi(1,1)*x(1,1) + dNxi(2,1)*x(2,1) + dNxi(3,1)*x(3,1);
// - determinant and inverse of the Jacobian
double Jdet = inv(J, Jinv);
// - shape function gradients wrt global coordinates (loops partly unrolled for efficiency)
// dNx(m,i) += Jinv(i,j) * dNxi(m,j);
for (size_t m = 0 ; m < m_nne ; ++m)
{
dNx(m,0) = Jinv(0,0) * dNxi(m,0) + Jinv(0,1) * dNxi(m,1);
dNx(m,1) = Jinv(1,0) * dNxi(m,0) + Jinv(1,1) * dNxi(m,1);
}
// - integration point volume
m_vol(e,q) = m_w(q) * Jdet * m_thick;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::gradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
// zero-initialize (zero z-components not written below)
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_tdim,m_tdim>());
// - evaluate dyadic product (loops unrolled for efficiency)
// gradu(i,j) += dNx(m,i) * u(m,j)
gradu(0,0) = dNx(0,0)*u(0,0) + dNx(1,0)*u(1,0) + dNx(2,0)*u(2,0) + dNx(3,0)*u(3,0);
gradu(0,1) = dNx(0,0)*u(0,1) + dNx(1,0)*u(1,1) + dNx(2,0)*u(2,1) + dNx(3,0)*u(3,1);
gradu(1,0) = dNx(0,1)*u(0,0) + dNx(1,1)*u(1,0) + dNx(2,1)*u(2,0) + dNx(3,1)*u(3,0);
gradu(1,1) = dNx(0,1)*u(0,1) + dNx(1,1)*u(1,1) + dNx(2,1)*u(2,1) + dNx(3,1)*u(3,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::gradN_vector_T(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
// zero-initialize (zero z-components not written below)
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto gradu = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_tdim,m_tdim>());
// - evaluate transpose of dyadic product (loops unrolled for efficiency)
// gradu(j,i) += dNx(m,i) * u(m,j)
gradu(0,0) = dNx(0,0)*u(0,0) + dNx(1,0)*u(1,0) + dNx(2,0)*u(2,0) + dNx(3,0)*u(3,0);
gradu(1,0) = dNx(0,0)*u(0,1) + dNx(1,0)*u(1,1) + dNx(2,0)*u(2,1) + dNx(3,0)*u(3,1);
gradu(0,1) = dNx(0,1)*u(0,0) + dNx(1,1)*u(1,0) + dNx(2,1)*u(2,0) + dNx(3,1)*u(3,0);
gradu(1,1) = dNx(0,1)*u(0,1) + dNx(1,1)*u(1,1) + dNx(2,1)*u(2,1) + dNx(3,1)*u(3,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::symGradN_vector(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,4>& qtensor) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
// zero-initialize (zero z-components not written below)
qtensor.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias element vector (e.g. nodal displacements)
auto u = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto eps = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_tdim,m_tdim>());
// - evaluate symmetrized dyadic product (loops unrolled for efficiency)
// grad(i,j) += dNx(m,i) * u(m,j)
// eps (j,i) = 0.5 * ( grad(i,j) + grad(j,i) )
eps(0,0) = dNx(0,0)*u(0,0) + dNx(1,0)*u(1,0) + dNx(2,0)*u(2,0) + dNx(3,0)*u(3,0);
eps(1,1) = dNx(0,1)*u(0,1) + dNx(1,1)*u(1,1) + dNx(2,1)*u(2,1) + dNx(3,1)*u(3,1);
eps(0,1) = ( dNx(0,0)*u(0,1) + dNx(1,0)*u(1,1) + dNx(2,0)*u(2,1) + dNx(3,0)*u(3,1) +
dNx(0,1)*u(0,0) + dNx(1,1)*u(1,0) + dNx(2,1)*u(2,0) + dNx(3,1)*u(3,0) ) * 0.5;
eps(1,0) = eps(0,1);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qscalar.shape() ==\
std::decay_t<decltype(qscalar)>::shape_type({m_nelem, m_nip}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize: matrix of matrices
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. mass matrix)
auto M = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto N = xt::adapt(&m_N(q,0), xt::xshape<m_nne>());
auto& vol = m_vol (e,q);
auto& rho = qscalar(e,q);
// - evaluate scalar product, for all dimensions, and assemble
// M(m*ndim+i,n*ndim+i) += N(m) * scalar * N(n) * dV
for (size_t m = 0 ; m < m_nne ; ++m ){
for (size_t n = 0 ; n < m_nne ; ++n ){
M(m*m_ndim+0, n*m_ndim+0) += N(m) * rho * N(n) * vol;
M(m*m_ndim+1, n*m_ndim+1) += N(m) * rho * N(n) * vol;
}
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim}));
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
// zero-initialize output: matrix of vectors
elemvec.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto f = xt::adapt(&elemvec(e,0,0), xt::xshape<m_nne,m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx (e,q,0,0), xt::xshape<m_nne ,m_ndim>());
auto sig = xt::adapt(&qtensor(e,q,0,0), xt::xshape<m_tdim,m_tdim>());
auto& vol = m_vol(e,q);
// - evaluate dot product, and assemble
for (size_t m = 0 ; m < m_nne ; ++m)
{
f(m,0) += ( dNx(m,0) * sig(0,0) + dNx(m,1) * sig(1,0) ) * vol;
f(m,1) += ( dNx(m,0) * sig(0,1) + dNx(m,1) * sig(1,1) ) * vol;
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void QuadraturePlanar::int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor,
xt::xtensor<double,3>& elemmat) const
{
GOOSEFEM_ASSERT(qtensor.shape() ==\
std::decay_t<decltype(qtensor)>::shape_type({m_nelem, m_nip, m_tdim, m_tdim, m_tdim, m_tdim}));
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
// zero-initialize output: matrix of vector
elemmat.fill(0.0);
// loop over all elements (in parallel)
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
{
// alias (e.g. nodal force)
auto K = xt::adapt(&elemmat(e,0,0), xt::xshape<m_nne*m_ndim,m_nne*m_ndim>());
// loop over all integration points in element "e"
for (size_t q = 0 ; q < m_nip ; ++q)
{
// - alias
auto dNx = xt::adapt(&m_dNx(e,q,0,0), xt::xshape<m_nne,m_ndim>());
auto C = xt::adapt(&qtensor(e,q,0,0,0,0), xt::xshape<m_tdim,m_tdim,m_tdim,m_tdim>());
auto& vol = m_vol(e,q);
// - evaluate dot product, and assemble
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t n = 0 ; n < m_nne ; ++n)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t j = 0 ; j < m_ndim ; ++j)
for (size_t k = 0 ; k < m_ndim ; ++k)
for (size_t l = 0 ; l < m_ndim ; ++l)
K(m*m_ndim+j, n*m_ndim+k) += dNx(m,i) * C(i,j,k,l) * dNx(n,l) * vol;
}
}
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> QuadraturePlanar::DV() const
{
xt::xtensor<double,2> out = xt::empty<double>({m_nelem, m_nip});
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xarray<double> QuadraturePlanar::DV(size_t rank) const
{
std::vector<size_t> shape = {m_nelem, m_nip};
for (size_t i = 0; i < rank; ++i)
shape.push_back(static_cast<size_t>(m_tdim));
xt::xarray<double> out = xt::empty<double>(shape);
this->dV(out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> QuadraturePlanar::GradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_tdim, m_tdim});
this->gradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> QuadraturePlanar::GradN_vector_T(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_tdim, m_tdim});
this->gradN_vector_T(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,4> QuadraturePlanar::SymGradN_vector(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,4> qtensor = xt::empty<double>({m_nelem, m_nip, m_tdim, m_tdim});
this->symGradN_vector(elemvec, qtensor);
return qtensor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> QuadraturePlanar::Int_N_scalar_NT_dV(
const xt::xtensor<double,2>& qscalar) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_nne*m_ndim, m_nne*m_ndim});
this->int_N_scalar_NT_dV(qscalar, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> QuadraturePlanar::Int_gradN_dot_tensor2_dV(
const xt::xtensor<double,4>& qtensor) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->int_gradN_dot_tensor2_dV(qtensor, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> QuadraturePlanar::Int_gradN_dot_tensor4_dot_gradNT_dV(
const xt::xtensor<double,6>& qtensor) const
{
xt::xtensor<double,3> elemmat = xt::empty<double>({m_nelem, m_ndim*m_nne, m_ndim*m_nne});
this->int_gradN_dot_tensor4_dot_gradNT_dV(qtensor, elemmat);
return elemmat;
}
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/Matrix.h b/include/GooseFEM/Matrix.h
index 43a15d5..159f0c9 100644
--- a/include/GooseFEM/Matrix.h
+++ b/include/GooseFEM/Matrix.h
@@ -1,118 +1,118 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIX_H
#define GOOSEFEM_MATRIX_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
+template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class Matrix
{
public:
// Constructors
Matrix() = default;
Matrix(
- const xt::xtensor<size_t,2> &conn,
- const xt::xtensor<size_t,2> &dofs);
+ const xt::xtensor<size_t,2>& conn,
+ const xt::xtensor<size_t,2>& dofs);
// Dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
// DOF lists
xt::xtensor<size_t,2> dofs() const; // DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
- void assemble(const xt::xtensor<double,3> &elemmat);
+ void assemble(const xt::xtensor<double,3>& elemmat);
// Solve
// x_u = A_uu \ ( b_u - A_up * x_p )
void solve(
- const xt::xtensor<double,2> &b,
- xt::xtensor<double,2> &x); // overwritten
+ const xt::xtensor<double,2>& b,
+ xt::xtensor<double,2>& x); // overwritten
void solve(
- const xt::xtensor<double,1> &b,
- xt::xtensor<double,1> &x); // overwritten
+ const xt::xtensor<double,1>& b,
+ xt::xtensor<double,1>& x); // overwritten
// Auto-allocation of the functions above
xt::xtensor<double,2> Solve(
- const xt::xtensor<double,2> &b);
+ const xt::xtensor<double,2>& b);
xt::xtensor<double,1> Solve(
- const xt::xtensor<double,1> &b);
+ const xt::xtensor<double,1>& b);
private:
// The matrix
Eigen::SparseMatrix<double> m_A;
// Matrix entries
std::vector<Eigen::Triplet<double>> m_T;
// Solver (re-used to solve different RHS)
- Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> m_solver;
+ Solver m_solver;
// Signal changes to data compare to the last inverse
bool m_factor=false;
// Bookkeeping
xt::xtensor<size_t,2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t,2> m_dofs; // DOF-numbers per node [nnode, ndim]
// Dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
// Compute inverse (automatically evaluated by "solve")
-
void factorize();
// Convert arrays (Eigen version of Vector, which contains public functions)
- Eigen::VectorXd asDofs(const xt::xtensor<double,2> &nodevec) const;
+ Eigen::VectorXd asDofs(const xt::xtensor<double,2>& nodevec) const;
- void asNode(const Eigen::VectorXd &dofval, xt::xtensor<double,2> &nodevec) const;
+ void asNode(const Eigen::VectorXd& dofval, xt::xtensor<double,2>& nodevec) const;
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#include "Matrix.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/Matrix.hpp b/include/GooseFEM/Matrix.hpp
index 51df0d9..45835b6 100644
--- a/include/GooseFEM/Matrix.hpp
+++ b/include/GooseFEM/Matrix.hpp
@@ -1,205 +1,222 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIX_HPP
#define GOOSEFEM_MATRIX_HPP
// -------------------------------------------------------------------------------------------------
#include "Matrix.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
-inline Matrix::Matrix(
+template <class Solver>
+inline Matrix<Solver>::Matrix(
const xt::xtensor<size_t,2> &conn,
const xt::xtensor<size_t,2> &dofs) :
m_conn(conn), m_dofs(dofs)
{
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
- m_ndof = xt::amax(m_dofs)[0] + 1;
+ m_ndof = xt::amax(m_dofs)[0] + 1;
- m_T.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
+ m_T.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
m_A.resize(m_ndof,m_ndof);
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
// -------------------------------------------------------------------------------------------------
-inline size_t Matrix::nelem() const
+template <class Solver>
+inline size_t Matrix<Solver>::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
-inline size_t Matrix::nne() const
+template <class Solver>
+inline size_t Matrix<Solver>::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
-inline size_t Matrix::nnode() const
+template <class Solver>
+inline size_t Matrix<Solver>::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
-inline size_t Matrix::ndim() const
+template <class Solver>
+inline size_t Matrix<Solver>::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
-inline size_t Matrix::ndof() const
+template <class Solver>
+inline size_t Matrix<Solver>::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
-inline xt::xtensor<size_t,2> Matrix::dofs() const
+template <class Solver>
+inline xt::xtensor<size_t,2> Matrix<Solver>::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
-inline void Matrix::factorize()
+template <class Solver>
+inline void Matrix<Solver>::factorize()
{
if ( ! m_factor ) return;
m_solver.compute(m_A);
m_factor = false;
}
// -------------------------------------------------------------------------------------------------
-inline void Matrix::assemble(const xt::xtensor<double,3> &elemmat)
+template <class Solver>
+inline void Matrix<Solver>::assemble(const xt::xtensor<double,3> &elemmat)
{
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
m_T.clear();
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
for (size_t n = 0 ; n < m_nne ; ++n)
for (size_t j = 0 ; j < m_ndim ; ++j)
m_T.push_back(Eigen::Triplet<double>(
m_dofs(m_conn(e,m),i), m_dofs(m_conn(e,n),j), elemmat(e,m*m_ndim+i,n*m_ndim+j)
));
m_A.setFromTriplets(m_T.begin(), m_T.end());
m_factor = true;
}
// -------------------------------------------------------------------------------------------------
-inline void Matrix::solve(
+template <class Solver>
+inline void Matrix<Solver>::solve(
const xt::xtensor<double,2> &b,
xt::xtensor<double,2> &x)
{
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
this->factorize();
Eigen::VectorXd B = this->asDofs(b);
Eigen::VectorXd X = m_solver.solve(B);
this->asNode(X, x);
}
// -------------------------------------------------------------------------------------------------
-inline void Matrix::solve(
+template <class Solver>
+inline void Matrix<Solver>::solve(
const xt::xtensor<double,1> &b,
xt::xtensor<double,1> &x)
{
GOOSEFEM_ASSERT(b.size() == m_ndof);
GOOSEFEM_ASSERT(x.size() == m_ndof);
this->factorize();
Eigen::VectorXd B(m_ndof,1);
std::copy(b.begin(), b.end(), B.data());
Eigen::VectorXd X = m_solver.solve(B);
std::copy(X.data(), X.data()+m_ndof, x.begin());
}
// -------------------------------------------------------------------------------------------------
-inline xt::xtensor<double,2> Matrix::Solve(
+template <class Solver>
+inline xt::xtensor<double,2> Matrix<Solver>::Solve(
const xt::xtensor<double,2> &b)
{
xt::xtensor<double,2> x = xt::empty<double>({m_nnode, m_ndim});
this->solve(b, x);
return x;
}
// -------------------------------------------------------------------------------------------------
-inline xt::xtensor<double,1> Matrix::Solve(
+template <class Solver>
+inline xt::xtensor<double,1> Matrix<Solver>::Solve(
const xt::xtensor<double,1> &b)
{
xt::xtensor<double,1> x = xt::empty<double>({m_ndof});
this->solve(b, x);
return x;
}
// -------------------------------------------------------------------------------------------------
-inline Eigen::VectorXd Matrix::asDofs(const xt::xtensor<double,2> &nodevec) const
+template <class Solver>
+inline Eigen::VectorXd Matrix<Solver>::asDofs(const xt::xtensor<double,2> &nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval(m_ndof,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m,i)) = nodevec(m,i);
return dofval;
}
// -------------------------------------------------------------------------------------------------
-inline void Matrix::asNode(const Eigen::VectorXd &dofval, xt::xtensor<double,2> &nodevec) const
+template <class Solver>
+inline void Matrix<Solver>::asNode(
+ const Eigen::VectorXd &dofval,
+ xt::xtensor<double,2> &nodevec) const
{
assert(static_cast<size_t>(dofval.size()) == m_ndof);
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
nodevec(m,i) = dofval(m_dofs(m,i));
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixDiagonal.h b/include/GooseFEM/MatrixDiagonal.h
index 05f1422..5d91ff0 100644
--- a/include/GooseFEM/MatrixDiagonal.h
+++ b/include/GooseFEM/MatrixDiagonal.h
@@ -1,123 +1,123 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXDIAGONAL_H
#define GOOSEFEM_MATRIXDIAGONAL_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
class MatrixDiagonal
{
public:
// Constructors
MatrixDiagonal() = default;
MatrixDiagonal(
- const xt::xtensor<size_t,2> &conn,
- const xt::xtensor<size_t,2> &dofs);
+ const xt::xtensor<size_t,2>& conn,
+ const xt::xtensor<size_t,2>& dofs);
// Dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
// DOF lists
xt::xtensor<size_t,2> dofs() const; // DOFs
// Set matrix components
- void set(const xt::xtensor<double,1> &A);
+ void set(const xt::xtensor<double,1>& A);
// assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
// WARNING: ignores any off-diagonal terms
- void assemble(const xt::xtensor<double,3> &elemmat);
+ void assemble(const xt::xtensor<double,3>& elemmat);
// Dot-product:
// b_i = A_ij * x_j
void dot(
- const xt::xtensor<double,2> &x,
- xt::xtensor<double,2> &b) const;
+ const xt::xtensor<double,2>& x,
+ xt::xtensor<double,2>& b) const;
void dot(
- const xt::xtensor<double,1> &x,
- xt::xtensor<double,1> &b) const;
+ const xt::xtensor<double,1>& x,
+ xt::xtensor<double,1>& b) const;
// Solve:
// x = A \ b
void solve(
- const xt::xtensor<double,2> &b,
- xt::xtensor<double,2> &x);
+ const xt::xtensor<double,2>& b,
+ xt::xtensor<double,2>& x);
void solve(
- const xt::xtensor<double,1> &b,
- xt::xtensor<double,1> &x);
+ const xt::xtensor<double,1>& b,
+ xt::xtensor<double,1>& x);
// Return matrix as diagonal matrix (column)
xt::xtensor<double,1> AsDiagonal() const;
// Auto-allocation of the functions above
- xt::xtensor<double,2> Dot(const xt::xtensor<double,2> &x) const;
+ xt::xtensor<double,2> Dot(const xt::xtensor<double,2>& x) const;
- xt::xtensor<double,1> Dot(const xt::xtensor<double,1> &x) const;
+ xt::xtensor<double,1> Dot(const xt::xtensor<double,1>& x) const;
- xt::xtensor<double,2> Solve(const xt::xtensor<double,2> &b);
+ xt::xtensor<double,2> Solve(const xt::xtensor<double,2>& b);
- xt::xtensor<double,1> Solve(const xt::xtensor<double,1> &b);
+ xt::xtensor<double,1> Solve(const xt::xtensor<double,1>& b);
private:
// The diagonal matrix, and its inverse (re-used to solve different RHS)
xt::xtensor<double,1> m_A;
xt::xtensor<double,1> m_inv;
// Signal changes to data compare to the last inverse
bool m_factor=false;
// Bookkeeping
xt::xtensor<size_t,2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t,2> m_dofs; // DOF-numbers per node [nnode, ndim]
// Dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
// Compute inverse (automatically evaluated by "solve")
void factorize();
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#include "MatrixDiagonal.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixDiagonal.hpp b/include/GooseFEM/MatrixDiagonal.hpp
index 647a5eb..3957c75 100644
--- a/include/GooseFEM/MatrixDiagonal.hpp
+++ b/include/GooseFEM/MatrixDiagonal.hpp
@@ -1,233 +1,233 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXDIAGONAL_HPP
#define GOOSEFEM_MATRIXDIAGONAL_HPP
// -------------------------------------------------------------------------------------------------
#include "MatrixDiagonal.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
inline MatrixDiagonal::MatrixDiagonal(
const xt::xtensor<size_t,2> &conn,
const xt::xtensor<size_t,2> &dofs) :
m_conn(conn), m_dofs(dofs)
{
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
m_ndof = xt::amax(m_dofs)[0] + 1;
m_A = xt::empty<double>({m_ndof});
m_inv = xt::empty<double>({m_ndof});
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonal::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonal::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonal::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonal::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonal::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> MatrixDiagonal::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonal::factorize()
{
if (!m_factor) return;
#pragma omp parallel for
for (size_t d = 0 ; d < m_ndof ; ++d)
m_inv(d) = 1. / m_A(d);
m_factor = false;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonal::set(const xt::xtensor<double,1> &A)
{
GOOSEFEM_ASSERT(A.size() == m_ndof);
std::copy(A.begin(), A.end(), m_A.begin());
m_factor = true;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonal::assemble(const xt::xtensor<double,3> &elemmat)
{
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
GOOSEFEM_ASSERT(Element::isDiagonal(elemmat));
m_A.fill(0.0);
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
m_A(m_dofs(m_conn(e,m),i)) += elemmat(e,m*m_ndim+i,m*m_ndim+i);
m_factor = true;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonal::dot(
const xt::xtensor<double,2> &x,
xt::xtensor<double,2> &b) const
{
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
b(m,i) = m_A(m_dofs(m,i)) * x(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonal::dot(
const xt::xtensor<double,1> &x,
xt::xtensor<double,1> &b) const
{
GOOSEFEM_ASSERT(x.size() == m_ndof);
GOOSEFEM_ASSERT(b.size() == m_ndof);
xt::noalias(b) = m_A * x;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonal::solve(
const xt::xtensor<double,2> &b,
xt::xtensor<double,2> &x)
{
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
this->factorize();
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
x(m,i) = m_inv(m_dofs(m,i)) * b(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonal::solve(
const xt::xtensor<double,1> &b,
xt::xtensor<double,1> &x)
{
GOOSEFEM_ASSERT(b.size() == m_ndof);
GOOSEFEM_ASSERT(x.size() == m_ndof);
this->factorize();
xt::noalias(x) = m_inv * b;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::AsDiagonal() const
{
return m_A;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> MatrixDiagonal::Dot(const xt::xtensor<double,2> &x) const
{
xt::xtensor<double,2> b = xt::empty<double>({m_nnode, m_ndim});
this->dot(x, b);
return b;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::Dot(const xt::xtensor<double,1> &x) const
{
xt::xtensor<double,1> b = xt::empty<double>({m_ndof});
this->dot(x, b);
return b;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> MatrixDiagonal::Solve(const xt::xtensor<double,2> &b)
{
xt::xtensor<double,2> x = xt::empty<double>({m_nnode, m_ndim});
this->solve(b, x);
return x;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonal::Solve(const xt::xtensor<double,1> &b)
{
xt::xtensor<double,1> x = xt::empty<double>({m_ndof});
this->solve(b, x);
return x;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixDiagonalPartitioned.h b/include/GooseFEM/MatrixDiagonalPartitioned.h
index 8d8f2eb..51e1068 100644
--- a/include/GooseFEM/MatrixDiagonalPartitioned.h
+++ b/include/GooseFEM/MatrixDiagonalPartitioned.h
@@ -1,191 +1,191 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXDIAGONALPARTITIONED_H
#define GOOSEFEM_MATRIXDIAGONALPARTITIONED_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
class MatrixDiagonalPartitioned
{
public:
// Constructors
MatrixDiagonalPartitioned() = default;
MatrixDiagonalPartitioned(
- const xt::xtensor<size_t,2> &conn,
- const xt::xtensor<size_t,2> &dofs,
- const xt::xtensor<size_t,1> &iip);
+ const xt::xtensor<size_t,2>& conn,
+ const xt::xtensor<size_t,2>& dofs,
+ const xt::xtensor<size_t,1>& iip);
// Dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
size_t nnu() const; // number of unknown DOFs
size_t nnp() const; // number of prescribed DOFs
// DOF lists
xt::xtensor<size_t,2> dofs() const; // DOFs
xt::xtensor<size_t,1> iiu() const; // unknown DOFs
xt::xtensor<size_t,1> iip() const; // prescribed DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
// WARNING: ignores any off-diagonal terms
- void assemble(const xt::xtensor<double,3> &elemmat);
+ void assemble(const xt::xtensor<double,3>& elemmat);
// Dot-product:
// b_i = A_ij * x_j
void dot(
- const xt::xtensor<double,2> &x,
- xt::xtensor<double,2> &b) const; // overwritten
+ const xt::xtensor<double,2>& x,
+ xt::xtensor<double,2>& b) const; // overwritten
void dot(
- const xt::xtensor<double,1> &x,
- xt::xtensor<double,1> &b) const; // overwritten
+ const xt::xtensor<double,1>& x,
+ xt::xtensor<double,1>& b) const; // overwritten
void dot_u(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p,
- xt::xtensor<double,1> &b_u) const; // overwritten
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p,
+ xt::xtensor<double,1>& b_u) const; // overwritten
void dot_p(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p,
- xt::xtensor<double,1> &b_p) const; // overwritten
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p,
+ xt::xtensor<double,1>& b_p) const; // overwritten
// Solve:
// x_u = A_uu \ ( b_u - A_up * x_p ) = A_uu \ b_u
void solve(
- const xt::xtensor<double,2> &b,
- xt::xtensor<double,2> &x); // modified with "x_u"
+ const xt::xtensor<double,2>& b,
+ xt::xtensor<double,2>& x); // modified with "x_u"
void solve(
- const xt::xtensor<double,1> &b,
- xt::xtensor<double,1> &x); // modified with "x_u"
+ const xt::xtensor<double,1>& b,
+ xt::xtensor<double,1>& x); // modified with "x_u"
void solve_u(
- const xt::xtensor<double,1> &b_u,
- const xt::xtensor<double,1> &x_p,
- xt::xtensor<double,1> &x_u); // overwritten
+ const xt::xtensor<double,1>& b_u,
+ const xt::xtensor<double,1>& x_p,
+ xt::xtensor<double,1>& x_u); // overwritten
// Get right-hand-size for corresponding to the prescribed DOFs:
// b_p = A_pu * x_u + A_pp * x_p = A_pp * x_p
void reaction(
- const xt::xtensor<double,2> &x,
- xt::xtensor<double,2> &b) const; // modified with "b_p"
+ const xt::xtensor<double,2>& x,
+ xt::xtensor<double,2>& b) const; // modified with "b_p"
void reaction(
- const xt::xtensor<double,1> &x,
- xt::xtensor<double,1> &b) const; // modified with "b_p"
+ const xt::xtensor<double,1>& x,
+ xt::xtensor<double,1>& b) const; // modified with "b_p"
void reaction_p(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p,
- xt::xtensor<double,1> &b_p) const; // overwritten
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p,
+ xt::xtensor<double,1>& b_p) const; // overwritten
// Return matrix as diagonal matrix (column)
xt::xtensor<double,1> AsDiagonal() const;
// Auto-allocation of the functions above
xt::xtensor<double,2> Dot(
- const xt::xtensor<double,2> &x) const;
+ const xt::xtensor<double,2>& x) const;
xt::xtensor<double,1> Dot(
- const xt::xtensor<double,1> &x) const;
+ const xt::xtensor<double,1>& x) const;
xt::xtensor<double,1> Dot_u(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p) const;
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p) const;
xt::xtensor<double,1> Dot_p(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p) const;
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p) const;
xt::xtensor<double,2> Solve(
- const xt::xtensor<double,2> &b,
- const xt::xtensor<double,2> &x);
+ const xt::xtensor<double,2>& b,
+ const xt::xtensor<double,2>& x);
xt::xtensor<double,1> Solve(
- const xt::xtensor<double,1> &b,
- const xt::xtensor<double,1> &x);
+ const xt::xtensor<double,1>& b,
+ const xt::xtensor<double,1>& x);
xt::xtensor<double,1> Solve_u(
- const xt::xtensor<double,1> &b_u,
- const xt::xtensor<double,1> &x_p);
+ const xt::xtensor<double,1>& b_u,
+ const xt::xtensor<double,1>& x_p);
xt::xtensor<double,2> Reaction(
- const xt::xtensor<double,2> &x,
- const xt::xtensor<double,2> &b) const;
+ const xt::xtensor<double,2>& x,
+ const xt::xtensor<double,2>& b) const;
xt::xtensor<double,1> Reaction(
- const xt::xtensor<double,1> &x,
- const xt::xtensor<double,1> &b) const;
+ const xt::xtensor<double,1>& x,
+ const xt::xtensor<double,1>& b) const;
xt::xtensor<double,1> Reaction_p(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p) const;
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p) const;
private:
// The diagonal matrix, and its inverse (re-used to solve different RHS)
xt::xtensor<double,1> m_Auu;
xt::xtensor<double,1> m_App;
xt::xtensor<double,1> m_inv_uu;
// Signal changes to data compare to the last inverse
bool m_factor=false;
// Bookkeeping
xt::xtensor<size_t,2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t,2> m_dofs; // DOF-numbers per node [nnode, ndim]
xt::xtensor<size_t,2> m_part; // DOF-numbers per node, renumbered [nnode, ndim]
xt::xtensor<size_t,1> m_iiu; // DOF-numbers that are unknown [nnu]
xt::xtensor<size_t,1> m_iip; // DOF-numbers that are prescribed [nnp]
// Dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
size_t m_nnu; // number of unknown DOFs
size_t m_nnp; // number of prescribed DOFs
// Compute inverse (automatically evaluated by "solve")
void factorize();
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#include "MatrixDiagonalPartitioned.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixDiagonalPartitioned.hpp b/include/GooseFEM/MatrixDiagonalPartitioned.hpp
index 8e92c20..c089401 100644
--- a/include/GooseFEM/MatrixDiagonalPartitioned.hpp
+++ b/include/GooseFEM/MatrixDiagonalPartitioned.hpp
@@ -1,475 +1,475 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXDIAGONALPARTITIONED_HPP
#define GOOSEFEM_MATRIXDIAGONALPARTITIONED_HPP
// -------------------------------------------------------------------------------------------------
#include "MatrixDiagonalPartitioned.h"
#include "Mesh.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
inline MatrixDiagonalPartitioned::MatrixDiagonalPartitioned(
const xt::xtensor<size_t,2> &conn,
const xt::xtensor<size_t,2> &dofs,
const xt::xtensor<size_t,1> &iip) :
m_conn(conn), m_dofs(dofs), m_iip(iip)
{
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
m_iiu = xt::setdiff1d(dofs, iip);
m_ndof = xt::amax(m_dofs)[0] + 1;
m_nnp = m_iip.size();
m_nnu = m_iiu.size();
m_part = Mesh::Reorder({m_iiu, m_iip}).get(m_dofs);
m_Auu = xt::empty<double>({m_nnu});
m_App = xt::empty<double>({m_nnp});
m_inv_uu = xt::empty<double>({m_nnu});
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(xt::amax(m_iip)[0] <= xt::amax(m_dofs)[0]);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonalPartitioned::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonalPartitioned::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonalPartitioned::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonalPartitioned::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonalPartitioned::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonalPartitioned::nnu() const
{
return m_nnu;
}
// -------------------------------------------------------------------------------------------------
inline size_t MatrixDiagonalPartitioned::nnp() const
{
return m_nnp;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> MatrixDiagonalPartitioned::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> MatrixDiagonalPartitioned::iiu() const
{
return m_iiu;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> MatrixDiagonalPartitioned::iip() const
{
return m_iip;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::factorize()
{
if (!m_factor) return;
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
m_inv_uu(d) = 1. / m_Auu(d);
m_factor = false;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::assemble(const xt::xtensor<double,3> &elemmat)
{
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
GOOSEFEM_ASSERT(Element::isDiagonal(elemmat));
m_Auu.fill(0.0);
m_App.fill(0.0);
for (size_t e = 0 ; e < m_nelem ; ++e) {
for (size_t m = 0 ; m < m_nne ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
size_t d = m_part(m_conn(e,m),i);
if ( d < m_nnu )
m_Auu(d ) += elemmat(e,m*m_ndim+i,m*m_ndim+i);
else
m_App(d-m_nnu) += elemmat(e,m*m_ndim+i,m*m_ndim+i);
}
}
}
m_factor = true;
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::dot(
const xt::xtensor<double,2> &x,
xt::xtensor<double,2> &b) const
{
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
size_t d = m_part(m,i);
if ( d < m_nnu ) b(m,i) = m_Auu(d ) * x(m,i);
else b(m,i) = m_App(d-m_nnu) * x(m,i);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::dot(
const xt::xtensor<double,1> &x,
xt::xtensor<double,1> &b) const
{
GOOSEFEM_ASSERT(x.size() == m_ndof);
GOOSEFEM_ASSERT(b.size() == m_ndof);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
b(m_iiu(d)) = m_Auu(d) * x(m_iiu(d));
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
b(m_iip(d)) = m_App(d) * x(m_iip(d));
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::dot_u(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &b_u) const
{
UNUSED(x_p);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
b_u(d) = m_Auu(d) * x_u(d);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::dot_p(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &b_p) const
{
UNUSED(x_u);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_p.size() == m_nnp);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
b_p(d) = m_App(d) * x_p(d);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::solve(
const xt::xtensor<double,2> &b,
xt::xtensor<double,2> &x)
{
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
this->factorize();
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if ( m_part(m,i) < m_nnu )
x(m,i) = m_inv_uu(m_part(m,i)) * b(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::solve(
const xt::xtensor<double,1> &b,
xt::xtensor<double,1> &x)
{
GOOSEFEM_ASSERT(b.size() == m_ndof);
GOOSEFEM_ASSERT(x.size() == m_ndof);
this->factorize();
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
x(m_iiu(d)) = m_inv_uu(d) * b(m_iiu(d));
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::solve_u(
const xt::xtensor<double,1> &b_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &x_u)
{
UNUSED(x_p);
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
this->factorize();
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
x_u(d) = m_inv_uu(d) * b_u(d);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::reaction(
const xt::xtensor<double,2> &x,
xt::xtensor<double,2> &b) const
{
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) >= m_nnu)
b(m,i) = m_App(m_part(m,i)-m_nnu) * x(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::reaction(
const xt::xtensor<double,1> &x,
xt::xtensor<double,1> &b) const
{
GOOSEFEM_ASSERT(x.size() == m_ndof);
GOOSEFEM_ASSERT(b.size() == m_ndof);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
b(m_iip(d)) = m_App(d) * x(m_iip(d));
}
// -------------------------------------------------------------------------------------------------
inline void MatrixDiagonalPartitioned::reaction_p(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &b_p) const
{
UNUSED(x_u);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_p.size() == m_nnp);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
b_p(d) = m_App(d) * x_p(d);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::AsDiagonal() const
{
xt::xtensor<double,1> out = xt::zeros<double>({m_ndof});
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
out(m_iiu(d)) = m_Auu(d);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
out(m_iip(d)) = m_App(d);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> MatrixDiagonalPartitioned::Dot(
const xt::xtensor<double,2> &x) const
{
xt::xtensor<double,2> b = xt::empty<double>({m_nnode, m_ndim});
this->dot(x, b);
return b;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::Dot(
const xt::xtensor<double,1> &x) const
{
xt::xtensor<double,1> b = xt::empty<double>({m_ndof});
this->dot(x, b);
return b;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::Dot_u(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p) const
{
xt::xtensor<double,1> b_u = xt::empty<double>({m_nnu});
this->dot_u(x_u, x_p, b_u);
return b_u;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::Dot_p(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p) const
{
xt::xtensor<double,1> b_p = xt::empty<double>({m_nnp});
this->dot_p(x_u, x_p, b_p);
return b_p;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> MatrixDiagonalPartitioned::Solve(
const xt::xtensor<double,2> &b,
const xt::xtensor<double,2> &x)
{
xt::xtensor<double,2> out = x;
this->solve(b, out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::Solve(
const xt::xtensor<double,1> &b,
const xt::xtensor<double,1> &x)
{
xt::xtensor<double,1> out = x;
this->solve(b, out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::Solve_u(
const xt::xtensor<double,1> &b_u,
const xt::xtensor<double,1> &x_p)
{
xt::xtensor<double,1> x_u = xt::empty<double>({m_nnu});
this->solve_u(b_u, x_p, x_u);
return x_u;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> MatrixDiagonalPartitioned::Reaction(
const xt::xtensor<double,2> &x,
const xt::xtensor<double,2> &b) const
{
xt::xtensor<double,2> out = b;
this->reaction(x, out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::Reaction(
const xt::xtensor<double,1> &x,
const xt::xtensor<double,1> &b) const
{
xt::xtensor<double,1> out = b;
this->reaction(x, out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> MatrixDiagonalPartitioned::Reaction_p(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p) const
{
xt::xtensor<double,1> b_p = xt::empty<double>({m_nnp});
this->reaction_p(x_u, x_p, b_p);
return b_p;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixPartitioned.h b/include/GooseFEM/MatrixPartitioned.h
index bd7b12b..5f13c24 100644
--- a/include/GooseFEM/MatrixPartitioned.h
+++ b/include/GooseFEM/MatrixPartitioned.h
@@ -1,173 +1,173 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXPARTITIONED_H
#define GOOSEFEM_MATRIXPARTITIONED_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class MatrixPartitioned
{
public:
// Constructors
MatrixPartitioned() = default;
MatrixPartitioned(
- const xt::xtensor<size_t,2> &conn,
- const xt::xtensor<size_t,2> &dofs,
- const xt::xtensor<size_t,1> &iip);
+ const xt::xtensor<size_t,2>& conn,
+ const xt::xtensor<size_t,2>& dofs,
+ const xt::xtensor<size_t,1>& iip);
// Dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
size_t nnu() const; // number of unknown DOFs
size_t nnp() const; // number of prescribed DOFs
// DOF lists
xt::xtensor<size_t,2> dofs() const; // DOFs
xt::xtensor<size_t,1> iiu() const; // unknown DOFs
xt::xtensor<size_t,1> iip() const; // prescribed DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
- void assemble(const xt::xtensor<double,3> &elemmat);
+ void assemble(const xt::xtensor<double,3>& elemmat);
// Solve:
// x_u = A_uu \ ( b_u - A_up * x_p )
void solve(
- const xt::xtensor<double,2> &b,
- xt::xtensor<double,2> &x); // modified with "x_u"
+ const xt::xtensor<double,2>& b,
+ xt::xtensor<double,2>& x); // modified with "x_u"
void solve(
- const xt::xtensor<double,1> &b,
- xt::xtensor<double,1> &x); // modified with "x_u"
+ const xt::xtensor<double,1>& b,
+ xt::xtensor<double,1>& x); // modified with "x_u"
void solve_u(
- const xt::xtensor<double,1> &b_u,
- const xt::xtensor<double,1> &x_p,
- xt::xtensor<double,1> &x_u); // overwritten
+ const xt::xtensor<double,1>& b_u,
+ const xt::xtensor<double,1>& x_p,
+ xt::xtensor<double,1>& x_u); // overwritten
// Get right-hand-size for corresponding to the prescribed DOFs:
// b_p = A_pu * x_u + A_pp * x_p = A_pp * x_p
void reaction(
- const xt::xtensor<double,2> &x,
- xt::xtensor<double,2> &b) const; // modified with "b_p"
+ const xt::xtensor<double,2>& x,
+ xt::xtensor<double,2>& b) const; // modified with "b_p"
void reaction(
- const xt::xtensor<double,1> &x,
- xt::xtensor<double,1> &b) const; // modified with "b_p"
+ const xt::xtensor<double,1>& x,
+ xt::xtensor<double,1>& b) const; // modified with "b_p"
void reaction_p(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p,
- xt::xtensor<double,1> &b_p) const; // overwritten
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p,
+ xt::xtensor<double,1>& b_p) const; // overwritten
// Auto-allocation of the functions above
xt::xtensor<double,2> Solve(
- const xt::xtensor<double,2> &b,
- const xt::xtensor<double,2> &x);
+ const xt::xtensor<double,2>& b,
+ const xt::xtensor<double,2>& x);
xt::xtensor<double,1> Solve(
- const xt::xtensor<double,1> &b,
- const xt::xtensor<double,1> &x);
+ const xt::xtensor<double,1>& b,
+ const xt::xtensor<double,1>& x);
xt::xtensor<double,1> Solve_u(
- const xt::xtensor<double,1> &b_u,
- const xt::xtensor<double,1> &x_p);
+ const xt::xtensor<double,1>& b_u,
+ const xt::xtensor<double,1>& x_p);
xt::xtensor<double,2> Reaction(
- const xt::xtensor<double,2> &x,
- const xt::xtensor<double,2> &b) const;
+ const xt::xtensor<double,2>& x,
+ const xt::xtensor<double,2>& b) const;
xt::xtensor<double,1> Reaction(
- const xt::xtensor<double,1> &x,
- const xt::xtensor<double,1> &b) const;
+ const xt::xtensor<double,1>& x,
+ const xt::xtensor<double,1>& b) const;
xt::xtensor<double,1> Reaction_p(
- const xt::xtensor<double,1> &x_u,
- const xt::xtensor<double,1> &x_p) const;
+ const xt::xtensor<double,1>& x_u,
+ const xt::xtensor<double,1>& x_p) const;
private:
// The matrix
Eigen::SparseMatrix<double> m_Auu;
Eigen::SparseMatrix<double> m_Aup;
Eigen::SparseMatrix<double> m_Apu;
Eigen::SparseMatrix<double> m_App;
// Matrix entries
std::vector<Eigen::Triplet<double>> m_Tuu;
std::vector<Eigen::Triplet<double>> m_Tup;
std::vector<Eigen::Triplet<double>> m_Tpu;
std::vector<Eigen::Triplet<double>> m_Tpp;
// Solver (re-used to solve different RHS)
Solver m_solver;
// Signal changes to data compare to the last inverse
bool m_factor=false;
// Bookkeeping
xt::xtensor<size_t,2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t,2> m_dofs; // DOF-numbers per node [nnode, ndim]
xt::xtensor<size_t,2> m_part; // DOF-numbers per node, renumbered [nnode, ndim]
xt::xtensor<size_t,1> m_iiu; // unknown DOFs [nnu]
xt::xtensor<size_t,1> m_iip; // prescribed DOFs [nnp]
// Dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
size_t m_nnu; // number of unknown DOFs
size_t m_nnp; // number of prescribed DOFs
// Compute inverse (automatically evaluated by "solve")
void factorize();
// Convert arrays (Eigen version of VectorPartitioned, which contains public functions)
- Eigen::VectorXd asDofs_u(const xt::xtensor<double,1> &dofval ) const;
- Eigen::VectorXd asDofs_u(const xt::xtensor<double,2> &nodevec) const;
- Eigen::VectorXd asDofs_p(const xt::xtensor<double,1> &dofval ) const;
- Eigen::VectorXd asDofs_p(const xt::xtensor<double,2> &nodevec) const;
+ Eigen::VectorXd asDofs_u(const xt::xtensor<double,1>& dofval ) const;
+ Eigen::VectorXd asDofs_u(const xt::xtensor<double,2>& nodevec) const;
+ Eigen::VectorXd asDofs_p(const xt::xtensor<double,1>& dofval ) const;
+ Eigen::VectorXd asDofs_p(const xt::xtensor<double,2>& nodevec) const;
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#include "MatrixPartitioned.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixPartitioned.hpp b/include/GooseFEM/MatrixPartitioned.hpp
index cddb322..33efd49 100644
--- a/include/GooseFEM/MatrixPartitioned.hpp
+++ b/include/GooseFEM/MatrixPartitioned.hpp
@@ -1,487 +1,500 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXPARTITIONED_HPP
#define GOOSEFEM_MATRIXPARTITIONED_HPP
// -------------------------------------------------------------------------------------------------
#include "MatrixPartitioned.h"
#include "Mesh.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline MatrixPartitioned<Solver>::MatrixPartitioned(
const xt::xtensor<size_t,2> &conn,
const xt::xtensor<size_t,2> &dofs,
const xt::xtensor<size_t,1> &iip) :
m_conn(conn), m_dofs(dofs), m_iip(iip)
{
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
- m_iiu = xt::setdiff1d(dofs, iip);
+ m_iiu = xt::setdiff1d(dofs, iip);
- m_ndof = xt::amax(m_dofs)[0] + 1;
- m_nnp = m_iip.size();
- m_nnu = m_iiu.size();
+ m_ndof = xt::amax(m_dofs)[0] + 1;
+ m_nnp = m_iip.size();
+ m_nnu = m_iiu.size();
- m_part = Mesh::Reorder({m_iiu, m_iip}).get(m_dofs);
+ m_part = Mesh::Reorder({m_iiu, m_iip}).get(m_dofs);
- m_Tuu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
- m_Tup.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
- m_Tpu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
- m_Tpp.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
+ m_Tuu.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
+ m_Tup.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
+ m_Tpu.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
+ m_Tpp.reserve(m_nelem * m_nne * m_ndim * m_nne * m_ndim);
- m_Auu.resize(m_nnu,m_nnu);
- m_Aup.resize(m_nnu,m_nnp);
- m_Apu.resize(m_nnp,m_nnu);
- m_App.resize(m_nnp,m_nnp);
+ m_Auu.resize(m_nnu, m_nnu);
+ m_Aup.resize(m_nnu, m_nnp);
+ m_Apu.resize(m_nnp, m_nnu);
+ m_App.resize(m_nnp, m_nnp);
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(xt::amax(m_iip)[0] <= xt::amax(m_dofs)[0]);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nnu() const
{
return m_nnu;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitioned<Solver>::nnp() const
{
return m_nnp;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,2> MatrixPartitioned<Solver>::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitioned<Solver>::iiu() const
{
return m_iiu;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitioned<Solver>::iip() const
{
return m_iip;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::factorize()
{
if (!m_factor) return;
-
-
m_solver.compute(m_Auu);
-
m_factor = false;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::assemble(const xt::xtensor<double,3> &elemmat)
{
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
m_Tuu.clear();
m_Tup.clear();
m_Tpu.clear();
m_Tpp.clear();
for (size_t e = 0 ; e < m_nelem ; ++e) {
for (size_t m = 0 ; m < m_nne ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
size_t di = m_part(m_conn(e,m),i);
for (size_t n = 0 ; n < m_nne ; ++n) {
for (size_t j = 0 ; j < m_ndim ; ++j) {
size_t dj = m_part(m_conn(e,n),j);
- if (di < m_nnu and dj < m_nnu)
- m_Tuu.push_back(Eigen::Triplet<double>(di ,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (di < m_nnu)
- m_Tup.push_back(Eigen::Triplet<double>(di ,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (dj < m_nnu)
- m_Tpu.push_back(Eigen::Triplet<double>(di-m_nnu,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else
- m_Tpp.push_back(Eigen::Triplet<double>(di-m_nnu,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
+ if (di < m_nnu && dj < m_nnu) {
+ m_Tuu.push_back(Eigen::Triplet<double>(
+ di,
+ dj,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (di < m_nnu) {
+ m_Tup.push_back(Eigen::Triplet<double>(
+ di,
+ dj - m_nnu,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (dj < m_nnu) {
+ m_Tpu.push_back(Eigen::Triplet<double>(
+ di - m_nnu,
+ dj,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else {
+ m_Tpp.push_back(Eigen::Triplet<double>(
+ di - m_nnu,
+ dj - m_nnu,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
}
}
}
}
}
m_Auu.setFromTriplets(m_Tuu.begin(), m_Tuu.end());
m_Aup.setFromTriplets(m_Tup.begin(), m_Tup.end());
m_Apu.setFromTriplets(m_Tpu.begin(), m_Tpu.end());
m_App.setFromTriplets(m_Tpp.begin(), m_Tpp.end());
m_factor = true;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::solve(
const xt::xtensor<double,2> &b,
xt::xtensor<double,2> &x)
{
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
this->factorize();
Eigen::VectorXd B_u = this->asDofs_u(b);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_Aup * X_p));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if ( m_part(m,i) < m_nnu )
x(m,i) = X_u(m_part(m,i));
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::solve(
const xt::xtensor<double,1> &b,
xt::xtensor<double,1> &x)
{
GOOSEFEM_ASSERT(b.size() == m_ndof);
GOOSEFEM_ASSERT(x.size() == m_ndof);
this->factorize();
Eigen::VectorXd B_u = this->asDofs_u(b);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_Aup * X_p));
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
x(m_iiu(d)) = X_u(d);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::solve_u(
const xt::xtensor<double,1> &b_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &x_u)
{
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
this->factorize();
Eigen::VectorXd B_u(m_nnu,1);
Eigen::VectorXd X_p(m_nnp,1);
std::copy(b_u.begin(), b_u.end(), B_u.data());
std::copy(x_p.begin(), x_p.end(), X_p.data());
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_Aup * X_p));
std::copy(X_u.data(), X_u.data()+m_nnu, x_u.begin());
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::reaction(
const xt::xtensor<double,2> &x,
xt::xtensor<double,2> &b) const
{
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd X_u = this->asDofs_u(x);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) >= m_nnu)
b(m,i) = B_p(m_part(m,i)-m_nnu);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::reaction(
const xt::xtensor<double,1> &x,
xt::xtensor<double,1> &b) const
{
GOOSEFEM_ASSERT(x.size() == m_ndof);
GOOSEFEM_ASSERT(b.size() == m_ndof);
Eigen::VectorXd X_u = this->asDofs_u(x);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
b(m_iip(d)) = B_p(d);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitioned<Solver>::reaction_p(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &b_p) const
{
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(b_p.size() == m_nnp);
Eigen::VectorXd X_u(m_nnu,1);
Eigen::VectorXd X_p(m_nnp,1);
std::copy(x_u.begin(), x_u.end(), X_u.data());
std::copy(x_p.begin(), x_p.end(), X_p.data());
Eigen::VectorXd B_p = m_Apu * X_u + m_App * X_p;
std::copy(B_p.data(), B_p.data()+m_nnp, b_p.begin());
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,2> MatrixPartitioned<Solver>::Solve(
const xt::xtensor<double,2> &b,
const xt::xtensor<double,2> &x)
{
xt::xtensor<double,2> out = x;
this->solve(b, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::Solve(
const xt::xtensor<double,1> &b,
const xt::xtensor<double,1> &x)
{
xt::xtensor<double,1> out = x;
this->solve(b, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::Solve_u(
const xt::xtensor<double,1> &b_u,
const xt::xtensor<double,1> &x_p)
{
xt::xtensor<double,1> x_u = xt::empty<double>({m_nnu});
this->solve_u(b_u, x_p, x_u);
return x_u;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,2> MatrixPartitioned<Solver>::Reaction(
const xt::xtensor<double,2> &x,
const xt::xtensor<double,2> &b) const
{
xt::xtensor<double,2> out = b;
this->reaction(x, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::Reaction(
const xt::xtensor<double,1> &x,
const xt::xtensor<double,1> &b) const
{
xt::xtensor<double,1> out = b;
this->reaction(x, out);
return out;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<double,1> MatrixPartitioned<Solver>::Reaction_p(
const xt::xtensor<double,1> &x_u,
const xt::xtensor<double,1> &x_p) const
{
xt::xtensor<double,1> b_p = xt::empty<double>({m_nnp});
this->reaction_p(x_u, x_p, b_p);
return b_p;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::asDofs_u(
const xt::xtensor<double,1> &dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_u(m_nnu,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
dofval_u(d) = dofval(m_iiu(d));
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::asDofs_u(
const xt::xtensor<double,2> &nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_u(m_nnu,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) < m_nnu)
dofval_u(m_part(m,i)) = nodevec(m,i);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::asDofs_p(
const xt::xtensor<double,1> &dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_p(m_nnp,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
dofval_p(d) = dofval(m_iip(d));
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitioned<Solver>::asDofs_p(
const xt::xtensor<double,2> &nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_p(m_nnp,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) >= m_nnu)
dofval_p(m_part(m,i)-m_nnu) = nodevec(m,i);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixPartitionedTyings.h b/include/GooseFEM/MatrixPartitionedTyings.h
index 930b3d0..44e4bd3 100644
--- a/include/GooseFEM/MatrixPartitionedTyings.h
+++ b/include/GooseFEM/MatrixPartitionedTyings.h
@@ -1,167 +1,182 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXPARTITIONEDTYINGS_H
#define GOOSEFEM_MATRIXPARTITIONEDTYINGS_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class MatrixPartitionedTyings
{
public:
// Constructors
MatrixPartitionedTyings() = default;
MatrixPartitionedTyings(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<size_t,2>& dofs,
const Eigen::SparseMatrix<double>& Cdu,
const Eigen::SparseMatrix<double>& Cdp);
// Dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
size_t nnu() const; // number of independent, unknown DOFs
size_t nnp() const; // number of independent, prescribed DOFs
size_t nni() const; // number of independent DOFs
size_t nnd() const; // number of dependent DOFs
// DOF lists
xt::xtensor<size_t,2> dofs() const; // DOFs
xt::xtensor<size_t,1> iiu() const; // independent, unknown DOFs
xt::xtensor<size_t,1> iip() const; // independent, prescribed DOFs
xt::xtensor<size_t,1> iii() const; // independent DOFs
xt::xtensor<size_t,1> iid() const; // dependent DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
- void assemble(const xt::xtensor<double,3> &elemmat);
+ void assemble(const xt::xtensor<double,3>& elemmat);
// Solve:
// A' = A_ii + K_id * C_di + C_di^T * K_di + C_di^T * K_dd * C_di
// b' = b_i + C_di^T * b_d
// x_u = A'_uu \ ( b'_u - A'_up * x_p )
// x_i = [x_u, x_p]
// x_d = C_di * x_i
void solve(
- const xt::xtensor<double,2> &b,
- xt::xtensor<double,2> &x); // modified with "x_u", "x_d"
+ const xt::xtensor<double,2>& b,
+ xt::xtensor<double,2>& x); // modified with "x_u", "x_d"
void solve(
- const xt::xtensor<double,1> &b,
- xt::xtensor<double,1> &x); // modified with "x_u", "x_d"
+ const xt::xtensor<double,1>& b,
+ xt::xtensor<double,1>& x); // modified with "x_u", "x_d"
void solve_u(
- const xt::xtensor<double,1> &b_u,
- const xt::xtensor<double,1> &b_d,
- const xt::xtensor<double,1> &x_p,
- xt::xtensor<double,1> &x_u); // overwritten
+ const xt::xtensor<double,1>& b_u,
+ const xt::xtensor<double,1>& b_d,
+ const xt::xtensor<double,1>& x_p,
+ xt::xtensor<double,1>& x_u); // overwritten
+
+ // Auto-allocation of the functions above
+
+ xt::xtensor<double,2> Solve(
+ const xt::xtensor<double,2>& b,
+ const xt::xtensor<double,2>& x);
+
+ xt::xtensor<double,1> Solve(
+ const xt::xtensor<double,1>& b,
+ const xt::xtensor<double,1>& x);
+
+ xt::xtensor<double,1> Solve_u(
+ const xt::xtensor<double,1>& b_u,
+ const xt::xtensor<double,1>& b_d,
+ const xt::xtensor<double,1>& x_p);
private:
// The matrix
Eigen::SparseMatrix<double> m_Auu;
Eigen::SparseMatrix<double> m_Aup;
Eigen::SparseMatrix<double> m_Apu;
Eigen::SparseMatrix<double> m_App;
Eigen::SparseMatrix<double> m_Aud;
Eigen::SparseMatrix<double> m_Apd;
Eigen::SparseMatrix<double> m_Adu;
Eigen::SparseMatrix<double> m_Adp;
Eigen::SparseMatrix<double> m_Add;
// The matrix for which the tyings have been applied
Eigen::SparseMatrix<double> m_ACuu;
Eigen::SparseMatrix<double> m_ACup;
Eigen::SparseMatrix<double> m_ACpu;
Eigen::SparseMatrix<double> m_ACpp;
// Matrix entries
std::vector<Eigen::Triplet<double>> m_Tuu;
std::vector<Eigen::Triplet<double>> m_Tup;
std::vector<Eigen::Triplet<double>> m_Tpu;
std::vector<Eigen::Triplet<double>> m_Tpp;
std::vector<Eigen::Triplet<double>> m_Tud;
std::vector<Eigen::Triplet<double>> m_Tpd;
std::vector<Eigen::Triplet<double>> m_Tdu;
std::vector<Eigen::Triplet<double>> m_Tdp;
std::vector<Eigen::Triplet<double>> m_Tdd;
// Solver (re-used to solve different RHS)
Solver m_solver;
// Signal changes to data compare to the last inverse
bool m_factor=false;
// Bookkeeping
xt::xtensor<size_t,2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t,2> m_dofs; // DOF-numbers per node [nnode, ndim]
xt::xtensor<size_t,1> m_iiu; // unknown DOFs [nnu]
xt::xtensor<size_t,1> m_iip; // prescribed DOFs [nnp]
xt::xtensor<size_t,1> m_iid; // dependent DOFs [nnd]
// Dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
size_t m_nnu; // number of independent, unknown DOFs
size_t m_nnp; // number of independent, prescribed DOFs
size_t m_nni; // number of independent DOFs
size_t m_nnd; // number of dependent DOFs
// Tyings
Eigen::SparseMatrix<double> m_Cdu;
Eigen::SparseMatrix<double> m_Cdp;
Eigen::SparseMatrix<double> m_Cud;
Eigen::SparseMatrix<double> m_Cpd;
// Compute inverse (automatically evaluated by "solve")
void factorize();
// Convert arrays (Eigen version of VectorPartitioned, which contains public functions)
- Eigen::VectorXd asDofs_u(const xt::xtensor<double,1> &dofval ) const;
- Eigen::VectorXd asDofs_u(const xt::xtensor<double,2> &nodevec) const;
- Eigen::VectorXd asDofs_p(const xt::xtensor<double,1> &dofval ) const;
- Eigen::VectorXd asDofs_p(const xt::xtensor<double,2> &nodevec) const;
- Eigen::VectorXd asDofs_d(const xt::xtensor<double,1> &dofval ) const;
- Eigen::VectorXd asDofs_d(const xt::xtensor<double,2> &nodevec) const;
+ Eigen::VectorXd asDofs_u(const xt::xtensor<double,1>& dofval ) const;
+ Eigen::VectorXd asDofs_u(const xt::xtensor<double,2>& nodevec) const;
+ Eigen::VectorXd asDofs_p(const xt::xtensor<double,1>& dofval ) const;
+ Eigen::VectorXd asDofs_p(const xt::xtensor<double,2>& nodevec) const;
+ Eigen::VectorXd asDofs_d(const xt::xtensor<double,1>& dofval ) const;
+ Eigen::VectorXd asDofs_d(const xt::xtensor<double,2>& nodevec) const;
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#include "MatrixPartitionedTyings.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MatrixPartitionedTyings.hpp b/include/GooseFEM/MatrixPartitionedTyings.hpp
index 1590494..15d3783 100644
--- a/include/GooseFEM/MatrixPartitionedTyings.hpp
+++ b/include/GooseFEM/MatrixPartitionedTyings.hpp
@@ -1,462 +1,537 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXPARTITIONEDTYINGS_HPP
#define GOOSEFEM_MATRIXPARTITIONEDTYINGS_HPP
// -------------------------------------------------------------------------------------------------
#include "MatrixPartitionedTyings.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline MatrixPartitionedTyings<Solver>::MatrixPartitionedTyings(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<size_t,2>& dofs,
const Eigen::SparseMatrix<double>& Cdu,
const Eigen::SparseMatrix<double>& Cdp) :
m_conn(conn),
m_dofs(dofs),
m_Cdu(Cdu),
m_Cdp(Cdp)
{
GOOSEFEM_ASSERT(Cdu.rows() == Cdp.rows());
- m_nnu = static_cast<size_t>(m_Cdu.cols());
- m_nnp = static_cast<size_t>(m_Cdp.cols());
- m_nnd = static_cast<size_t>(m_Cdp.rows());
- m_nni = m_nnu + m_nnp;
- m_ndof = m_nni + m_nnd;
+ m_nnu = static_cast<size_t>(m_Cdu.cols());
+ m_nnp = static_cast<size_t>(m_Cdp.cols());
+ m_nnd = static_cast<size_t>(m_Cdp.rows());
+ m_nni = m_nnu + m_nnp;
+ m_ndof = m_nni + m_nnd;
- m_iiu = xt::arange<size_t>(m_nnu);
- m_iip = xt::arange<size_t>(m_nnu, m_nnu + m_nnp);
- m_iid = xt::arange<size_t>(m_nni, m_nni + m_nnd);
+ m_iiu = xt::arange<size_t>(m_nnu);
+ m_iip = xt::arange<size_t>(m_nnu, m_nnu + m_nnp);
+ m_iid = xt::arange<size_t>(m_nni, m_nni + m_nnd);
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
- m_Cud = m_Cdu.transpose();
- m_Cpd = m_Cdp.transpose();
+ m_Cud = m_Cdu.transpose();
+ m_Cpd = m_Cdp.transpose();
m_Tuu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tup.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tpu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tpp.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tud.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tpd.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tdu.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tdp.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Tdd.reserve(m_nelem*m_nne*m_ndim*m_nne*m_ndim);
m_Auu.resize(m_nnu,m_nnu);
m_Aup.resize(m_nnu,m_nnp);
m_Apu.resize(m_nnp,m_nnu);
m_App.resize(m_nnp,m_nnp);
m_Aud.resize(m_nnu,m_nnd);
m_Apd.resize(m_nnp,m_nnd);
m_Adu.resize(m_nnd,m_nnu);
m_Adp.resize(m_nnd,m_nnp);
m_Add.resize(m_nnd,m_nnd);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
GOOSEFEM_ASSERT(m_ndof == xt::amax(m_dofs)[0] + 1);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitionedTyings<Solver>::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitionedTyings<Solver>::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitionedTyings<Solver>::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitionedTyings<Solver>::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitionedTyings<Solver>::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitionedTyings<Solver>::nnu() const
{
return m_nnu;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline size_t MatrixPartitionedTyings<Solver>::nnp() const
{
return m_nnp;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,2> MatrixPartitionedTyings<Solver>::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitionedTyings<Solver>::iiu() const
{
return m_iiu;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitionedTyings<Solver>::iip() const
{
return m_iip;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitionedTyings<Solver>::iii() const
{
return xt::arange<size_t>(m_nni);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline xt::xtensor<size_t,1> MatrixPartitionedTyings<Solver>::iid() const
{
return m_iid;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitionedTyings<Solver>::factorize()
{
if (!m_factor) return;
m_ACuu = m_Auu + m_Aud * m_Cdu + m_Cud * m_Adu + m_Cud * m_Add * m_Cdu;
m_ACup = m_Aup + m_Aud * m_Cdp + m_Cud * m_Adp + m_Cud * m_Add * m_Cdp;
// m_ACpu = m_Apu + m_Apd * m_Cdu + m_Cpd * m_Adu + m_Cpd * m_Add * m_Cdu;
// m_ACpp = m_App + m_Apd * m_Cdp + m_Cpd * m_Adp + m_Cpd * m_Add * m_Cdp;
m_solver.compute(m_ACuu);
m_factor = false;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitionedTyings<Solver>::assemble(const xt::xtensor<double,3>& elemmat)
{
GOOSEFEM_ASSERT(elemmat.shape() ==\
std::decay_t<decltype(elemmat)>::shape_type({m_nelem, m_nne*m_ndim, m_nne*m_ndim}));
m_Tuu.clear();
m_Tup.clear();
m_Tpu.clear();
m_Tpp.clear();
m_Tud.clear();
m_Tpd.clear();
m_Tdu.clear();
m_Tdp.clear();
m_Tdd.clear();
for (size_t e = 0 ; e < m_nelem ; ++e) {
for (size_t m = 0 ; m < m_nne ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
size_t di = m_dofs(m_conn(e,m),i);
for (size_t n = 0 ; n < m_nne ; ++n) {
for (size_t j = 0 ; j < m_ndim ; ++j) {
size_t dj = m_dofs(m_conn(e,n),j);
- if (di < m_nnu and dj < m_nnu)
- m_Tuu.push_back(Eigen::Triplet<double>(di ,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (di < m_nnu and dj < m_nni)
- m_Tup.push_back(Eigen::Triplet<double>(di ,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (di < m_nnu)
- m_Tud.push_back(Eigen::Triplet<double>(di ,dj-m_nni,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (di < m_nni and dj < m_nnu)
- m_Tpu.push_back(Eigen::Triplet<double>(di-m_nnu,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (di < m_nni and dj < m_nni)
- m_Tpp.push_back(Eigen::Triplet<double>(di-m_nnu,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (di < m_nni)
- m_Tpd.push_back(Eigen::Triplet<double>(di-m_nnu,dj-m_nni,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (dj < m_nnu)
- m_Tdu.push_back(Eigen::Triplet<double>(di-m_nni,dj ,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else if (dj < m_nni)
- m_Tdp.push_back(Eigen::Triplet<double>(di-m_nni,dj-m_nnu,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
- else
- m_Tdd.push_back(Eigen::Triplet<double>(di-m_nni,dj-m_nni,elemmat(e,m*m_ndim+i,n*m_ndim+j)));
+ if (di < m_nnu && dj < m_nnu) {
+ m_Tuu.push_back(Eigen::Triplet<double>(
+ di,
+ dj,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (di < m_nnu && dj < m_nni) {
+ m_Tup.push_back(Eigen::Triplet<double>(
+ di,
+ dj - m_nnu,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (di < m_nnu) {
+ m_Tud.push_back(Eigen::Triplet<double>(
+ di,
+ dj - m_nni,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (di < m_nni && dj < m_nnu) {
+ m_Tpu.push_back(Eigen::Triplet<double>(
+ di - m_nnu,
+ dj,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (di < m_nni && dj < m_nni) {
+ m_Tpp.push_back(Eigen::Triplet<double>(
+ di - m_nnu,
+ dj - m_nnu,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (di < m_nni) {
+ m_Tpd.push_back(Eigen::Triplet<double>(
+ di - m_nnu,
+ dj - m_nni,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (dj < m_nnu) {
+ m_Tdu.push_back(Eigen::Triplet<double>(
+ di - m_nni,
+ dj,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else if (dj < m_nni) {
+ m_Tdp.push_back(Eigen::Triplet<double>(
+ di - m_nni,
+ dj - m_nnu,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
+ else {
+ m_Tdd.push_back(Eigen::Triplet<double>(
+ di - m_nni,
+ dj - m_nni,
+ elemmat(e, m * m_ndim + i, n * m_ndim + j)));
+ }
}
}
}
}
}
m_Auu.setFromTriplets(m_Tuu.begin(), m_Tuu.end());
m_Aup.setFromTriplets(m_Tup.begin(), m_Tup.end());
m_Apu.setFromTriplets(m_Tpu.begin(), m_Tpu.end());
m_App.setFromTriplets(m_Tpp.begin(), m_Tpp.end());
m_Aud.setFromTriplets(m_Tud.begin(), m_Tud.end());
m_Apd.setFromTriplets(m_Tpd.begin(), m_Tpd.end());
m_Adu.setFromTriplets(m_Tdu.begin(), m_Tdu.end());
m_Adp.setFromTriplets(m_Tdp.begin(), m_Tdp.end());
m_Add.setFromTriplets(m_Tdd.begin(), m_Tdd.end());
m_factor = true;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitionedTyings<Solver>::solve(
const xt::xtensor<double,2>& b,
xt::xtensor<double,2>& x)
{
GOOSEFEM_ASSERT(b.shape() ==\
std::decay_t<decltype(b)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(x.shape() ==\
std::decay_t<decltype(x)>::shape_type({m_nnode, m_ndim}));
this->factorize();
Eigen::VectorXd B_u = this->asDofs_u(b);
Eigen::VectorXd B_d = this->asDofs_d(b);
Eigen::VectorXd X_p = this->asDofs_p(x);
B_u += m_Cud * B_d;
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_ACup * X_p));
Eigen::VectorXd X_d = m_Cdu * X_u + m_Cdp * X_p;
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
if (m_dofs(m,i) < m_nnu)
x(m,i) = X_u(m_dofs(m,i));
else if (m_dofs(m,i) >= m_nni)
x(m,i) = X_d(m_dofs(m,i)-m_nni);
}
}
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitionedTyings<Solver>::solve(
const xt::xtensor<double,1>& b,
xt::xtensor<double,1>& x)
{
GOOSEFEM_ASSERT(b.size() == m_ndof);
GOOSEFEM_ASSERT(x.size() == m_ndof);
this->factorize();
Eigen::VectorXd B_u = this->asDofs_u(b);
Eigen::VectorXd B_d = this->asDofs_d(b);
Eigen::VectorXd X_p = this->asDofs_p(x);
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_ACup * X_p));
Eigen::VectorXd X_d = m_Cdu * X_u + m_Cdp * X_p;
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
x(m_iiu(d)) = X_u(d);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnd ; ++d)
x(m_iid(d)) = X_d(d);
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline void MatrixPartitionedTyings<Solver>::solve_u(
const xt::xtensor<double,1>& b_u,
const xt::xtensor<double,1>& b_d,
const xt::xtensor<double,1>& x_p,
xt::xtensor<double,1>& x_u)
{
GOOSEFEM_ASSERT(b_u.size() == m_nnu);
GOOSEFEM_ASSERT(b_d.size() == m_nnd);
GOOSEFEM_ASSERT(x_p.size() == m_nnp);
GOOSEFEM_ASSERT(x_u.size() == m_nnu);
this->factorize();
Eigen::VectorXd B_u(m_nnu,1);
Eigen::VectorXd B_d(m_nnd,1);
Eigen::VectorXd X_p(m_nnp,1);
std::copy(b_u.begin(), b_u.end(), B_u.data());
std::copy(b_d.begin(), b_d.end(), B_d.data());
std::copy(x_p.begin(), x_p.end(), X_p.data());
Eigen::VectorXd X_u = m_solver.solve(Eigen::VectorXd(B_u - m_ACup * X_p));
std::copy(X_u.data(), X_u.data()+m_nnu, x_u.begin());
}
// -------------------------------------------------------------------------------------------------
+// -------------------------------------------------------------------------------------------------
+
+template <class Solver>
+inline xt::xtensor<double,2> MatrixPartitionedTyings<Solver>::Solve(
+ const xt::xtensor<double,2> &b,
+ const xt::xtensor<double,2> &x)
+{
+ xt::xtensor<double,2> out = x;
+ this->solve(b, out);
+ return out;
+}
+
+// -------------------------------------------------------------------------------------------------
+
+template <class Solver>
+inline xt::xtensor<double,1> MatrixPartitionedTyings<Solver>::Solve(
+ const xt::xtensor<double,1> &b,
+ const xt::xtensor<double,1> &x)
+{
+ xt::xtensor<double,1> out = x;
+ this->solve(b, out);
+ return out;
+}
+
+// -------------------------------------------------------------------------------------------------
+
+template <class Solver>
+inline xt::xtensor<double,1> MatrixPartitionedTyings<Solver>::Solve_u(
+ const xt::xtensor<double,1> &b_u,
+ const xt::xtensor<double,1> &b_d,
+ const xt::xtensor<double,1> &x_p)
+{
+ xt::xtensor<double,1> x_u = xt::empty<double>({m_nnu});
+ this->solve_u(b_u, b_d, x_p, x_u);
+ return x_u;
+}
+
+// -------------------------------------------------------------------------------------------------
+
template <class Solver>
inline Eigen::VectorXd MatrixPartitionedTyings<Solver>::asDofs_u(
const xt::xtensor<double,1>& dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_u(m_nnu,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
dofval_u(d) = dofval(m_iiu(d));
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitionedTyings<Solver>::asDofs_u(
const xt::xtensor<double,2>& nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_u(m_nnu,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_dofs(m,i) < m_nnu)
dofval_u(m_dofs(m,i)) = nodevec(m,i);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitionedTyings<Solver>::asDofs_p(
const xt::xtensor<double,1>& dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_p(m_nnp,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
dofval_p(d) = dofval(m_iip(d));
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitionedTyings<Solver>::asDofs_p(
const xt::xtensor<double,2>& nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_p(m_nnp,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
- if (m_dofs(m,i) >= m_nnu and m_dofs(m,i) < m_nni)
+ if (m_dofs(m,i) >= m_nnu && m_dofs(m,i) < m_nni)
dofval_p(m_dofs(m,i)-m_nnu) = nodevec(m,i);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitionedTyings<Solver>::asDofs_d(
const xt::xtensor<double,1>& dofval) const
{
assert(dofval.size() == m_ndof);
Eigen::VectorXd dofval_d(m_nnd,1);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnd ; ++d)
dofval_d(d) = dofval(m_iip(d));
return dofval_d;
}
// -------------------------------------------------------------------------------------------------
template <class Solver>
inline Eigen::VectorXd MatrixPartitionedTyings<Solver>::asDofs_d(
const xt::xtensor<double,2>& nodevec) const
{
assert(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_d(m_nnd,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_dofs(m,i) >= m_nni)
dofval_d(m_dofs(m,i)-m_nni) = nodevec(m,i);
return dofval_d;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/Mesh.hpp b/include/GooseFEM/Mesh.hpp
index 4c89666..e672a5b 100644
--- a/include/GooseFEM/Mesh.hpp
+++ b/include/GooseFEM/Mesh.hpp
@@ -1,193 +1,193 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MESH_HPP
#define GOOSEFEM_MESH_HPP
// -------------------------------------------------------------------------------------------------
#include "Mesh.h"
// =================================================================================================
namespace GooseFEM {
namespace Mesh {
// -------------------------------------------------------------------------------------------------
inline Renumber::Renumber(const xt::xarray<size_t>& dofs)
{
size_t n = xt::amax(dofs)[0]+1;
size_t i = 0;
xt::xtensor<size_t,1> unique = xt::unique(dofs);
m_renum = xt::empty<size_t>({n});
for (auto& j : unique) {
m_renum(j) = i;
++i;
}
}
// -------------------------------------------------------------------------------------------------
// apply renumbering, e.g. for a matrix:
//
// out(i,j) = renum(list(i,j))
template <class T>
T Renumber::apply(const T& list) const
{
T out = T::from_shape(list.shape());
auto jt = out.begin();
- for ( auto it = list.begin() ; it != list.end() ; ++it, ++jt )
+ for (auto it = list.begin(); it != list.end(); ++it, ++jt)
*jt = m_renum(*it);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Renumber::get(const xt::xtensor<size_t,2>& dofs) const
{
return this->apply(dofs);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Renumber::index() const
{
return m_renum;
}
// -------------------------------------------------------------------------------------------------
inline Reorder::Reorder(const std::initializer_list<xt::xtensor<size_t,1>> args)
{
size_t n = 0;
size_t i = 0;
for (auto& arg : args) {
if (arg.size() == 0) continue;
n = std::max(n, xt::amax(arg)[0]+1);
}
#ifdef GOOSEFEM_ENABLE_ASSERT
for (auto& arg : args)
GOOSEFEM_ASSERT(xt::unique(arg) == xt::sort(arg));
#endif
m_renum = xt::empty<size_t>({n});
for (auto& arg : args)
{
for (auto& j : arg)
{
m_renum(j) = i;
++i;
}
}
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Reorder::get(const xt::xtensor<size_t,2>& dofs) const
{
return this->apply(dofs);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Reorder::index() const
{
return m_renum;
}
// -------------------------------------------------------------------------------------------------
// apply renumbering, e.g. for a matrix:
//
// out(i,j) = renum(list(i,j))
template <class T>
T Reorder::apply(const T& list) const
{
T out = T::from_shape(list.shape());
auto jt = out.begin();
- for ( auto it = list.begin() ; it != list.end() ; ++it, ++jt )
+ for (auto it = list.begin(); it != list.end(); ++it, ++jt)
*jt = m_renum(*it);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> renumber(const xt::xtensor<size_t,2> &dofs)
{
return Renumber(dofs).get(dofs);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> dofs(size_t nnode, size_t ndim)
{
return xt::reshape_view(xt::arange<size_t>(nnode*ndim),{nnode,ndim});
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> coordination(const xt::xtensor<size_t,2> &conn)
{
// get number of nodes
size_t nnode = xt::amax(conn)[0] + 1;
// number of elements connected to each node
// - allocate
xt::xtensor<size_t,1> N = xt::zeros<size_t>({nnode});
// - fill from connectivity
- for ( auto it = conn.begin(); it != conn.end(); ++it ) N(*it) += 1;
+ for (auto it = conn.begin(); it != conn.end(); ++it) N(*it) += 1;
return N;
}
// -------------------------------------------------------------------------------------------------
inline std::vector<std::vector<size_t>> elem2node(const xt::xtensor<size_t,2> &conn)
{
// get coordination per node
auto N = coordination(conn);
// get number of nodes
auto nnode = N.size();
// allocate
std::vector<std::vector<size_t>> out;
// reserve outer size
out.resize(nnode);
// reserve inner sizes
- for ( size_t i = 0 ; i < nnode ; ++i )
+ for (size_t i = 0; i < nnode; ++i )
out[i].reserve(N(i));
// fill
- for ( size_t e = 0 ; e < conn.shape()[0] ; ++e )
- for ( size_t m = 0 ; m < conn.shape()[1] ; ++m )
+ for (size_t e = 0; e < conn.shape(0); ++e)
+ for (size_t m = 0; m < conn.shape(1); ++m)
out[conn(e,m)].push_back(e);
return out;
}
// -------------------------------------------------------------------------------------------------
}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MeshHex8.hpp b/include/GooseFEM/MeshHex8.hpp
index 076fdf0..5ea91ae 100644
--- a/include/GooseFEM/MeshHex8.hpp
+++ b/include/GooseFEM/MeshHex8.hpp
@@ -1,2633 +1,2633 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MESHHEX8_HPP
#define GOOSEFEM_MESHHEX8_HPP
// -------------------------------------------------------------------------------------------------
#include "MeshHex8.h"
// =================================================================================================
namespace GooseFEM {
namespace Mesh {
namespace Hex8 {
// -------------------------------------------------------------------------------------------------
inline Regular::Regular(size_t nelx, size_t nely, size_t nelz, double h):
m_h(h), m_nelx(nelx), m_nely(nely), m_nelz(nelz)
{
GOOSEFEM_ASSERT(m_nelx >= 1ul);
GOOSEFEM_ASSERT(m_nely >= 1ul);
GOOSEFEM_ASSERT(m_nelz >= 1ul);
m_nnode = (m_nelx+1) * (m_nely+1) * (m_nelz+1);
m_nelem = m_nelx * m_nely * m_nelz ;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline ElementType Regular::getElementType() const
{
return ElementType::Hex8;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Regular::coor() const
{
xt::xtensor<double,2> out = xt::empty<double>({m_nnode, m_ndim});
xt::xtensor<double,1> x = xt::linspace<double>(0.0, m_h*static_cast<double>(m_nelx), m_nelx+1);
xt::xtensor<double,1> y = xt::linspace<double>(0.0, m_h*static_cast<double>(m_nely), m_nely+1);
xt::xtensor<double,1> z = xt::linspace<double>(0.0, m_h*static_cast<double>(m_nelz), m_nelz+1);
size_t inode = 0;
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz ) {
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy ) {
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix ) {
out(inode,0) = x(ix);
out(inode,1) = y(iy);
out(inode,2) = z(iz);
++inode;
}
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::conn() const
{
xt::xtensor<size_t,2> out = xt::empty<size_t>({m_nelem,m_nne});
size_t ielem = 0;
for ( size_t iz = 0 ; iz < m_nelz ; ++iz ) {
for ( size_t iy = 0 ; iy < m_nely ; ++iy ) {
for ( size_t ix = 0 ; ix < m_nelx ; ++ix ) {
out(ielem,0) = (iy )*(m_nelx+1) + (ix ) + (iz )*(m_nely+1)*(m_nelx+1);
out(ielem,1) = (iy )*(m_nelx+1) + (ix+1) + (iz )*(m_nely+1)*(m_nelx+1);
out(ielem,3) = (iy+1)*(m_nelx+1) + (ix ) + (iz )*(m_nely+1)*(m_nelx+1);
out(ielem,2) = (iy+1)*(m_nelx+1) + (ix+1) + (iz )*(m_nely+1)*(m_nelx+1);
out(ielem,4) = (iy )*(m_nelx+1) + (ix ) + (iz+1)*(m_nely+1)*(m_nelx+1);
out(ielem,5) = (iy )*(m_nelx+1) + (ix+1) + (iz+1)*(m_nely+1)*(m_nelx+1);
out(ielem,7) = (iy+1)*(m_nelx+1) + (ix ) + (iz+1)*(m_nely+1)*(m_nelx+1);
out(ielem,6) = (iy+1)*(m_nelx+1) + (ix+1) + (iz+1)*(m_nely+1)*(m_nelx+1);
++ielem;
}
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesFront() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx+1)*(m_nely+1)});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(iy*(m_nelx+1)+ix) = iy*(m_nelx+1) + ix;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBack() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx+1)*(m_nely+1)});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(iy*(m_nelx+1)+ix) = iy*(m_nelx+1) + ix + m_nelz*(m_nely+1)*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesLeft() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nely+1)*(m_nelz+1)});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iz*(m_nely+1)+iy) = iy*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesRight() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nely+1)*(m_nelz+1)});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iz*(m_nely+1)+iy) = iy*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottom() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx+1)*(m_nelz+1)});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(iz*(m_nelx+1)+ix) = ix + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTop() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx+1)*(m_nelz+1)});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(iz*(m_nelx+1)+ix) = ix + m_nely*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontFace() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx-1)*(m_nely-1)});
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out((iy-1)*(m_nelx-1)+(ix-1)) = iy*(m_nelx+1) + ix;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBackFace() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx-1)*(m_nely-1)});
for ( size_t iy = 1 ; iy < m_nely ; ++iy ) {
for ( size_t ix = 1 ; ix < m_nelx ; ++ix ) {
out((iy-1)*(m_nelx-1)+(ix-1)) = iy*(m_nelx+1) + ix + m_nelz*(m_nely+1)*(m_nelx+1);
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesLeftFace() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nely-1)*(m_nelz-1)});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out((iz-1)*(m_nely-1)+(iy-1)) = iy*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesRightFace() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nely-1)*(m_nelz-1)});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out((iz-1)*(m_nely-1)+(iy-1)) = iy*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomFace() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx-1)*(m_nelz-1)});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out((iz-1)*(m_nelx-1)+(ix-1)) = ix + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopFace() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx-1)*(m_nelz-1)});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out((iz-1)*(m_nelx-1)+(ix-1)) = ix + m_nely*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontBottomEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(ix) = ix;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontTopEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(ix) = ix + m_nely*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontLeftEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iy) = iy*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontRightEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iy) = iy*(m_nelx+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBackBottomEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(ix) = ix + m_nelz*(m_nely+1)*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBackTopEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(ix) = m_nely*(m_nelx+1) + ix + m_nelz*(m_nely+1)*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBackLeftEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iy) = iy*(m_nelx+1) + m_nelz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBackRightEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iy) = iy*(m_nelx+1) + m_nelz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomLeftEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz+1});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
out(iz) = iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomRightEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz+1});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
out(iz) = iz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopLeftEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz+1});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
out(iz) = m_nely*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopRightEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz+1});
for ( size_t iz = 0 ; iz < m_nelz+1 ; ++iz )
out(iz) = m_nely*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomFrontEdge() const { return nodesFrontBottomEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesBottomBackEdge() const { return nodesBackBottomEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesTopFrontEdge() const { return nodesFrontTopEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesTopBackEdge() const { return nodesBackTopEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftBottomEdge() const { return nodesBottomLeftEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftFrontEdge() const { return nodesFrontLeftEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftBackEdge() const { return nodesBackLeftEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftTopEdge() const { return nodesTopLeftEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightBottomEdge() const { return nodesBottomRightEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightTopEdge() const { return nodesTopRightEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightFrontEdge() const { return nodesFrontRightEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightBackEdge() const { return nodesBackRightEdge(); }
// ------------------- node-numbers along the front-bottom edge, without corners -------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontBottomOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out(ix-1) = ix;
return out;
}
// -------------------- node-numbers along the front-top edge, without corners ---------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontTopOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out(ix-1) = ix + m_nely*(m_nelx+1);
return out;
}
// -------------------- node-numbers along the front-left edge, without corners --------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontLeftOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out(iy-1) = iy*(m_nelx+1);
return out;
}
// ------------------- node-numbers along the front-right edge, without corners --------------------
inline xt::xtensor<size_t,1> Regular::nodesFrontRightOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out(iy-1) = iy*(m_nelx+1) + m_nelx;
return out;
}
// ------------------- node-numbers along the back-bottom edge, without corners --------------------
inline xt::xtensor<size_t,1> Regular::nodesBackBottomOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out(ix-1) = ix + m_nelz*(m_nely+1)*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBackTopOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out(ix-1) = m_nely*(m_nelx+1) + ix + m_nelz*(m_nely+1)*(m_nelx+1);
return out;
}
// -------------------- node-numbers along the back-left edge, without corners ---------------------
inline xt::xtensor<size_t,1> Regular::nodesBackLeftOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out(iy-1) = iy*(m_nelx+1) + m_nelz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------- node-numbers along the back-right edge, without corners --------------------
inline xt::xtensor<size_t,1> Regular::nodesBackRightOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out(iy-1) = iy*(m_nelx+1) + m_nelz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// ------------------- node-numbers along the bottom-left edge, without corners --------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomLeftOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz-1});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
out(iz-1) = iz*(m_nelx+1)*(m_nely+1);
return out;
}
// ------------------- node-numbers along the bottom-right edge, without corners -------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomRightOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz-1});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
out(iz-1) = iz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopLeftOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz-1});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
out(iz-1) = m_nely*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1);
return out;
}
// -------------------- node-numbers along the top-right edge, without corners ---------------------
inline xt::xtensor<size_t,1> Regular::nodesTopRightOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz-1});
for ( size_t iz = 1 ; iz < m_nelz ; ++iz )
out(iz-1) = m_nely*(m_nelx+1) + iz*(m_nelx+1)*(m_nely+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomFrontOpenEdge() const { return nodesFrontBottomOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesBottomBackOpenEdge() const { return nodesBackBottomOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesTopFrontOpenEdge() const { return nodesFrontTopOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesTopBackOpenEdge() const { return nodesBackTopOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftBottomOpenEdge() const { return nodesBottomLeftOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftFrontOpenEdge() const { return nodesFrontLeftOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftBackOpenEdge() const { return nodesBackLeftOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesLeftTopOpenEdge() const { return nodesTopLeftOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightBottomOpenEdge() const { return nodesBottomRightOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightTopOpenEdge() const { return nodesTopRightOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightFrontOpenEdge() const { return nodesFrontRightOpenEdge(); }
inline xt::xtensor<size_t,1> Regular::nodesRightBackOpenEdge() const { return nodesBackRightOpenEdge(); }
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesFrontBottomLeftCorner() const
{
return 0;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesFrontBottomRightCorner() const
{
return m_nelx;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesFrontTopLeftCorner() const
{
return m_nely*(m_nelx+1);
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesFrontTopRightCorner() const
{
return m_nely*(m_nelx+1) + m_nelx;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesBackBottomLeftCorner() const
{
return m_nelz*(m_nely+1)*(m_nelx+1);
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesBackBottomRightCorner() const
{
return m_nelx + m_nelz*(m_nely+1)*(m_nelx+1);
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesBackTopLeftCorner() const
{
return m_nely*(m_nelx+1) + m_nelz*(m_nely+1)*(m_nelx+1);
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesBackTopRightCorner() const
{
return m_nely*(m_nelx+1) + m_nelx + m_nelz*(m_nely+1)*(m_nelx+1);
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesFrontLeftBottomCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t Regular::nodesBottomFrontLeftCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t Regular::nodesBottomLeftFrontCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t Regular::nodesLeftFrontBottomCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t Regular::nodesLeftBottomFrontCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t Regular::nodesFrontRightBottomCorner()const { return nodesFrontBottomRightCorner(); }
inline size_t Regular::nodesBottomFrontRightCorner()const { return nodesFrontBottomRightCorner(); }
inline size_t Regular::nodesBottomRightFrontCorner()const { return nodesFrontBottomRightCorner(); }
inline size_t Regular::nodesRightFrontBottomCorner()const { return nodesFrontBottomRightCorner(); }
inline size_t Regular::nodesRightBottomFrontCorner()const { return nodesFrontBottomRightCorner(); }
inline size_t Regular::nodesFrontLeftTopCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t Regular::nodesTopFrontLeftCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t Regular::nodesTopLeftFrontCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t Regular::nodesLeftFrontTopCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t Regular::nodesLeftTopFrontCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t Regular::nodesFrontRightTopCorner() const { return nodesFrontTopRightCorner(); }
inline size_t Regular::nodesTopFrontRightCorner() const { return nodesFrontTopRightCorner(); }
inline size_t Regular::nodesTopRightFrontCorner() const { return nodesFrontTopRightCorner(); }
inline size_t Regular::nodesRightFrontTopCorner() const { return nodesFrontTopRightCorner(); }
inline size_t Regular::nodesRightTopFrontCorner() const { return nodesFrontTopRightCorner(); }
inline size_t Regular::nodesBackLeftBottomCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t Regular::nodesBottomBackLeftCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t Regular::nodesBottomLeftBackCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t Regular::nodesLeftBackBottomCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t Regular::nodesLeftBottomBackCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t Regular::nodesBackRightBottomCorner() const { return nodesBackBottomRightCorner(); }
inline size_t Regular::nodesBottomBackRightCorner() const { return nodesBackBottomRightCorner(); }
inline size_t Regular::nodesBottomRightBackCorner() const { return nodesBackBottomRightCorner(); }
inline size_t Regular::nodesRightBackBottomCorner() const { return nodesBackBottomRightCorner(); }
inline size_t Regular::nodesRightBottomBackCorner() const { return nodesBackBottomRightCorner(); }
inline size_t Regular::nodesBackLeftTopCorner() const { return nodesBackTopLeftCorner(); }
inline size_t Regular::nodesTopBackLeftCorner() const { return nodesBackTopLeftCorner(); }
inline size_t Regular::nodesTopLeftBackCorner() const { return nodesBackTopLeftCorner(); }
inline size_t Regular::nodesLeftBackTopCorner() const { return nodesBackTopLeftCorner(); }
inline size_t Regular::nodesLeftTopBackCorner() const { return nodesBackTopLeftCorner(); }
inline size_t Regular::nodesBackRightTopCorner() const { return nodesBackTopRightCorner(); }
inline size_t Regular::nodesTopBackRightCorner() const { return nodesBackTopRightCorner(); }
inline size_t Regular::nodesTopRightBackCorner() const { return nodesBackTopRightCorner(); }
inline size_t Regular::nodesRightBackTopCorner() const { return nodesBackTopRightCorner(); }
inline size_t Regular::nodesRightTopBackCorner() const { return nodesBackTopRightCorner(); }
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::nodesPeriodic() const
{
// faces
xt::xtensor<size_t,1> fro = nodesFrontFace();
xt::xtensor<size_t,1> bck = nodesBackFace();
xt::xtensor<size_t,1> lft = nodesLeftFace();
xt::xtensor<size_t,1> rgt = nodesRightFace();
xt::xtensor<size_t,1> bot = nodesBottomFace();
xt::xtensor<size_t,1> top = nodesTopFace();
// edges
xt::xtensor<size_t,1> froBot = nodesFrontBottomOpenEdge();
xt::xtensor<size_t,1> froTop = nodesFrontTopOpenEdge();
xt::xtensor<size_t,1> froLft = nodesFrontLeftOpenEdge();
xt::xtensor<size_t,1> froRgt = nodesFrontRightOpenEdge();
xt::xtensor<size_t,1> bckBot = nodesBackBottomOpenEdge();
xt::xtensor<size_t,1> bckTop = nodesBackTopOpenEdge();
xt::xtensor<size_t,1> bckLft = nodesBackLeftOpenEdge();
xt::xtensor<size_t,1> bckRgt = nodesBackRightOpenEdge();
xt::xtensor<size_t,1> botLft = nodesBottomLeftOpenEdge();
xt::xtensor<size_t,1> botRgt = nodesBottomRightOpenEdge();
xt::xtensor<size_t,1> topLft = nodesTopLeftOpenEdge();
xt::xtensor<size_t,1> topRgt = nodesTopRightOpenEdge();
// allocate nodal ties
// - number of tying per category
size_t tface = fro.size() + lft.size() + bot.size();
size_t tedge = 3*froBot.size() + 3*froLft.size() + 3*botLft.size();
size_t tnode = 7;
// - allocate
xt::xtensor<size_t,2> out = xt::empty<size_t>({tface+tedge+tnode, std::size_t(2)});
// counter
size_t i = 0;
// tie all corners to one corner
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesFrontBottomRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackBottomRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackBottomLeftCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesFrontTopLeftCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesFrontTopRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackTopRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackTopLeftCorner(); ++i;
// tie all corresponding edges to each other (exclude corners)
for ( size_t j = 0 ; j<froBot.size() ; ++j ){ out(i,0) = froBot(j); out(i,1) = bckBot(j); ++i; }
for ( size_t j = 0 ; j<froBot.size() ; ++j ){ out(i,0) = froBot(j); out(i,1) = bckTop(j); ++i; }
for ( size_t j = 0 ; j<froBot.size() ; ++j ){ out(i,0) = froBot(j); out(i,1) = froTop(j); ++i; }
for ( size_t j = 0 ; j<botLft.size() ; ++j ){ out(i,0) = botLft(j); out(i,1) = botRgt(j); ++i; }
for ( size_t j = 0 ; j<botLft.size() ; ++j ){ out(i,0) = botLft(j); out(i,1) = topRgt(j); ++i; }
for ( size_t j = 0 ; j<botLft.size() ; ++j ){ out(i,0) = botLft(j); out(i,1) = topLft(j); ++i; }
for ( size_t j = 0 ; j<froLft.size() ; ++j ){ out(i,0) = froLft(j); out(i,1) = froRgt(j); ++i; }
for ( size_t j = 0 ; j<froLft.size() ; ++j ){ out(i,0) = froLft(j); out(i,1) = bckRgt(j); ++i; }
for ( size_t j = 0 ; j<froLft.size() ; ++j ){ out(i,0) = froLft(j); out(i,1) = bckLft(j); ++i; }
// tie faces to each-other
for ( size_t j = 0 ; j<fro.size() ; ++j ){ out(i,0) = fro(j); out(i,1) = bck(j); ++i; }
for ( size_t j = 0 ; j<lft.size() ; ++j ){ out(i,0) = lft(j); out(i,1) = rgt(j); ++i; }
for ( size_t j = 0 ; j<bot.size() ; ++j ){ out(i,0) = bot(j); out(i,1) = top(j); ++i; }
return out;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesOrigin() const
{
return nodesFrontBottomLeftCorner();
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::dofs() const
{
return GooseFEM::Mesh::dofs(m_nnode,m_ndim);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::dofsPeriodic() const
{
// DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t,2> out = GooseFEM::Mesh::dofs(m_nnode,m_ndim);
// periodic node-pairs
xt::xtensor<size_t,2> nodePer = nodesPeriodic();
// eliminate 'dependent' DOFs; renumber "out" to be sequential for the remaining DOFs
- for ( size_t i = 0 ; i < nodePer.shape()[0] ; ++i )
- for ( size_t j = 0 ; j < m_ndim ; ++j )
+ for (size_t i = 0; i < nodePer.shape(0); ++i)
+ for (size_t j = 0; j < m_ndim; ++j)
out(nodePer(i,1),j) = out(nodePer(i,0),j);
// renumber "out" to be sequential
return GooseFEM::Mesh::renumber(out);
}
// -------------------------------------------------------------------------------------------------
inline FineLayer::FineLayer(size_t nelx, size_t nely, size_t nelz, double h, size_t nfine):
m_h(h)
{
// basic assumptions
GOOSEFEM_ASSERT(nelx >= 1ul);
GOOSEFEM_ASSERT(nely >= 1ul);
GOOSEFEM_ASSERT(nelz >= 1ul);
// store basic info
m_Lx = m_h * static_cast<double>(nelx);
m_Lz = m_h * static_cast<double>(nelz);
// compute element size in y-direction (use symmetry, compute upper half)
// -------------------------------------------------------------------------------------------------
// temporary variables
size_t nmin, ntot;
xt::xtensor<size_t,1> nhx = xt::ones<size_t>({nely});
xt::xtensor<size_t,1> nhy = xt::ones<size_t>({nely});
xt::xtensor<size_t,1> nhz = xt::ones<size_t>({nely});
xt::xtensor<int ,1> refine = -1 * xt::ones<int> ({nely});
// minimum height in y-direction (half of the height because of symmetry)
if ( nely % 2 == 0 ) nmin = nely /2;
else nmin = (nely +1)/2;
// minimum number of fine layers in y-direction (minimum 1, middle layer part of this half)
if ( nfine % 2 == 0 ) nfine = nfine /2 + 1;
else nfine = (nfine+1)/2;
if ( nfine < 1 ) nfine = 1;
if ( nfine > nmin ) nfine = nmin;
// loop over element layers in y-direction, try to coarsen using these rules:
// (1) element size in y-direction <= distance to origin in y-direction
// (2) element size in x-(z-)direction should fit the total number of elements in x-(z-)direction
// (3) a certain number of layers have the minimum size "1" (are fine)
for ( size_t iy = nfine ; ; )
{
// initialize current size in y-direction
if ( iy == nfine ) ntot = nfine;
// check to stop
- if ( iy >= nely or ntot >= nmin ) { nely = iy; break; }
+ if ( iy >= nely || ntot >= nmin ) { nely = iy; break; }
// rules (1,2) satisfied: coarsen in x-direction (and z-direction)
- if ( 3*nhy(iy) <= ntot and nelx%(3*nhx(iy)) == 0 and ntot+nhy(iy) < nmin )
+ if ( 3*nhy(iy) <= ntot && nelx%(3*nhx(iy)) == 0 && ntot+nhy(iy) < nmin )
{
// - process refinement in x-direction
refine(iy) = 0;
nhy (iy) *= 2;
auto vnhy = xt::view(nhy, xt::range(iy+1, _));
auto vnhx = xt::view(nhx, xt::range(iy , _));
vnhy *= 3;
vnhx *= 3;
// - rule (2) satisfied: coarsen next element layer in z-direction
- if ( iy+1 < nely and ntot+2*nhy(iy) < nmin )
+ if ( iy+1 < nely && ntot+2*nhy(iy) < nmin )
{
if ( nelz%(3*nhz(iy+1)) == 0 )
{
// - update the number of elements in y-direction
ntot += nhy(iy);
// - proceed to next element layer in y-direction
++iy;
// - process refinement in z-direction
refine(iy) = 2;
nhy (iy) = nhy(iy-1);
auto vnhz = xt::view(nhz, xt::range(iy, _));
vnhz *= 3;
}
}
}
// rules (1,2) satisfied: coarse in z-direction
- else if ( 3*nhy(iy) <= ntot and nelz%(3*nhz(iy)) == 0 and ntot+nhy(iy) < nmin )
+ else if ( 3*nhy(iy) <= ntot && nelz%(3*nhz(iy)) == 0 && ntot+nhy(iy) < nmin )
{
// - process refinement in z-direction
refine(iy) = 2;
nhy (iy) *= 2;
auto vnhy = xt::view(nhy, xt::range(iy+1, _));
auto vnhz = xt::view(nhz, xt::range(iy , _));
vnhy *= 3;
vnhz *= 3;
}
// update the number of elements in y-direction
ntot += nhy(iy);
// proceed to next element layer in y-direction
++iy;
// check to stop
- if ( iy >= nely or ntot >= nmin ) { nely = iy; break; }
+ if ( iy >= nely || ntot >= nmin ) { nely = iy; break; }
}
// symmetrize, compute full information
// -------------------------------------------------------------------------------------------------
// allocate mesh constructor parameters
m_nhx = xt::empty<size_t>({nely*2-1});
m_nhy = xt::empty<size_t>({nely*2-1});
m_nhz = xt::empty<size_t>({nely*2-1});
m_refine = xt::empty<int> ({nely*2-1});
m_nelx = xt::empty<size_t>({nely*2-1});
m_nelz = xt::empty<size_t>({nely*2-1});
m_nnd = xt::empty<size_t>({nely*2 });
m_startElem = xt::empty<size_t>({nely*2-1});
m_startNode = xt::empty<size_t>({nely*2 });
// fill
// - lower half
for ( size_t iy = 0 ; iy < nely ; ++iy )
{
m_nhx (iy) = nhx (nely-iy-1);
m_nhy (iy) = nhy (nely-iy-1);
m_nhz (iy) = nhz (nely-iy-1);
m_refine(iy) = refine(nely-iy-1);
}
// - upper half
for ( size_t iy = 0 ; iy < nely-1 ; ++iy )
{
m_nhx (iy+nely) = nhx (iy+1);
m_nhy (iy+nely) = nhy (iy+1);
m_nhz (iy+nely) = nhz (iy+1);
m_refine(iy+nely) = refine(iy+1);
}
// update size
nely = m_nhx.size();
// compute the number of elements per element layer in y-direction
for ( size_t iy = 0 ; iy < nely ; ++iy )
{
m_nelx(iy) = nelx / m_nhx(iy);
m_nelz(iy) = nelz / m_nhz(iy);
}
// compute the number of nodes per node layer in y-direction
// - bottom half
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
m_nnd(iy) = (m_nelx(iy)+1) * (m_nelz(iy)+1);
// - top half
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
m_nnd(iy+1) = (m_nelx(iy)+1) * (m_nelz(iy)+1);
// compute mesh dimensions
// -------------------------------------------------------------------------------------------------
// initialize
m_nnode = 0;
m_nelem = 0;
m_startNode(0) = 0;
// loop over element layers (bottom -> middle, elements become finer)
for ( size_t i = 0 ; i < (nely-1)/2 ; ++i )
{
// - store the first element of the layer
m_startElem(i) = m_nelem;
// - add the nodes of this layer
if ( m_refine(i) == 0 ) { m_nnode += (3*m_nelx(i)+1) * ( m_nelz(i)+1); }
else if ( m_refine(i) == 2 ) { m_nnode += ( m_nelx(i)+1) * (3*m_nelz(i)+1); }
else { m_nnode += ( m_nelx(i)+1) * ( m_nelz(i)+1); }
// - add the elements of this layer
if ( m_refine(i) == 0 ) { m_nelem += (4*m_nelx(i) ) * ( m_nelz(i) ); }
else if ( m_refine(i) == 2 ) { m_nelem += ( m_nelx(i) ) * (4*m_nelz(i) ); }
else { m_nelem += ( m_nelx(i) ) * ( m_nelz(i) ); }
// - store the starting node of the next layer
m_startNode(i+1) = m_nnode;
}
// loop over element layers (middle -> top, elements become coarser)
for ( size_t i = (nely-1)/2 ; i < nely ; ++i )
{
// - store the first element of the layer
m_startElem(i) = m_nelem;
// - add the nodes of this layer
if ( m_refine(i) == 0 ) { m_nnode += (5*m_nelx(i)+1) * ( m_nelz(i)+1); }
else if ( m_refine(i) == 2 ) { m_nnode += ( m_nelx(i)+1) * (5*m_nelz(i)+1); }
else { m_nnode += ( m_nelx(i)+1) * ( m_nelz(i)+1); }
// - add the elements of this layer
if ( m_refine(i) == 0 ) { m_nelem += (4*m_nelx(i) ) * ( m_nelz(i) ); }
else if ( m_refine(i) == 2 ) { m_nelem += ( m_nelx(i) ) * (4*m_nelz(i) ); }
else { m_nelem += ( m_nelx(i) ) * ( m_nelz(i) ); }
// - store the starting node of the next layer
m_startNode(i+1) = m_nnode;
}
// - add the top row of nodes
m_nnode += (m_nelx(nely-1)+1) * (m_nelz(nely-1)+1);
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::shape(size_t i) const
{
GOOSEFEM_ASSERT(i <= 2ul);
if ( i == 0 ) return xt::amax(m_nelx)[0];
else if ( i == 2 ) return xt::amax(m_nelz)[0];
else return xt::sum (m_nhy )[0];
}
// -------------------------------------------------------------------------------------------------
inline ElementType FineLayer::getElementType() const
{
return ElementType::Hex8;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> FineLayer::coor() const
{
// allocate output
xt::xtensor<double,2> out = xt::empty<double>({m_nnode, m_ndim});
// current node, number of element layers
size_t inode = 0;
size_t nely = static_cast<size_t>(m_nhy.size());
// y-position of each main node layer (i.e. excluding node layers for refinement/coarsening)
// - allocate
xt::xtensor<double,1> y = xt::empty<double>({nely+1});
// - initialize
y(0) = 0.0;
// - compute
for ( size_t iy = 1 ; iy < nely+1 ; ++iy )
y(iy) = y(iy-1) + m_nhy(iy-1) * m_h;
// loop over element layers (bottom -> middle) : add bottom layer (+ refinement layer) of nodes
// -------------------------------------------------------------------------------------------------
for ( size_t iy = 0 ; ; ++iy )
{
// get positions along the x- and z-axis
xt::xtensor<double,1> x = xt::linspace<double>(0.0, m_Lx, m_nelx(iy)+1);
xt::xtensor<double,1> z = xt::linspace<double>(0.0, m_Lz, m_nelz(iy)+1);
// add nodes of the bottom layer of this element
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(inode,0) = x(ix);
out(inode,1) = y(iy);
out(inode,2) = z(iz);
++inode;
}
}
// stop at middle layer
if ( iy == (nely-1)/2 )
break;
// add extra nodes of the intermediate layer, for refinement in x-direction
if ( m_refine(iy) == 0 )
{
// - get position offset in x- and y-direction
double dx = m_h * static_cast<double>(m_nhx(iy)/3);
double dy = m_h * static_cast<double>(m_nhy(iy)/2);
// - add nodes of the intermediate layer
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix ) {
for ( size_t j = 0 ; j < 2 ; ++j ) {
out(inode,0) = x(ix) + dx * static_cast<double>(j+1);
out(inode,1) = y(iy) + dy;
out(inode,2) = z(iz);
++inode;
}
}
}
}
// add extra nodes of the intermediate layer, for refinement in z-direction
else if ( m_refine(iy) == 2 )
{
// - get position offset in y- and z-direction
double dz = m_h * static_cast<double>(m_nhz(iy)/3);
double dy = m_h * static_cast<double>(m_nhy(iy)/2);
// - add nodes of the intermediate layer
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz ) {
for ( size_t j = 0 ; j < 2 ; ++j ) {
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(inode,0) = x(ix);
out(inode,1) = y(iy) + dy;
out(inode,2) = z(iz) + dz * static_cast<double>(j+1);
++inode;
}
}
}
}
}
// loop over element layers (middle -> top) : add (refinement layer +) top layer of nodes
// -------------------------------------------------------------------------------------------------
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
// get positions along the x- and z-axis
xt::xtensor<double,1> x = xt::linspace<double>(0.0, m_Lx, m_nelx(iy)+1);
xt::xtensor<double,1> z = xt::linspace<double>(0.0, m_Lz, m_nelz(iy)+1);
// add extra nodes of the intermediate layer, for refinement in x-direction
if ( m_refine(iy) == 0 )
{
// - get position offset in x- and y-direction
double dx = m_h * static_cast<double>(m_nhx(iy)/3);
double dy = m_h * static_cast<double>(m_nhy(iy)/2);
// - add nodes of the intermediate layer
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix ) {
for ( size_t j = 0 ; j < 2 ; ++j ) {
out(inode,0) = x(ix) + dx * static_cast<double>(j+1);
out(inode,1) = y(iy) + dy;
out(inode,2) = z(iz);
++inode;
}
}
}
}
// add extra nodes of the intermediate layer, for refinement in z-direction
else if ( m_refine(iy) == 2 )
{
// - get position offset in y- and z-direction
double dz = m_h * static_cast<double>(m_nhz(iy)/3);
double dy = m_h * static_cast<double>(m_nhy(iy)/2);
// - add nodes of the intermediate layer
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz ) {
for ( size_t j = 0 ; j < 2 ; ++j ) {
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(inode,0) = x(ix);
out(inode,1) = y(iy) + dy;
out(inode,2) = z(iz) + dz * static_cast<double>(j+1);
++inode;
}
}
}
}
// add nodes of the top layer of this element
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(inode,0) = x(ix );
out(inode,1) = y(iy+1);
out(inode,2) = z(iz );
++inode;
}
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> FineLayer::conn() const
{
// allocate output
xt::xtensor<size_t,2> out = xt::empty<size_t>({m_nelem, m_nne});
// current element, number of element layers, starting nodes of each node layer
size_t ielem = 0;
size_t nely = static_cast<size_t>(m_nhy.size());
size_t bot,mid,top;
// loop over all element layers
for ( size_t iy = 0 ; iy < nely ; ++iy )
{
// - get: starting nodes of bottom(, middle) and top layer
bot = m_startNode(iy );
mid = m_startNode(iy ) + m_nnd(iy);
top = m_startNode(iy+1);
// - define connectivity: no coarsening/refinement
if ( m_refine(iy) == -1 )
{
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix ) {
out(ielem,0) = bot + (ix ) + (iz ) * (m_nelx(iy)+1);
out(ielem,1) = bot + (ix+1) + (iz ) * (m_nelx(iy)+1);
out(ielem,2) = top + (ix+1) + (iz ) * (m_nelx(iy)+1);
out(ielem,3) = top + (ix ) + (iz ) * (m_nelx(iy)+1);
out(ielem,4) = bot + (ix ) + (iz+1) * (m_nelx(iy)+1);
out(ielem,5) = bot + (ix+1) + (iz+1) * (m_nelx(iy)+1);
out(ielem,6) = top + (ix+1) + (iz+1) * (m_nelx(iy)+1);
out(ielem,7) = top + (ix ) + (iz+1) * (m_nelx(iy)+1);
ielem++;
}
}
}
// - define connectivity: refinement along the x-direction (below the middle layer)
- else if ( m_refine(iy) == 0 and iy <= (nely-1)/2 )
+ else if ( m_refine(iy) == 0 && iy <= (nely-1)/2 )
{
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix ) {
// -- bottom element
out(ielem,0) = bot + ( ix ) + (iz ) * ( m_nelx(iy)+1);
out(ielem,1) = bot + ( ix+1) + (iz ) * ( m_nelx(iy)+1);
out(ielem,2) = mid + (2*ix+1) + (iz ) * (2*m_nelx(iy) );
out(ielem,3) = mid + (2*ix ) + (iz ) * (2*m_nelx(iy) );
out(ielem,4) = bot + ( ix ) + (iz+1) * ( m_nelx(iy)+1);
out(ielem,5) = bot + ( ix+1) + (iz+1) * ( m_nelx(iy)+1);
out(ielem,6) = mid + (2*ix+1) + (iz+1) * (2*m_nelx(iy) );
out(ielem,7) = mid + (2*ix ) + (iz+1) * (2*m_nelx(iy) );
ielem++;
// -- top-right element
out(ielem,0) = bot + ( ix+1) + (iz ) * ( m_nelx(iy)+1);
out(ielem,1) = top + (3*ix+3) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,2) = top + (3*ix+2) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,3) = mid + (2*ix+1) + (iz ) * (2*m_nelx(iy) );
out(ielem,4) = bot + ( ix+1) + (iz+1) * ( m_nelx(iy)+1);
out(ielem,5) = top + (3*ix+3) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,6) = top + (3*ix+2) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,7) = mid + (2*ix+1) + (iz+1) * (2*m_nelx(iy) );
ielem++;
// -- top-center element
out(ielem,0) = mid + (2*ix ) + (iz ) * (2*m_nelx(iy) );
out(ielem,1) = mid + (2*ix+1) + (iz ) * (2*m_nelx(iy) );
out(ielem,2) = top + (3*ix+2) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,3) = top + (3*ix+1) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,4) = mid + (2*ix ) + (iz+1) * (2*m_nelx(iy) );
out(ielem,5) = mid + (2*ix+1) + (iz+1) * (2*m_nelx(iy) );
out(ielem,6) = top + (3*ix+2) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,7) = top + (3*ix+1) + (iz+1) * (3*m_nelx(iy)+1);
ielem++;
// -- top-left element
out(ielem,0) = bot + ( ix ) + (iz ) * ( m_nelx(iy)+1);
out(ielem,1) = mid + (2*ix ) + (iz ) * (2*m_nelx(iy) );
out(ielem,2) = top + (3*ix+1) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,3) = top + (3*ix ) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,4) = bot + ( ix ) + (iz+1) * ( m_nelx(iy)+1);
out(ielem,5) = mid + (2*ix ) + (iz+1) * (2*m_nelx(iy) );
out(ielem,6) = top + (3*ix+1) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,7) = top + (3*ix ) + (iz+1) * (3*m_nelx(iy)+1);
ielem++;
}
}
}
// - define connectivity: coarsening along the x-direction (above the middle layer)
- else if ( m_refine(iy) == 0 and iy > (nely-1)/2 )
+ else if ( m_refine(iy) == 0 && iy > (nely-1)/2 )
{
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix ) {
// -- lower-left element
out(ielem,0) = bot + (3*ix ) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,1) = bot + (3*ix+1) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,2) = mid + (2*ix ) + (iz ) * (2*m_nelx(iy) );
out(ielem,3) = top + ( ix ) + (iz ) * ( m_nelx(iy)+1);
out(ielem,4) = bot + (3*ix ) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,5) = bot + (3*ix+1) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,6) = mid + (2*ix ) + (iz+1) * (2*m_nelx(iy) );
out(ielem,7) = top + ( ix ) + (iz+1) * ( m_nelx(iy)+1);
ielem++;
// -- lower-center element
out(ielem,0) = bot + (3*ix+1) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,1) = bot + (3*ix+2) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,2) = mid + (2*ix+1) + (iz ) * (2*m_nelx(iy) );
out(ielem,3) = mid + (2*ix ) + (iz ) * (2*m_nelx(iy) );
out(ielem,4) = bot + (3*ix+1) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,5) = bot + (3*ix+2) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,6) = mid + (2*ix+1) + (iz+1) * (2*m_nelx(iy) );
out(ielem,7) = mid + (2*ix ) + (iz+1) * (2*m_nelx(iy) );
ielem++;
// -- lower-right element
out(ielem,0) = bot + (3*ix+2) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,1) = bot + (3*ix+3) + (iz ) * (3*m_nelx(iy)+1);
out(ielem,2) = top + ( ix+1) + (iz ) * ( m_nelx(iy)+1);
out(ielem,3) = mid + (2*ix+1) + (iz ) * (2*m_nelx(iy) );
out(ielem,4) = bot + (3*ix+2) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,5) = bot + (3*ix+3) + (iz+1) * (3*m_nelx(iy)+1);
out(ielem,6) = top + ( ix+1) + (iz+1) * ( m_nelx(iy)+1);
out(ielem,7) = mid + (2*ix+1) + (iz+1) * (2*m_nelx(iy) );
ielem++;
// -- upper element
out(ielem,0) = mid + (2*ix ) + (iz ) * (2*m_nelx(iy) );
out(ielem,1) = mid + (2*ix+1) + (iz ) * (2*m_nelx(iy) );
out(ielem,2) = top + ( ix+1) + (iz ) * ( m_nelx(iy)+1);
out(ielem,3) = top + ( ix ) + (iz ) * ( m_nelx(iy)+1);
out(ielem,4) = mid + (2*ix ) + (iz+1) * (2*m_nelx(iy) );
out(ielem,5) = mid + (2*ix+1) + (iz+1) * (2*m_nelx(iy) );
out(ielem,6) = top + ( ix+1) + (iz+1) * ( m_nelx(iy)+1);
out(ielem,7) = top + ( ix ) + (iz+1) * ( m_nelx(iy)+1);
ielem++;
}
}
}
// - define connectivity: refinement along the z-direction (below the middle layer)
- else if ( m_refine(iy) == 2 and iy <= (nely-1)/2 )
+ else if ( m_refine(iy) == 2 && iy <= (nely-1)/2 )
{
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix ) {
// -- bottom element
out(ielem,0) = bot + (ix ) + iz * (m_nelx(iy)+1);
out(ielem,1) = bot + (ix ) + ( iz+1) * (m_nelx(iy)+1);
out(ielem,2) = bot + (ix+1) + ( iz+1) * (m_nelx(iy)+1);
out(ielem,3) = bot + (ix+1) + iz * (m_nelx(iy)+1);
out(ielem,4) = mid + (ix ) + 2*iz * (m_nelx(iy)+1);
out(ielem,5) = mid + (ix ) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,6) = mid + (ix+1) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,7) = mid + (ix+1) + 2*iz * (m_nelx(iy)+1);
ielem++;
// -- top-back element
out(ielem,0) = mid + (ix ) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,1) = mid + (ix+1) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,2) = top + (ix+1) + (3*iz+2) * (m_nelx(iy)+1);
out(ielem,3) = top + (ix ) + (3*iz+2) * (m_nelx(iy)+1);
out(ielem,4) = bot + (ix ) + ( iz+1) * (m_nelx(iy)+1);
out(ielem,5) = bot + (ix+1) + ( iz+1) * (m_nelx(iy)+1);
out(ielem,6) = top + (ix+1) + (3*iz+3) * (m_nelx(iy)+1);
out(ielem,7) = top + (ix ) + (3*iz+3) * (m_nelx(iy)+1);
ielem++;
// -- top-center element
out(ielem,0) = mid + (ix ) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,1) = mid + (ix+1) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,2) = top + (ix+1) + (3*iz+1) * (m_nelx(iy)+1);
out(ielem,3) = top + (ix ) + (3*iz+1) * (m_nelx(iy)+1);
out(ielem,4) = mid + (ix ) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,5) = mid + (ix+1) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,6) = top + (ix+1) + (3*iz+2) * (m_nelx(iy)+1);
out(ielem,7) = top + (ix ) + (3*iz+2) * (m_nelx(iy)+1);
ielem++;
// -- top-front element
out(ielem,0) = bot + (ix ) + ( iz ) * (m_nelx(iy)+1);
out(ielem,1) = bot + (ix+1) + ( iz ) * (m_nelx(iy)+1);
out(ielem,2) = top + (ix+1) + (3*iz ) * (m_nelx(iy)+1);
out(ielem,3) = top + (ix ) + (3*iz ) * (m_nelx(iy)+1);
out(ielem,4) = mid + (ix ) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,5) = mid + (ix+1) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,6) = top + (ix+1) + (3*iz+1) * (m_nelx(iy)+1);
out(ielem,7) = top + (ix ) + (3*iz+1) * (m_nelx(iy)+1);
ielem++;
}
}
}
// - define connectivity: coarsening along the z-direction (above the middle layer)
- else if ( m_refine(iy) == 2 and iy > (nely-1)/2 )
+ else if ( m_refine(iy) == 2 && iy > (nely-1)/2 )
{
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz ) {
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix ) {
// -- bottom-front element
out(ielem,0) = bot + (ix ) + (3*iz ) * (m_nelx(iy)+1);
out(ielem,1) = bot + (ix+1) + (3*iz ) * (m_nelx(iy)+1);
out(ielem,2) = top + (ix+1) + ( iz ) * (m_nelx(iy)+1);
out(ielem,3) = top + (ix ) + ( iz ) * (m_nelx(iy)+1);
out(ielem,4) = bot + (ix ) + (3*iz+1) * (m_nelx(iy)+1);
out(ielem,5) = bot + (ix+1) + (3*iz+1) * (m_nelx(iy)+1);
out(ielem,6) = mid + (ix+1) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,7) = mid + (ix ) + (2*iz ) * (m_nelx(iy)+1);
ielem++;
// -- bottom-center element
out(ielem,0) = bot + (ix ) + (3*iz+1) * (m_nelx(iy)+1);
out(ielem,1) = bot + (ix+1) + (3*iz+1) * (m_nelx(iy)+1);
out(ielem,2) = mid + (ix+1) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,3) = mid + (ix ) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,4) = bot + (ix ) + (3*iz+2) * (m_nelx(iy)+1);
out(ielem,5) = bot + (ix+1) + (3*iz+2) * (m_nelx(iy)+1);
out(ielem,6) = mid + (ix+1) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,7) = mid + (ix ) + (2*iz+1) * (m_nelx(iy)+1);
ielem++;
// -- bottom-back element
out(ielem,0) = bot + (ix ) + (3*iz+2) * (m_nelx(iy)+1);
out(ielem,1) = bot + (ix+1) + (3*iz+2) * (m_nelx(iy)+1);
out(ielem,2) = mid + (ix+1) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,3) = mid + (ix ) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,4) = bot + (ix ) + (3*iz+3) * (m_nelx(iy)+1);
out(ielem,5) = bot + (ix+1) + (3*iz+3) * (m_nelx(iy)+1);
out(ielem,6) = top + (ix+1) + ( iz+1) * (m_nelx(iy)+1);
out(ielem,7) = top + (ix ) + ( iz+1) * (m_nelx(iy)+1);
ielem++;
// -- top element
out(ielem,0) = mid + (ix ) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,1) = mid + (ix+1) + (2*iz ) * (m_nelx(iy)+1);
out(ielem,2) = top + (ix+1) + ( iz ) * (m_nelx(iy)+1);
out(ielem,3) = top + (ix ) + ( iz ) * (m_nelx(iy)+1);
out(ielem,4) = mid + (ix ) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,5) = mid + (ix+1) + (2*iz+1) * (m_nelx(iy)+1);
out(ielem,6) = top + (ix+1) + ( iz+1) * (m_nelx(iy)+1);
out(ielem,7) = top + (ix ) + ( iz+1) * (m_nelx(iy)+1);
ielem++;
}
}
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::elementsMiddleLayer() const
{
// number of element layers in y-direction, the index of the middle layer
size_t nely = static_cast<size_t>(m_nhy.size());
size_t iy = (nely-1)/2;
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(iy)*m_nelz(iy)});
for ( size_t ix = 0 ; ix < m_nelx(iy) ; ++ix )
for ( size_t iz = 0 ; iz < m_nelz(iy) ; ++iz )
out(ix+iz*m_nelx(iy)) = m_startElem(iy) + ix + iz*m_nelx(iy);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFront() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 + 1;
else n += m_nelx(iy) + 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 + 1;
else n += m_nelx(iy) + 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(j) = m_startNode(iy) + ix;
++j;
}
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy);
++j;
}
}
// -- top node layer
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(j) = m_startNode(iy+1) + ix;
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBack() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 + 1;
else n += m_nelx(iy) + 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 + 1;
else n += m_nelx(iy) + 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(j) = m_startNode(iy) + ix + (m_nelx(iy)+1)*m_nelz(iy);
++j;
}
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy) + 2*m_nelx(iy)*m_nelz(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy) + 2*m_nelx(iy)*m_nelz(iy);
++j;
}
}
// -- top node layer
for ( size_t ix = 0 ; ix < m_nelx(iy)+1 ; ++ix ) {
out(j) = m_startNode(iy+1) + ix + (m_nelx(iy)+1)*m_nelz(iy);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesLeft() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 + 1;
else n += m_nelz(iy) + 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 + 1;
else n += m_nelz(iy) + 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1);
++j;
}
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1) + m_nnd(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1) + m_nnd(iy);
++j;
}
}
// -- top node layer
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
out(j) = m_startNode(iy+1) + iz * (m_nelx(iy)+1);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesRight() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 + 1;
else n += m_nelz(iy) + 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 + 1;
else n += m_nelz(iy) + 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + m_nnd(iy) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + m_nnd(iy) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
}
// -- top node layer
for ( size_t iz = 0 ; iz < m_nelz(iy)+1 ; ++iz ) {
out(j) = m_startNode(iy+1) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottom() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// allocate node list
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nnd(nely)});
// counter
size_t j = 0;
// fill node list
for ( size_t ix = 0 ; ix < m_nelx(0)+1 ; ++ix ) {
for ( size_t iz = 0 ; iz < m_nelz(0)+1 ; ++iz ) {
out(j) = m_startNode(0) + ix + iz * (m_nelx(0)+1);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesTop() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// allocate node list
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nnd(nely)});
// counter
size_t j = 0;
// fill node list
for ( size_t ix = 0 ; ix < m_nelx(nely-1)+1 ; ++ix ) {
for ( size_t iz = 0 ; iz < m_nelz(nely-1)+1 ; ++iz ) {
out(j) = m_startNode(nely) + ix + iz * (m_nelx(nely-1)+1);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontFace() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 - 1;
else n += m_nelx(iy) - 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 - 1;
else n += m_nelx(iy) - 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t ix = 1 ; ix < m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix;
++j;
}
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy);
++j;
}
}
// -- top node layer
for ( size_t ix = 1 ; ix < m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy+1) + ix;
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackFace() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 - 1;
else n += m_nelx(iy) - 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
if ( m_refine(iy) == 0 ) n += m_nelx(iy) * 3 - 1;
else n += m_nelx(iy) - 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t ix = 1 ; ix < m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + (m_nelx(iy)+1)*m_nelz(iy);
++j;
}
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy) + 2*m_nelx(iy)*m_nelz(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 0 ) {
for ( size_t ix = 0 ; ix < 2*m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy) + ix + m_nnd(iy) + 2*m_nelx(iy)*m_nelz(iy);
++j;
}
}
// -- top node layer
for ( size_t ix = 1 ; ix < m_nelx(iy) ; ++ix ) {
out(j) = m_startNode(iy+1) + ix + (m_nelx(iy)+1)*m_nelz(iy);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesLeftFace() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 - 1;
else n += m_nelz(iy) - 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 - 1;
else n += m_nelz(iy) - 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t iz = 1 ; iz < m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1);
++j;
}
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1) + m_nnd(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1) + m_nnd(iy);
++j;
}
}
// -- top node layer
for ( size_t iz = 1 ; iz < m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy+1) + iz * (m_nelx(iy)+1);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesRightFace() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// number of boundary nodes
// - initialize
size_t n = 0;
// - bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 - 1;
else n += m_nelz(iy) - 1;
}
// - top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
if ( m_refine(iy) == 2 ) n += m_nelz(iy) * 3 - 1;
else n += m_nelz(iy) - 1;
}
// allocate node-list
xt::xtensor<size_t,1> out = xt::empty<size_t>({n});
// initialize counter: current index in the node-list "out"
size_t j = 0;
// bottom half: bottom node layer (+ middle node layer)
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
{
// -- bottom node layer
for ( size_t iz = 1 ; iz < m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + m_nnd(iy) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
}
}
// top half: (middle node layer +) top node layer
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
{
// -- refinement layer
if ( m_refine(iy) == 2 ) {
for ( size_t iz = 0 ; iz < 2*m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy) + m_nnd(iy) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
}
// -- top node layer
for ( size_t iz = 1 ; iz < m_nelz(iy) ; ++iz ) {
out(j) = m_startNode(iy+1) + iz * (m_nelx(iy)+1) + m_nelx(iy);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottomFace() const
{
// allocate node list
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx(0)-1)*(m_nelz(0)-1)});
// counter
size_t j = 0;
// fill node list
for ( size_t ix = 1 ; ix < m_nelx(0) ; ++ix ) {
for ( size_t iz = 1 ; iz < m_nelz(0) ; ++iz ) {
out(j) = m_startNode(0) + ix + iz * (m_nelx(0)+1);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesTopFace() const
{
// number of element layers in y-direction
size_t nely = static_cast<size_t>(m_nhy.size());
// allocate node list
xt::xtensor<size_t,1> out = xt::empty<size_t>({(m_nelx(nely-1)-1)*(m_nelz(nely-1)-1)});
// counter
size_t j = 0;
// fill node list
for ( size_t ix = 1 ; ix < m_nelx(nely-1) ; ++ix ) {
for ( size_t iz = 1 ; iz < m_nelz(nely-1) ; ++iz ) {
out(j) = m_startNode(nely) + ix + iz * (m_nelx(nely-1)+1);
++j;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontBottomEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(0)+1});
for ( size_t ix = 0 ; ix < m_nelx(0)+1 ; ++ix )
out(ix) = m_startNode(0) + ix;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontTopEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(nely-1)+1});
for ( size_t ix = 0 ; ix < m_nelx(nely-1)+1 ; ++ix )
out(ix) = m_startNode(nely) + ix;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontLeftEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely+1});
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
out(iy) = m_startNode(iy);
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
out(iy+1) = m_startNode(iy+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontRightEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely+1});
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
out(iy) = m_startNode(iy) + m_nelx(iy);
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
out(iy+1) = m_startNode(iy+1) + m_nelx(iy);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackBottomEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(0)+1});
for ( size_t ix = 0 ; ix < m_nelx(0)+1 ; ++ix )
out(ix) = m_startNode(0) + ix + (m_nelx(0)+1)*(m_nelz(0));
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackTopEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(nely-1)+1});
for ( size_t ix = 0 ; ix < m_nelx(nely-1)+1 ; ++ix )
out(ix) = m_startNode(nely) + ix + (m_nelx(nely-1)+1)*(m_nelz(nely-1));
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackLeftEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely+1});
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
out(iy) = m_startNode(iy) + (m_nelx(iy)+1)*(m_nelz(iy));
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
out(iy+1) = m_startNode(iy+1) + (m_nelx(iy)+1)*(m_nelz(iy));
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackRightEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely+1});
for ( size_t iy = 0 ; iy < (nely+1)/2 ; ++iy )
out(iy) = m_startNode(iy) + m_nelx(iy) + (m_nelx(iy)+1)*(m_nelz(iy));
for ( size_t iy = (nely-1)/2 ; iy < nely ; ++iy )
out(iy+1) = m_startNode(iy+1) + m_nelx(iy) + (m_nelx(iy)+1)*(m_nelz(iy));
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottomLeftEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(0)+1});
for ( size_t iz = 0 ; iz < m_nelz(0)+1 ; ++iz )
out(iz) = m_startNode(0) + iz * (m_nelx(0)+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottomRightEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(0)+1});
for ( size_t iz = 0 ; iz < m_nelz(0)+1 ; ++iz )
out(iz) = m_startNode(0) + m_nelx(0) + iz * (m_nelx(0)+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesTopLeftEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(nely-1)+1});
for ( size_t iz = 0 ; iz < m_nelz(nely-1)+1 ; ++iz )
out(iz) = m_startNode(nely) + iz * (m_nelx(nely-1)+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesTopRightEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(nely-1)+1});
for ( size_t iz = 0 ; iz < m_nelz(nely-1)+1 ; ++iz )
out(iz) = m_startNode(nely) + m_nelx(nely-1) + iz * (m_nelx(nely-1)+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottomFrontEdge() const { return nodesFrontBottomEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesBottomBackEdge() const { return nodesBackBottomEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesTopFrontEdge() const { return nodesFrontTopEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesTopBackEdge() const { return nodesBackTopEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftBottomEdge() const { return nodesBottomLeftEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftFrontEdge() const { return nodesFrontLeftEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftBackEdge() const { return nodesBackLeftEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftTopEdge() const { return nodesTopLeftEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightBottomEdge() const { return nodesBottomRightEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightTopEdge() const { return nodesTopRightEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightFrontEdge() const { return nodesFrontRightEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightBackEdge() const { return nodesBackRightEdge(); }
// ------------------- node-numbers along the front-bottom edge, without corners -------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontBottomOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(0)-1});
for ( size_t ix = 1 ; ix < m_nelx(0) ; ++ix )
out(ix-1) = m_startNode(0) + ix;
return out;
}
// -------------------- node-numbers along the front-top edge, without corners ---------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontTopOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(nely-1)-1});
for ( size_t ix = 1 ; ix < m_nelx(nely-1) ; ++ix )
out(ix-1) = m_startNode(nely) + ix;
return out;
}
// -------------------- node-numbers along the front-left edge, without corners --------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontLeftOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely-1});
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
out(iy-1) = m_startNode(iy);
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
out(iy) = m_startNode(iy+1);
return out;
}
// ------------------- node-numbers along the front-right edge, without corners --------------------
inline xt::xtensor<size_t,1> FineLayer::nodesFrontRightOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely-1});
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
out(iy-1) = m_startNode(iy) + m_nelx(iy);
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
out(iy) = m_startNode(iy+1) + m_nelx(iy);
return out;
}
// ------------------- node-numbers along the back-bottom edge, without corners --------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackBottomOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(0)-1});
for ( size_t ix = 1 ; ix < m_nelx(0) ; ++ix )
out(ix-1) = m_startNode(0) + ix + (m_nelx(0)+1)*(m_nelz(0));
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackTopOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx(nely-1)-1});
for ( size_t ix = 1 ; ix < m_nelx(nely-1) ; ++ix )
out(ix-1) = m_startNode(nely) + ix + (m_nelx(nely-1)+1)*(m_nelz(nely-1));
return out;
}
// -------------------- node-numbers along the back-left edge, without corners ---------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackLeftOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely-1});
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
out(iy-1) = m_startNode(iy) + (m_nelx(iy)+1)*(m_nelz(iy));
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
out(iy) = m_startNode(iy+1) + (m_nelx(iy)+1)*(m_nelz(iy));
return out;
}
// -------------------- node-numbers along the back-right edge, without corners --------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBackRightOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({nely-1});
for ( size_t iy = 1 ; iy < (nely+1)/2 ; ++iy )
out(iy-1) = m_startNode(iy) + m_nelx(iy) + (m_nelx(iy)+1)*(m_nelz(iy));
for ( size_t iy = (nely-1)/2 ; iy < nely-1 ; ++iy )
out(iy) = m_startNode(iy+1) + m_nelx(iy) + (m_nelx(iy)+1)*(m_nelz(iy));
return out;
}
// ------------------- node-numbers along the bottom-left edge, without corners --------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottomLeftOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(0)-1});
for ( size_t iz = 1 ; iz < m_nelz(0) ; ++iz )
out(iz-1) = m_startNode(0) + iz * (m_nelx(0)+1);
return out;
}
// ------------------- node-numbers along the bottom-right edge, without corners -------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottomRightOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(0)-1});
for ( size_t iz = 1 ; iz < m_nelz(0) ; ++iz )
out(iz-1) = m_startNode(0) + m_nelx(0) + iz * (m_nelx(0)+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesTopLeftOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(nely-1)-1});
for ( size_t iz = 1 ; iz < m_nelz(nely-1) ; ++iz )
out(iz-1) = m_startNode(nely) + iz * (m_nelx(nely-1)+1);
return out;
}
// -------------------- node-numbers along the top-right edge, without corners ---------------------
inline xt::xtensor<size_t,1> FineLayer::nodesTopRightOpenEdge() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelz(nely-1)-1});
for ( size_t iz = 1 ; iz < m_nelz(nely-1) ; ++iz )
out(iz-1) = m_startNode(nely) + m_nelx(nely-1) + iz * (m_nelx(nely-1)+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> FineLayer::nodesBottomFrontOpenEdge() const { return nodesFrontBottomOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesBottomBackOpenEdge() const { return nodesBackBottomOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesTopFrontOpenEdge() const { return nodesFrontTopOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesTopBackOpenEdge() const { return nodesBackTopOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftBottomOpenEdge() const { return nodesBottomLeftOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftFrontOpenEdge() const { return nodesFrontLeftOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftBackOpenEdge() const { return nodesBackLeftOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesLeftTopOpenEdge() const { return nodesTopLeftOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightBottomOpenEdge() const { return nodesBottomRightOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightTopOpenEdge() const { return nodesTopRightOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightFrontOpenEdge() const { return nodesFrontRightOpenEdge(); }
inline xt::xtensor<size_t,1> FineLayer::nodesRightBackOpenEdge() const { return nodesBackRightOpenEdge(); }
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesFrontBottomLeftCorner() const
{
return m_startNode(0);
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesFrontBottomRightCorner() const
{
return m_startNode(0) + m_nelx(0);
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesFrontTopLeftCorner() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
return m_startNode(nely);
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesFrontTopRightCorner() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
return m_startNode(nely) + m_nelx(nely-1);
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesBackBottomLeftCorner() const
{
return m_startNode(0) + (m_nelx(0)+1)*(m_nelz(0));
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesBackBottomRightCorner() const
{
return m_startNode(0) + m_nelx(0) + (m_nelx(0)+1)*(m_nelz(0));
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesBackTopLeftCorner() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
return m_startNode(nely) + (m_nelx(nely-1)+1)*(m_nelz(nely-1));
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesBackTopRightCorner() const
{
size_t nely = static_cast<size_t>(m_nhy.size());
return m_startNode(nely) + m_nelx(nely-1) + (m_nelx(nely-1)+1)*(m_nelz(nely-1));
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesFrontLeftBottomCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t FineLayer::nodesBottomFrontLeftCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t FineLayer::nodesBottomLeftFrontCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t FineLayer::nodesLeftFrontBottomCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t FineLayer::nodesLeftBottomFrontCorner() const { return nodesFrontBottomLeftCorner(); }
inline size_t FineLayer::nodesFrontRightBottomCorner() const { return nodesFrontBottomRightCorner(); }
inline size_t FineLayer::nodesBottomFrontRightCorner() const { return nodesFrontBottomRightCorner(); }
inline size_t FineLayer::nodesBottomRightFrontCorner() const { return nodesFrontBottomRightCorner(); }
inline size_t FineLayer::nodesRightFrontBottomCorner() const { return nodesFrontBottomRightCorner(); }
inline size_t FineLayer::nodesRightBottomFrontCorner() const { return nodesFrontBottomRightCorner(); }
inline size_t FineLayer::nodesFrontLeftTopCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t FineLayer::nodesTopFrontLeftCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t FineLayer::nodesTopLeftFrontCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t FineLayer::nodesLeftFrontTopCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t FineLayer::nodesLeftTopFrontCorner() const { return nodesFrontTopLeftCorner(); }
inline size_t FineLayer::nodesFrontRightTopCorner() const { return nodesFrontTopRightCorner(); }
inline size_t FineLayer::nodesTopFrontRightCorner() const { return nodesFrontTopRightCorner(); }
inline size_t FineLayer::nodesTopRightFrontCorner() const { return nodesFrontTopRightCorner(); }
inline size_t FineLayer::nodesRightFrontTopCorner() const { return nodesFrontTopRightCorner(); }
inline size_t FineLayer::nodesRightTopFrontCorner() const { return nodesFrontTopRightCorner(); }
inline size_t FineLayer::nodesBackLeftBottomCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t FineLayer::nodesBottomBackLeftCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t FineLayer::nodesBottomLeftBackCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t FineLayer::nodesLeftBackBottomCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t FineLayer::nodesLeftBottomBackCorner() const { return nodesBackBottomLeftCorner(); }
inline size_t FineLayer::nodesBackRightBottomCorner() const { return nodesBackBottomRightCorner(); }
inline size_t FineLayer::nodesBottomBackRightCorner() const { return nodesBackBottomRightCorner(); }
inline size_t FineLayer::nodesBottomRightBackCorner() const { return nodesBackBottomRightCorner(); }
inline size_t FineLayer::nodesRightBackBottomCorner() const { return nodesBackBottomRightCorner(); }
inline size_t FineLayer::nodesRightBottomBackCorner() const { return nodesBackBottomRightCorner(); }
inline size_t FineLayer::nodesBackLeftTopCorner() const { return nodesBackTopLeftCorner(); }
inline size_t FineLayer::nodesTopBackLeftCorner() const { return nodesBackTopLeftCorner(); }
inline size_t FineLayer::nodesTopLeftBackCorner() const { return nodesBackTopLeftCorner(); }
inline size_t FineLayer::nodesLeftBackTopCorner() const { return nodesBackTopLeftCorner(); }
inline size_t FineLayer::nodesLeftTopBackCorner() const { return nodesBackTopLeftCorner(); }
inline size_t FineLayer::nodesBackRightTopCorner() const { return nodesBackTopRightCorner(); }
inline size_t FineLayer::nodesTopBackRightCorner() const { return nodesBackTopRightCorner(); }
inline size_t FineLayer::nodesTopRightBackCorner() const { return nodesBackTopRightCorner(); }
inline size_t FineLayer::nodesRightBackTopCorner() const { return nodesBackTopRightCorner(); }
inline size_t FineLayer::nodesRightTopBackCorner() const { return nodesBackTopRightCorner(); }
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> FineLayer::nodesPeriodic() const
{
// faces
xt::xtensor<size_t,1> fro = nodesFrontFace();
xt::xtensor<size_t,1> bck = nodesBackFace();
xt::xtensor<size_t,1> lft = nodesLeftFace();
xt::xtensor<size_t,1> rgt = nodesRightFace();
xt::xtensor<size_t,1> bot = nodesBottomFace();
xt::xtensor<size_t,1> top = nodesTopFace();
// edges
xt::xtensor<size_t,1> froBot = nodesFrontBottomOpenEdge();
xt::xtensor<size_t,1> froTop = nodesFrontTopOpenEdge();
xt::xtensor<size_t,1> froLft = nodesFrontLeftOpenEdge();
xt::xtensor<size_t,1> froRgt = nodesFrontRightOpenEdge();
xt::xtensor<size_t,1> bckBot = nodesBackBottomOpenEdge();
xt::xtensor<size_t,1> bckTop = nodesBackTopOpenEdge();
xt::xtensor<size_t,1> bckLft = nodesBackLeftOpenEdge();
xt::xtensor<size_t,1> bckRgt = nodesBackRightOpenEdge();
xt::xtensor<size_t,1> botLft = nodesBottomLeftOpenEdge();
xt::xtensor<size_t,1> botRgt = nodesBottomRightOpenEdge();
xt::xtensor<size_t,1> topLft = nodesTopLeftOpenEdge();
xt::xtensor<size_t,1> topRgt = nodesTopRightOpenEdge();
// allocate nodal ties
// - number of tying per category
size_t tface = fro.size() + lft.size() + bot.size();
size_t tedge = 3*froBot.size() + 3*froLft.size() + 3*botLft.size();
size_t tnode = 7;
// - allocate
xt::xtensor<size_t,2> out = xt::empty<size_t>({tface+tedge+tnode, std::size_t(2)});
// counter
size_t i = 0;
// tie all corners to one corner
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesFrontBottomRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackBottomRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackBottomLeftCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesFrontTopLeftCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesFrontTopRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackTopRightCorner(); ++i;
out(i,0) = nodesFrontBottomLeftCorner(); out(i,1) = nodesBackTopLeftCorner(); ++i;
// tie all corresponding edges to each other (exclude corners)
for ( size_t j = 0 ; j<froBot.size() ; ++j ){ out(i,0) = froBot(j); out(i,1) = bckBot(j); ++i; }
for ( size_t j = 0 ; j<froBot.size() ; ++j ){ out(i,0) = froBot(j); out(i,1) = bckTop(j); ++i; }
for ( size_t j = 0 ; j<froBot.size() ; ++j ){ out(i,0) = froBot(j); out(i,1) = froTop(j); ++i; }
for ( size_t j = 0 ; j<botLft.size() ; ++j ){ out(i,0) = botLft(j); out(i,1) = botRgt(j); ++i; }
for ( size_t j = 0 ; j<botLft.size() ; ++j ){ out(i,0) = botLft(j); out(i,1) = topRgt(j); ++i; }
for ( size_t j = 0 ; j<botLft.size() ; ++j ){ out(i,0) = botLft(j); out(i,1) = topLft(j); ++i; }
for ( size_t j = 0 ; j<froLft.size() ; ++j ){ out(i,0) = froLft(j); out(i,1) = froRgt(j); ++i; }
for ( size_t j = 0 ; j<froLft.size() ; ++j ){ out(i,0) = froLft(j); out(i,1) = bckRgt(j); ++i; }
for ( size_t j = 0 ; j<froLft.size() ; ++j ){ out(i,0) = froLft(j); out(i,1) = bckLft(j); ++i; }
// tie faces to each-other
for ( size_t j = 0 ; j<fro.size() ; ++j ){ out(i,0) = fro(j); out(i,1) = bck(j); ++i; }
for ( size_t j = 0 ; j<lft.size() ; ++j ){ out(i,0) = lft(j); out(i,1) = rgt(j); ++i; }
for ( size_t j = 0 ; j<bot.size() ; ++j ){ out(i,0) = bot(j); out(i,1) = top(j); ++i; }
return out;
}
// -------------------------------------------------------------------------------------------------
inline size_t FineLayer::nodesOrigin() const
{
return nodesFrontBottomLeftCorner();
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> FineLayer::dofs() const
{
return GooseFEM::Mesh::dofs(m_nnode,m_ndim);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> FineLayer::dofsPeriodic() const
{
// DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t,2> out = GooseFEM::Mesh::dofs(m_nnode,m_ndim);
// periodic node-pairs
xt::xtensor<size_t,2> nodePer = nodesPeriodic();
// eliminate 'dependent' DOFs; renumber "out" to be sequential for the remaining DOFs
- for ( size_t i = 0 ; i < nodePer.shape()[0] ; ++i )
- for ( size_t j = 0 ; j < m_ndim ; ++j )
+ for (size_t i = 0; i < nodePer.shape(0); ++i)
+ for (size_t j = 0; j < m_ndim; ++j)
out(nodePer(i,1),j) = out(nodePer(i,0),j);
// renumber "out" to be sequential
return GooseFEM::Mesh::renumber(out);
}
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/MeshTri3.hpp b/include/GooseFEM/MeshTri3.hpp
index e0c9277..5f30a8d 100644
--- a/include/GooseFEM/MeshTri3.hpp
+++ b/include/GooseFEM/MeshTri3.hpp
@@ -1,392 +1,414 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MESHTRI3_HPP
#define GOOSEFEM_MESHTRI3_HPP
// -------------------------------------------------------------------------------------------------
#include "MeshTri3.h"
// =================================================================================================
namespace GooseFEM {
namespace Mesh {
namespace Tri3 {
// -------------------------------------------------------------------------------------------------
inline Regular::Regular(size_t nelx, size_t nely, double h):
m_h(h), m_nelx(nelx), m_nely(nely)
{
GOOSEFEM_ASSERT(m_nelx >= 1ul);
GOOSEFEM_ASSERT(m_nely >= 1ul);
m_nnode = (m_nelx+1) * (m_nely+1);
m_nelem = m_nelx * m_nely * 2;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline ElementType Regular::getElementType() const
{
return ElementType::Tri3;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Regular::coor() const
{
xt::xtensor<double,2> out = xt::empty<double>({m_nnode, m_ndim});
xt::xtensor<double,1> x = xt::linspace<double>(0.0, m_h*static_cast<double>(m_nelx), m_nelx+1);
xt::xtensor<double,1> y = xt::linspace<double>(0.0, m_h*static_cast<double>(m_nely), m_nely+1);
size_t inode = 0;
- for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy ) {
- for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix ) {
+ for ( size_t iy = 0; iy < m_nely+1; ++iy) {
+ for ( size_t ix = 0; ix < m_nelx+1; ++ix) {
out(inode,0) = x(ix);
out(inode,1) = y(iy);
++inode;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::conn() const
{
xt::xtensor<size_t,2> out = xt::empty<size_t>({m_nelem,m_nne});
size_t ielem = 0;
- for ( size_t iy = 0 ; iy < m_nely ; ++iy ) {
- for ( size_t ix = 0 ; ix < m_nelx ; ++ix ) {
+ for ( size_t iy = 0; iy < m_nely; ++iy) {
+ for ( size_t ix = 0; ix < m_nelx; ++ix) {
out(ielem,0) = (iy )*(m_nelx+1) + (ix );
out(ielem,1) = (iy )*(m_nelx+1) + (ix+1);
out(ielem,2) = (iy+1)*(m_nelx+1) + (ix );
++ielem;
out(ielem,0) = (iy )*(m_nelx+1) + (ix+1);
out(ielem,1) = (iy+1)*(m_nelx+1) + (ix+1);
out(ielem,2) = (iy+1)*(m_nelx+1) + (ix );
++ielem;
}
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
- for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
+ for (size_t ix = 0; ix < m_nelx+1; ++ix)
out(ix) = ix;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
- for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
+ for (size_t ix = 0; ix < m_nelx+1; ++ix)
out(ix) = ix + m_nely*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesLeftEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
- for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
+ for (size_t iy = 0; iy < m_nely+1; ++iy)
out(iy) = iy*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesRightEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
- for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
+ for (size_t iy = 0; iy < m_nely+1; ++iy)
out(iy) = iy*(m_nelx+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
- for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
+ for (size_t ix = 1; ix < m_nelx; ++ix)
out(ix-1) = ix;
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
- for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
+ for (size_t ix = 1; ix < m_nelx; ++ix)
out(ix-1) = ix + m_nely*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesLeftOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
- for ( size_t iy = 1 ; iy < m_nely ; ++iy )
+ for (size_t iy = 1; iy < m_nely; ++iy)
out(iy-1) = iy*(m_nelx+1);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Regular::nodesRightOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
- for ( size_t iy = 1 ; iy < m_nely ; ++iy )
+ for (size_t iy = 1; iy < m_nely; ++iy)
out(iy-1) = iy*(m_nelx+1) + m_nelx;
return out;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesBottomLeftCorner() const
{
return 0;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesBottomRightCorner() const
{
return m_nelx;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesTopLeftCorner() const
{
return m_nely*(m_nelx+1);
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesTopRightCorner() const
{
return m_nely*(m_nelx+1) + m_nelx;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesLeftBottomCorner() const
-{ return nodesBottomLeftCorner(); }
+{
+ return nodesBottomLeftCorner();
+}
+
+// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesLeftTopCorner() const
-{ return nodesTopLeftCorner(); }
+{
+ return nodesTopLeftCorner();
+}
+
+// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesRightBottomCorner() const
-{ return nodesBottomRightCorner(); }
+{
+ return nodesBottomRightCorner();
+}
+
+// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesRightTopCorner() const
-{ return nodesTopRightCorner(); }
+{
+ return nodesTopRightCorner();
+}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::nodesPeriodic() const
{
// edges (without corners)
xt::xtensor<size_t,1> bot = nodesBottomOpenEdge();
xt::xtensor<size_t,1> top = nodesTopOpenEdge();
xt::xtensor<size_t,1> lft = nodesLeftOpenEdge();
xt::xtensor<size_t,1> rgt = nodesRightOpenEdge();
// allocate nodal ties
// - number of tying per category
size_t tedge = bot.size() + lft.size();
size_t tnode = 3;
// - allocate
xt::xtensor<size_t,2> out = xt::empty<size_t>({tedge+tnode, std::size_t(2)});
// counter
size_t i = 0;
// tie all corners to one corner
out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesBottomRightCorner(); ++i;
- out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesTopRightCorner(); ++i;
- out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesTopLeftCorner(); ++i;
+ out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesTopRightCorner(); ++i;
+ out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesTopLeftCorner(); ++i;
// tie all corresponding edges to each other
- for ( size_t j = 0 ; j<bot.size() ; ++j ){ out(i,0) = bot(j); out(i,1) = top(j); ++i; }
- for ( size_t j = 0 ; j<lft.size() ; ++j ){ out(i,0) = lft(j); out(i,1) = rgt(j); ++i; }
+ for (size_t j = 0; j < bot.size(); ++j) {
+ out(i,0) = bot(j);
+ out(i,1) = top(j);
+ ++i;
+ }
+ for (size_t j = 0; j < lft.size(); ++j) {
+ out(i,0) = lft(j);
+ out(i,1) = rgt(j);
+ ++i;
+ }
return out;
}
// -------------------------------------------------------------------------------------------------
inline size_t Regular::nodesOrigin() const
{
return nodesBottomLeftCorner();
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::dofs() const
{
return GooseFEM::Mesh::dofs(m_nnode,m_ndim);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Regular::dofsPeriodic() const
{
// DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t,2> out = GooseFEM::Mesh::dofs(m_nnode,m_ndim);
// periodic node-pairs
xt::xtensor<size_t,2> nodePer = nodesPeriodic();
// eliminate 'dependent' DOFs; renumber "out" to be sequential for the remaining DOFs
- for ( size_t i = 0 ; i < nodePer.shape()[0] ; ++i )
- for ( size_t j = 0 ; j < m_ndim ; ++j )
+ for (size_t i = 0; i < nodePer.shape(0); ++i)
+ for (size_t j = 0; j < m_ndim; ++j)
out(nodePer(i,1),j) = out(nodePer(i,0),j);
// renumber "out" to be sequential
return GooseFEM::Mesh::renumber(out);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<int,1> getOrientation(
const xt::xtensor<double,2> &coor,
const xt::xtensor<size_t,2> &conn)
{
- GOOSEFEM_ASSERT(conn.shape()[1] == 3ul);
- GOOSEFEM_ASSERT(coor.shape()[1] == 2ul);
+ GOOSEFEM_ASSERT(conn.shape(1) == 3ul);
+ GOOSEFEM_ASSERT(coor.shape(1) == 2ul);
double k;
- size_t nelem = conn.shape()[0];
+ size_t nelem = conn.shape(0);
xt::xtensor<int,1> out = xt::empty<int>({nelem});
- for ( size_t ielem = 0 ; ielem < nelem ; ++ielem )
+ for (size_t ielem = 0; ielem < nelem; ++ielem )
{
auto v1 = xt::view(coor, conn(ielem,0), xt::all()) - xt::view(coor, conn(ielem,1), xt::all());
auto v2 = xt::view(coor, conn(ielem,2), xt::all()) - xt::view(coor, conn(ielem,1), xt::all());
k = v1(0) * v2(1) - v2(0) * v1(1);
if ( k < 0 ) out(ielem) = -1;
else out(ielem) = +1;
}
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> setOrientation(
const xt::xtensor<double,2> &coor,
const xt::xtensor<size_t,2> &conn,
int orientation)
{
- GOOSEFEM_ASSERT(conn.shape()[1] == 3ul);
- GOOSEFEM_ASSERT(coor.shape()[1] == 2ul);
+ GOOSEFEM_ASSERT(conn.shape(1) == 3ul);
+ GOOSEFEM_ASSERT(coor.shape(1) == 2ul);
GOOSEFEM_ASSERT(orientation == -1 || orientation == +1);
xt::xtensor<int,1> val = getOrientation(coor, conn);
return setOrientation(coor, conn, val, orientation);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> setOrientation(
const xt::xtensor<double,2> &coor,
const xt::xtensor<size_t,2> &conn,
const xt::xtensor<int,1> &val,
int orientation)
{
- GOOSEFEM_ASSERT(conn.shape()[1] == 3ul);
- GOOSEFEM_ASSERT(coor.shape()[1] == 2ul);
- GOOSEFEM_ASSERT(conn.shape()[0] == val.size());
+ GOOSEFEM_ASSERT(conn.shape(1) == 3ul);
+ GOOSEFEM_ASSERT(coor.shape(1) == 2ul);
+ GOOSEFEM_ASSERT(conn.shape(0) == val.size());
GOOSEFEM_ASSERT(orientation == -1 || orientation == +1);
// avoid compiler warning
UNUSED(coor);
- size_t nelem = conn.shape()[0];
+ size_t nelem = conn.shape(0);
xt::xtensor<size_t,2> out = conn;
for (size_t ielem = 0; ielem < nelem; ++ielem)
if ((orientation == -1 && val(ielem) > 0) || (orientation == +1 && val(ielem) < 0))
std::swap(out(ielem,2) , out(ielem,1));
return out;
}
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/TyingsPeriodic.hpp b/include/GooseFEM/TyingsPeriodic.hpp
index 8259e66..7681647 100644
--- a/include/GooseFEM/TyingsPeriodic.hpp
+++ b/include/GooseFEM/TyingsPeriodic.hpp
@@ -1,285 +1,285 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_TYINGSPERIODIC_HPP
#define GOOSEFEM_TYINGSPERIODIC_HPP
// -------------------------------------------------------------------------------------------------
#include "TyingsPeriodic.h"
#include "Mesh.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
// =================================================================================================
namespace GooseFEM {
namespace Tyings {
// -------------------------------------------------------------------------------------------------
inline Periodic::Periodic(
const xt::xtensor<double,2>& coor,
const xt::xtensor<size_t,2>& dofs,
const xt::xtensor<size_t,2>& control,
const xt::xtensor<size_t,2>& nodal_tyings) :
Periodic(coor, dofs, control, nodal_tyings, xt::empty<size_t>({0}))
{
}
// -------------------------------------------------------------------------------------------------
inline Periodic::Periodic(
const xt::xtensor<double,2>& coor,
const xt::xtensor<size_t,2>& dofs,
const xt::xtensor<size_t,2>& control,
const xt::xtensor<size_t,2>& nodal_tyings,
const xt::xtensor<size_t,1>& iip) :
m_tyings(nodal_tyings),
m_coor(coor)
{
- m_ndim = m_coor .shape()[1];
- m_nties = m_tyings.shape()[0];
+ m_ndim = m_coor.shape(1);
+ m_nties = m_tyings.shape(0);
xt::xtensor<size_t,1> dependent = xt::view(m_tyings, xt::all(), 1);
xt::xtensor<size_t,2> dependent_dofs = xt::view(dofs, xt::keep(dependent), xt::all());
xt::xtensor<size_t,1> iid = xt::flatten(dependent_dofs);
xt::xtensor<size_t,1> iii = xt::setdiff1d(dofs, iid);
xt::xtensor<size_t,1> iiu = xt::setdiff1d(iii , iip);
m_nnu = iiu.size();
m_nnp = iip.size();
m_nni = iii.size();
m_nnd = iid.size();
GooseFEM::Mesh::Reorder reorder({iiu, iip, iid});
m_dofs = reorder.apply(dofs);
m_control = reorder.apply(control);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Periodic::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Periodic::control() const
{
return m_control;
}
// -------------------------------------------------------------------------------------------------
inline size_t Periodic::nnu() const
{
return m_nnu;
}
// -------------------------------------------------------------------------------------------------
inline size_t Periodic::nnp() const
{
return m_nnp;
}
// -------------------------------------------------------------------------------------------------
inline size_t Periodic::nni() const
{
return m_nni;
}
// -------------------------------------------------------------------------------------------------
inline size_t Periodic::nnd() const
{
return m_nnd;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Periodic::iiu() const
{
return xt::arange<size_t>(m_nnu);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Periodic::iip() const
{
return xt::arange<size_t>(m_nnp) + m_nnu;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Periodic::iii() const
{
return xt::arange<size_t>(m_nni);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Periodic::iid() const
{
return xt::arange<size_t>(m_nni, m_nni + m_nnd);
}
// -------------------------------------------------------------------------------------------------
inline Eigen::SparseMatrix<double> Periodic::Cdi() const
{
std::vector<Eigen::Triplet<double>> data;
data.reserve(m_nties*m_ndim*(m_ndim+1));
for (size_t i = 0; i < m_nties; ++i) {
for (size_t j = 0; j < m_ndim; ++j) {
size_t ni = m_tyings(i,0);
size_t nd = m_tyings(i,1);
data.push_back(Eigen::Triplet<double>(i*m_ndim+j, m_dofs(ni,j), +1.));
for (size_t k = 0; k < m_ndim; ++k)
data.push_back(Eigen::Triplet<double>(i*m_ndim+j, m_control(j,k), m_coor(nd,k)-m_coor(ni,k)));
}
}
Eigen::SparseMatrix<double> Cdi;
Cdi.resize(m_nnd, m_nni);
Cdi.setFromTriplets(data.begin(), data.end());
return Cdi;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::SparseMatrix<double> Periodic::Cdu() const
{
std::vector<Eigen::Triplet<double>> data;
data.reserve(m_nties*m_ndim*(m_ndim+1));
for (size_t i = 0; i < m_nties; ++i) {
for (size_t j = 0; j < m_ndim; ++j) {
size_t ni = m_tyings(i,0);
size_t nd = m_tyings(i,1);
if (m_dofs(ni,j) < m_nnu)
data.push_back(Eigen::Triplet<double>(i*m_ndim+j, m_dofs(ni,j), +1.));
for (size_t k = 0; k < m_ndim; ++k)
if (m_control(j,k) < m_nnu)
data.push_back(Eigen::Triplet<double>(i*m_ndim+j, m_control(j,k), m_coor(nd,k)-m_coor(ni,k)));
}
}
Eigen::SparseMatrix<double> Cdu;
Cdu.resize(m_nnd, m_nnu);
Cdu.setFromTriplets(data.begin(), data.end());
return Cdu;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::SparseMatrix<double> Periodic::Cdp() const
{
std::vector<Eigen::Triplet<double>> data;
data.reserve(m_nties*m_ndim*(m_ndim+1));
for (size_t i = 0; i < m_nties; ++i) {
for (size_t j = 0; j < m_ndim; ++j) {
size_t ni = m_tyings(i,0);
size_t nd = m_tyings(i,1);
if (m_dofs(ni,j) >= m_nnu)
data.push_back(Eigen::Triplet<double>(i*m_ndim+j, m_dofs(ni,j)-m_nnu, +1.));
for (size_t k = 0; k < m_ndim; ++k)
if (m_control(j,k) >= m_nnu)
data.push_back(Eigen::Triplet<double>(i*m_ndim+j, m_control(j,k)-m_nnu, m_coor(nd,k)-m_coor(ni,k)));
}
}
Eigen::SparseMatrix<double> Cdp;
Cdp.resize(m_nnd, m_nnp);
Cdp.setFromTriplets(data.begin(), data.end());
return Cdp;
}
// -------------------------------------------------------------------------------------------------
inline Control::Control(
const xt::xtensor<double,2>& coor,
const xt::xtensor<size_t,2>& dofs) :
m_coor(coor), m_dofs(dofs)
{
GOOSEFEM_ASSERT(coor.shape().size() == 2);
GOOSEFEM_ASSERT(coor.shape() == dofs.shape());
- size_t nnode = coor.shape()[0];
- size_t ndim = coor.shape()[1];
+ size_t nnode = coor.shape(0);
+ size_t ndim = coor.shape(1);
m_control_dofs = xt::arange<size_t>(ndim*ndim).reshape({ndim,ndim});
m_control_dofs += xt::amax(dofs)[0] + 1;
m_control_nodes = nnode + xt::arange<size_t>(ndim);
m_coor = xt::concatenate(xt::xtuple(coor, xt::zeros<double>({ndim,ndim})));
m_dofs = xt::concatenate(xt::xtuple(dofs, m_control_dofs));
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Control::coor() const
{
return m_coor;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Control::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Control::controlDofs() const
{
return m_control_dofs;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> Control::controlNodes() const
{
return m_control_nodes;
}
// -------------------------------------------------------------------------------------------------
}} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/Vector.hpp b/include/GooseFEM/Vector.hpp
index d7c6ca3..8bd8e13 100644
--- a/include/GooseFEM/Vector.hpp
+++ b/include/GooseFEM/Vector.hpp
@@ -1,347 +1,347 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_VECTOR_HPP
#define GOOSEFEM_VECTOR_HPP
// -------------------------------------------------------------------------------------------------
#include "Vector.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
inline Vector::Vector(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<size_t,2>& dofs) :
m_conn(conn),
m_dofs(dofs)
{
// mesh dimensions
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
// dimensions of the system
m_ndof = xt::amax(m_dofs)[0] + 1;
// check consistency
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
// -------------------------------------------------------------------------------------------------
inline size_t Vector::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t Vector::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t Vector::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t Vector::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t Vector::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> Vector::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
inline void Vector::copy(
const xt::xtensor<double,2>& nodevec_src,
xt::xtensor<double,2>& nodevec_dest) const
{
GOOSEFEM_ASSERT(nodevec_src.shape() ==\
std::decay_t<decltype(nodevec_src)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(nodevec_dest.shape() ==\
std::decay_t<decltype(nodevec_dest)>::shape_type({m_nnode, m_ndim}));
xt::noalias(nodevec_dest) = nodevec_src;
}
// -------------------------------------------------------------------------------------------------
inline void Vector::asDofs(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m,i)) = nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void Vector::asDofs(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m_conn(e,m),i)) = elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void Vector::asNode(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
nodevec(m,i) = dofval(m_dofs(m,i));
}
// -------------------------------------------------------------------------------------------------
inline void Vector::asNode(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
nodevec(m_conn(e,m),i) = elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void Vector::asElement(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
elemvec(e,m,i) = dofval(m_dofs(m_conn(e,m),i));
}
// -------------------------------------------------------------------------------------------------
inline void Vector::asElement(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
elemvec(e,m,i) = nodevec(m_conn(e,m),i);
}
// -------------------------------------------------------------------------------------------------
inline void Vector::assembleDofs(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
dofval.fill(0.0);
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m,i)) += nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void Vector::assembleDofs(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
dofval.fill(0.0);
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m_conn(e,m),i)) += elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void Vector::assembleNode(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
// assemble to DOFs
xt::xtensor<double,1> dofval = this->AssembleDofs(elemvec);
// read from DOFs
this->asNode(dofval, nodevec);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> Vector::AsDofs(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->asDofs(nodevec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> Vector::AsDofs(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->asDofs(elemvec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Vector::AsNode(
const xt::xtensor<double,1>& dofval) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
this->asNode(dofval, nodevec);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Vector::AsNode(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
this->asNode(elemvec, nodevec);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Vector::AsElement(
const xt::xtensor<double,1>& dofval) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->asElement(dofval, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> Vector::AsElement(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->asElement(nodevec, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> Vector::AssembleDofs(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->assembleDofs(nodevec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> Vector::AssembleDofs(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->assembleDofs(elemvec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> Vector::AssembleNode(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
this->assembleNode(elemvec, nodevec);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/VectorPartitioned.hpp b/include/GooseFEM/VectorPartitioned.hpp
index de6248a..87ce419 100644
--- a/include/GooseFEM/VectorPartitioned.hpp
+++ b/include/GooseFEM/VectorPartitioned.hpp
@@ -1,821 +1,821 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_VECTORPARTITIONED_HPP
#define GOOSEFEM_VECTORPARTITIONED_HPP
// -------------------------------------------------------------------------------------------------
#include "VectorPartitioned.h"
#include "Mesh.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
inline VectorPartitioned::VectorPartitioned(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<size_t,2>& dofs,
const xt::xtensor<size_t,1>& iip) :
m_conn(conn),
m_dofs(dofs),
m_iip(iip)
{
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
m_iiu = xt::setdiff1d(dofs, iip);
m_ndof = xt::amax(m_dofs)[0] + 1;
m_nnp = m_iip.size();
m_nnu = m_iiu.size();
m_part = Mesh::Reorder({m_iiu, m_iip}).get(m_dofs);
GOOSEFEM_ASSERT(xt::amax(m_conn)[0] + 1 == m_nnode);
GOOSEFEM_ASSERT(xt::amax(m_iip)[0] <= xt::amax(m_dofs)[0]);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitioned::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitioned::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitioned::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitioned::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitioned::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitioned::nnu() const
{
return m_nnu;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitioned::nnp() const
{
return m_nnp;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> VectorPartitioned::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> VectorPartitioned::iiu() const
{
return m_iiu;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> VectorPartitioned::iip() const
{
return m_iip;
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::copy(
const xt::xtensor<double,2>& nodevec_src,
xt::xtensor<double,2>& nodevec_dest) const
{
GOOSEFEM_ASSERT(nodevec_src.shape() ==\
std::decay_t<decltype(nodevec_src)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(nodevec_dest.shape() ==\
std::decay_t<decltype(nodevec_dest)>::shape_type({m_nnode, m_ndim}));
xt::noalias(nodevec_dest) = nodevec_src;
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::copy_u(
const xt::xtensor<double,2>& nodevec_src,
xt::xtensor<double,2>& nodevec_dest) const
{
GOOSEFEM_ASSERT(nodevec_src.shape() ==\
std::decay_t<decltype(nodevec_src)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(nodevec_dest.shape() ==\
std::decay_t<decltype(nodevec_dest)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) < m_nnu)
nodevec_dest(m,i) = nodevec_src(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::copy_p(
const xt::xtensor<double,2>& nodevec_src,
xt::xtensor<double,2>& nodevec_dest) const
{
GOOSEFEM_ASSERT(nodevec_src.shape() ==\
std::decay_t<decltype(nodevec_src)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(nodevec_dest.shape() ==\
std::decay_t<decltype(nodevec_dest)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) >= m_nnu)
nodevec_dest(m,i) = nodevec_src(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs(
const xt::xtensor<double,1>& dofval_u,
const xt::xtensor<double,1>& dofval_p,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
dofval(m_iiu(d)) = dofval_u(d);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
dofval(m_iip(d)) = dofval_p(d);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m,i)) = nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs_u(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,1>& dofval_u) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnu ; ++d)
dofval_u(d) = dofval(m_iiu(d));
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs_u(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval_u) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) < m_nnu)
dofval_u(m_part(m,i)) = nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs_p(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,1>& dofval_p) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
#pragma omp parallel for
for (size_t d = 0 ; d < m_nnp ; ++d)
dofval_p(d) = dofval(m_iip(d));
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs_p(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval_p) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) >= m_nnu)
dofval_p(m_part(m,i)-m_nnu) = nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m_conn(e,m),i)) = elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs_u(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval_u) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m_conn(e,m),i) < m_nnu)
dofval_u(m_part(m_conn(e,m),i)) = elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asDofs_p(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval_p) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m_conn(e,m),i) >= m_nnu)
dofval_p(m_part(m_conn(e,m),i)-m_nnu) = elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asNode(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
nodevec(m,i) = dofval(m_dofs(m,i));
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asNode(
const xt::xtensor<double,1>& dofval_u,
const xt::xtensor<double,1>& dofval_p,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
if (m_part(m,i) < m_nnu)
nodevec(m,i) = dofval_u(m_part(m,i));
else
nodevec(m,i) = dofval_p(m_part(m,i)-m_nnu);
}
}
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asNode(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
nodevec(m_conn(e,m),i) = elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asElement(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
elemvec(e,m,i) = dofval(m_dofs(m_conn(e,m),i));
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asElement(
const xt::xtensor<double,1>& dofval_u,
const xt::xtensor<double,1>& dofval_p,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e) {
for (size_t m = 0 ; m < m_nne ; ++m) {
for (size_t i = 0 ; i < m_ndim ; ++i) {
if (m_part(m_conn(e,m),i)<m_nnu)
elemvec(e,m,i) = dofval_u(m_part(m_conn(e,m),i));
else
elemvec(e,m,i) = dofval_p(m_part(m_conn(e,m),i)-m_nnu);
}
}
}
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::asElement(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
elemvec(e,m,i) = nodevec(m_conn(e,m),i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::assembleDofs(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
dofval.fill(0.0);
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m,i)) += nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::assembleDofs_u(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval_u) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
dofval_u.fill(0.0);
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) < m_nnu)
dofval_u(m_part(m,i)) += nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::assembleDofs_p(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval_p) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
dofval_p.fill(0.0);
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m,i) >= m_nnu)
dofval_p(m_part(m,i)-m_nnu) += nodevec(m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::assembleDofs(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
dofval.fill(0.0);
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m_conn(e,m),i)) += elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::assembleDofs_u(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval_u) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval_u.size() == m_nnu);
dofval_u.fill(0.0);
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m_conn(e,m),i) < m_nnu)
dofval_u(m_part(m_conn(e,m),i)) += elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::assembleDofs_p(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval_p) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval_p.size() == m_nnp);
dofval_p.fill(0.0);
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_part(m_conn(e,m),i) >= m_nnu)
dofval_p(m_part(m_conn(e,m),i)-m_nnu) += elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitioned::assembleNode(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
xt::xtensor<double,1> dofval = this->AssembleDofs(elemvec);
this->asNode(dofval, nodevec);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs(
const xt::xtensor<double,1>& dofval_u,
const xt::xtensor<double,1>& dofval_p) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->asDofs(dofval_u, dofval_p, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->asDofs(nodevec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs_u(
const xt::xtensor<double,1>& dofval) const
{
xt::xtensor<double,1> dofval_u = xt::empty<double>({m_nnu});
this->asDofs_u(dofval, dofval_u);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs_u(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval_u = xt::empty<double>({m_nnu});
this->asDofs_u(nodevec, dofval_u);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs_p(
const xt::xtensor<double,1>& dofval) const
{
xt::xtensor<double,1> dofval_p = xt::empty<double>({m_nnp});
this->asDofs_p(dofval, dofval_p);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs_p(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval_p = xt::empty<double>({m_nnp});
this->asDofs_p(nodevec, dofval_p);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->asDofs(elemvec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs_u(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval_u = xt::empty<double>({m_nnu});
this->asDofs_u(elemvec, dofval_u);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AsDofs_p(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval_p = xt::empty<double>({m_nnp});
this->asDofs_p(elemvec, dofval_p);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitioned::AsNode(
const xt::xtensor<double,1>& dofval) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
this->asNode(dofval, nodevec);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitioned::AsNode(
const xt::xtensor<double,1>& dofval_u,
const xt::xtensor<double,1>& dofval_p) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
this->asNode(dofval_u, dofval_p, nodevec);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitioned::AsNode(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
this->asNode(elemvec, nodevec);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> VectorPartitioned::AsElement(
const xt::xtensor<double,1>& dofval) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->asElement(dofval, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> VectorPartitioned::AsElement(
const xt::xtensor<double,1>& dofval_u,
const xt::xtensor<double,1>& dofval_p) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->asElement(dofval_u, dofval_p, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,3> VectorPartitioned::AsElement(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
this->asElement(nodevec, elemvec);
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AssembleDofs(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->assembleDofs(nodevec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AssembleDofs_u(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval_u = xt::empty<double>({m_nnu});
this->assembleDofs_u(nodevec, dofval_u);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AssembleDofs_p(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,1> dofval_p = xt::empty<double>({m_nnp});
this->assembleDofs_p(nodevec, dofval_p);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AssembleDofs(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
this->assembleDofs(elemvec, dofval);
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AssembleDofs_u(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval_u = xt::empty<double>({m_nnu});
this->assembleDofs_u(elemvec, dofval_u);
return dofval_u;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitioned::AssembleDofs_p(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval_p = xt::empty<double>({m_nnp});
this->assembleDofs_p(elemvec, dofval_p);
return dofval_p;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitioned::AssembleNode(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
this->assembleNode(elemvec, nodevec);
return nodevec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitioned::Copy(
const xt::xtensor<double,2>& nodevec_src,
const xt::xtensor<double,2>& nodevec_dest) const
{
xt::xtensor<double,2> out = nodevec_dest;
this->copy(nodevec_src, out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitioned::Copy_u(
const xt::xtensor<double,2>& nodevec_src,
const xt::xtensor<double,2>& nodevec_dest) const
{
xt::xtensor<double,2> out = nodevec_dest;
this->copy_u(nodevec_src, out);
return out;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitioned::Copy_p(
const xt::xtensor<double,2>& nodevec_src,
const xt::xtensor<double,2>& nodevec_dest) const
{
xt::xtensor<double,2> out = nodevec_dest;
this->copy_p(nodevec_src, out);
return out;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/include/GooseFEM/VectorPartitionedTyings.h b/include/GooseFEM/VectorPartitionedTyings.h
index 1ede0f6..6b3e11a 100644
--- a/include/GooseFEM/VectorPartitionedTyings.h
+++ b/include/GooseFEM/VectorPartitionedTyings.h
@@ -1,159 +1,165 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_VECTORPARTITIONEDTYINGS_H
#define GOOSEFEM_VECTORPARTITIONEDTYINGS_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
/*
"nodevec" - nodal vectors - [nnode, ndim]
"elemvec" - nodal vectors stored per element - [nelem, nne, ndim]
"dofval" - DOF values - [ndof]
"dofval_u" - DOF values (Unknown) "== dofval[iiu]" - [nnu]
"dofval_p" - DOF values (Prescribed) "== dofval[iiu]" - [nnp]
*/
class VectorPartitionedTyings
{
public:
// Constructor
VectorPartitionedTyings() = default;
VectorPartitionedTyings(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<size_t,2>& dofs,
const Eigen::SparseMatrix<double>& Cdu,
const Eigen::SparseMatrix<double>& Cdp,
const Eigen::SparseMatrix<double>& Cdi);
// Dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
size_t nnu() const; // number of independent, unknown DOFs
size_t nnp() const; // number of independent, prescribed DOFs
size_t nni() const; // number of independent DOFs
size_t nnd() const; // number of dependent DOFs
// DOF lists
xt::xtensor<size_t,2> dofs() const; // DOFs
xt::xtensor<size_t,1> iiu() const; // independent, unknown DOFs
xt::xtensor<size_t,1> iip() const; // independent, prescribed DOFs
xt::xtensor<size_t,1> iii() const; // independent DOFs
xt::xtensor<size_t,1> iid() const; // dependent DOFs
// Copy (part of) nodevec/dofval to another nodevec/dofval
void copy_p(
const xt::xtensor<double,1>& dofval_src,
xt::xtensor<double,1>& dofval_dest) const; // "iip" updated
// Convert to "dofval" (overwrite entries that occur more than once)
void asDofs_i(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval_i,
bool apply_tyings=true) const; // overwritten
// Convert to "nodevec" (overwrite entries that occur more than once) -- (auto allocation below)
void asNode(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,2>& nodevec) const;
// Convert to "elemvec" (overwrite entries that occur more than once) -- (auto allocation below)
void asElement(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,3>& elemvec) const;
// Assemble "dofval" (adds entries that occur more that once) -- (auto allocation below)
void assembleDofs(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval) const;
// Assemble "nodevec" (adds entries that occur more that once) -- (auto allocation below)
void assembleNode(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,2>& nodevec) const;
// Auto-allocation of the functions above
+ xt::xtensor<double,1> AsDofs_i(
+ const xt::xtensor<double,2>& nodevec) const;
+
+ xt::xtensor<double,2> AsNode(
+ const xt::xtensor<double,1>& dofval) const;
+
xt::xtensor<double,3> AsElement(
const xt::xtensor<double,2>& nodevec) const;
xt::xtensor<double,1> AssembleDofs(
const xt::xtensor<double,3>& elemvec) const;
xt::xtensor<double,2> AssembleNode(
const xt::xtensor<double,3>& elemvec) const;
private:
// Bookkeeping
xt::xtensor<size_t,2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t,2> m_dofs; // DOF-numbers per node [nnode, ndim]
xt::xtensor<size_t,1> m_iiu; // unknown DOFs [nnu]
xt::xtensor<size_t,1> m_iip; // prescribed DOFs [nnp]
xt::xtensor<size_t,1> m_iid; // dependent DOFs [nnd]
// Dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
size_t m_nnu; // number of independent, unknown DOFs
size_t m_nnp; // number of independent, prescribed DOFs
size_t m_nni; // number of independent DOFs
size_t m_nnd; // number of dependent DOFs
// Tyings
Eigen::SparseMatrix<double> m_Cdu;
Eigen::SparseMatrix<double> m_Cdp;
Eigen::SparseMatrix<double> m_Cdi;
Eigen::SparseMatrix<double> m_Cud;
Eigen::SparseMatrix<double> m_Cpd;
Eigen::SparseMatrix<double> m_Cid;
// equivalent Eigen functions
Eigen::VectorXd Eigen_asDofs_d(
const xt::xtensor<double,2>& nodevec) const;
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#include "VectorPartitionedTyings.hpp"
// =================================================================================================
#endif
diff --git a/include/GooseFEM/VectorPartitionedTyings.hpp b/include/GooseFEM/VectorPartitionedTyings.hpp
index d817c1b..907ade0 100644
--- a/include/GooseFEM/VectorPartitionedTyings.hpp
+++ b/include/GooseFEM/VectorPartitionedTyings.hpp
@@ -1,328 +1,342 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_VECTORPARTITIONEDTYINGS_HPP
#define GOOSEFEM_VECTORPARTITIONEDTYINGS_HPP
// -------------------------------------------------------------------------------------------------
#include "VectorPartitionedTyings.h"
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
inline VectorPartitionedTyings::VectorPartitionedTyings(
const xt::xtensor<size_t,2>& conn,
const xt::xtensor<size_t,2>& dofs,
const Eigen::SparseMatrix<double>& Cdu,
const Eigen::SparseMatrix<double>& Cdp,
const Eigen::SparseMatrix<double>& Cdi) :
m_conn(conn),
m_dofs(dofs),
m_Cdu(Cdu),
m_Cdp(Cdp),
m_Cdi(Cdi)
{
GOOSEFEM_ASSERT(Cdu.rows() == Cdp.rows());
GOOSEFEM_ASSERT(Cdi.rows() == Cdp.rows());
- m_nnu = static_cast<size_t>(m_Cdu.cols());
- m_nnp = static_cast<size_t>(m_Cdp.cols());
- m_nnd = static_cast<size_t>(m_Cdp.rows());
- m_nni = m_nnu + m_nnp;
- m_ndof = m_nni + m_nnd;
+ m_nnu = static_cast<size_t>(m_Cdu.cols());
+ m_nnp = static_cast<size_t>(m_Cdp.cols());
+ m_nnd = static_cast<size_t>(m_Cdp.rows());
+ m_nni = m_nnu + m_nnp;
+ m_ndof = m_nni + m_nnd;
- m_iiu = xt::arange<size_t>(m_nnu);
- m_iip = xt::arange<size_t>(m_nnu, m_nnu + m_nnp);
- m_iid = xt::arange<size_t>(m_nni, m_nni + m_nnd);
+ m_iiu = xt::arange<size_t>(m_nnu);
+ m_iip = xt::arange<size_t>(m_nnu, m_nnu + m_nnp);
+ m_iid = xt::arange<size_t>(m_nni, m_nni + m_nnd);
- m_nelem = m_conn.shape()[0];
- m_nne = m_conn.shape()[1];
- m_nnode = m_dofs.shape()[0];
- m_ndim = m_dofs.shape()[1];
+ m_nelem = m_conn.shape(0);
+ m_nne = m_conn.shape(1);
+ m_nnode = m_dofs.shape(0);
+ m_ndim = m_dofs.shape(1);
- m_Cud = m_Cdu.transpose();
- m_Cpd = m_Cdp.transpose();
- m_Cid = m_Cdi.transpose();
+ m_Cud = m_Cdu.transpose();
+ m_Cpd = m_Cdp.transpose();
+ m_Cid = m_Cdi.transpose();
GOOSEFEM_ASSERT(static_cast<size_t>(m_Cdi.cols()) == m_nni);
GOOSEFEM_ASSERT(m_ndof <= m_nnode * m_ndim);
GOOSEFEM_ASSERT(m_ndof == xt::amax(m_dofs)[0] + 1);
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::nelem() const
{
return m_nelem;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::nne() const
{
return m_nne;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::nnode() const
{
return m_nnode;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::ndim() const
{
return m_ndim;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::ndof() const
{
return m_ndof;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::nnu() const
{
return m_nnu;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::nnp() const
{
return m_nnp;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::nni() const
{
return m_nni;
}
// -------------------------------------------------------------------------------------------------
inline size_t VectorPartitionedTyings::nnd() const
{
return m_nnd;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,2> VectorPartitionedTyings::dofs() const
{
return m_dofs;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> VectorPartitionedTyings::iiu() const
{
return m_iiu;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> VectorPartitionedTyings::iip() const
{
return m_iip;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> VectorPartitionedTyings::iii() const
{
return xt::arange<size_t>(m_nni);
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<size_t,1> VectorPartitionedTyings::iid() const
{
return m_iid;
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitionedTyings::copy_p(
const xt::xtensor<double,1>& dofval_src,
xt::xtensor<double,1>& dofval_dest) const
{
GOOSEFEM_ASSERT(dofval_src.size() == m_ndof || dofval_src.size() == m_nni);
GOOSEFEM_ASSERT(dofval_dest.size() == m_ndof || dofval_dest.size() == m_nni);
#pragma omp parallel for
for (size_t i = m_nnu; i < m_nni; ++i)
dofval_dest(i) = dofval_src(i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitionedTyings::asDofs_i(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,1>& dofval_i,
bool apply_tyings) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(dofval_i.size() == m_nni);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_dofs(m,i) < m_nni)
dofval_i(m_dofs(m,i)) = nodevec(m,i);
if (!apply_tyings)
return;
Eigen::VectorXd Dofval_d = this->Eigen_asDofs_d(nodevec);
Eigen::VectorXd Dofval_i = m_Cid * Dofval_d;
#pragma omp parallel for
for (size_t i = 0 ; i < m_nni ; ++i)
dofval_i(i) += Dofval_i(i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitionedTyings::asNode(
const xt::xtensor<double,1>& dofval,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
nodevec(m,i) = dofval(m_dofs(m,i));
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitionedTyings::asElement(
const xt::xtensor<double,2>& nodevec,
xt::xtensor<double,3>& elemvec) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
#pragma omp parallel for
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
elemvec(e,m,i) = nodevec(m_conn(e,m),i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitionedTyings::assembleDofs(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,1>& dofval) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(dofval.size() == m_ndof);
dofval.fill(0.0);
for (size_t e = 0 ; e < m_nelem ; ++e)
for (size_t m = 0 ; m < m_nne ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
dofval(m_dofs(m_conn(e,m),i)) += elemvec(e,m,i);
}
// -------------------------------------------------------------------------------------------------
inline void VectorPartitionedTyings::assembleNode(
const xt::xtensor<double,3>& elemvec,
xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(elemvec.shape() ==\
std::decay_t<decltype(elemvec)>::shape_type({m_nelem, m_nne, m_ndim}));
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
xt::xtensor<double,1> dofval = this->AssembleDofs(elemvec);
this->asNode(dofval, nodevec);
}
// -------------------------------------------------------------------------------------------------
+inline xt::xtensor<double,1> VectorPartitionedTyings::AsDofs_i(
+ const xt::xtensor<double,2>& nodevec) const
+{
+ xt::xtensor<double,1> dofval = xt::empty<double>({m_nni});
+ this->asDofs_i(nodevec, dofval);
+ return dofval;
+}
+
+// -------------------------------------------------------------------------------------------------
+
+inline xt::xtensor<double,2> VectorPartitionedTyings::AsNode(
+ const xt::xtensor<double,1>& dofval) const
+{
+ xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
+ this->asNode(dofval, nodevec);
+ return nodevec;
+}
+
+// -------------------------------------------------------------------------------------------------
+
inline xt::xtensor<double,3> VectorPartitionedTyings::AsElement(
const xt::xtensor<double,2>& nodevec) const
{
xt::xtensor<double,3> elemvec = xt::empty<double>({m_nelem, m_nne, m_ndim});
-
this->asElement(nodevec, elemvec);
-
return elemvec;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,1> VectorPartitionedTyings::AssembleDofs(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,1> dofval = xt::empty<double>({m_ndof});
-
this->assembleDofs(elemvec, dofval);
-
return dofval;
}
// -------------------------------------------------------------------------------------------------
inline xt::xtensor<double,2> VectorPartitionedTyings::AssembleNode(
const xt::xtensor<double,3>& elemvec) const
{
xt::xtensor<double,2> nodevec = xt::empty<double>({m_nnode, m_ndim});
-
this->assembleNode(elemvec, nodevec);
-
return nodevec;
}
// -------------------------------------------------------------------------------------------------
inline Eigen::VectorXd VectorPartitionedTyings::Eigen_asDofs_d(
const xt::xtensor<double,2>& nodevec) const
{
GOOSEFEM_ASSERT(nodevec.shape() ==\
std::decay_t<decltype(nodevec)>::shape_type({m_nnode, m_ndim}));
Eigen::VectorXd dofval_d(m_nnd,1);
#pragma omp parallel for
for (size_t m = 0 ; m < m_nnode ; ++m)
for (size_t i = 0 ; i < m_ndim ; ++i)
if (m_dofs(m,i) >= m_nni)
dofval_d(m_dofs(m,i)-m_nni) = nodevec(m,i);
return dofval_d;
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/python/Element.hpp b/python/Element.hpp
index 84e5b58..bd9ba77 100644
--- a/python/Element.hpp
+++ b/python/Element.hpp
@@ -1,40 +1,35 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_Element(py::module &m)
{
m.def("asElementVector",
&GooseFEM::Element::asElementVector,
"Convert nodal vector [nnode, ndim] to nodal vector stored per element [nelem, nne, ndim]",
py::arg("conn"),
py::arg("nodevec"));
m.def("assembleElementVector",
&GooseFEM::Element::assembleNodeVector,
"Assemble nodal vector stored per element [nelem, nne, ndim] to nodal vector [nnode, ndim]",
py::arg("conn"),
py::arg("elemvec"));
}
// =================================================================================================
diff --git a/python/ElementHex8.hpp b/python/ElementHex8.hpp
index 2e94887..4e0755a 100644
--- a/python/ElementHex8.hpp
+++ b/python/ElementHex8.hpp
@@ -1,149 +1,144 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_ElementHex8(py::module &m)
{
py::class_<GooseFEM::Element::Hex8::Quadrature>(m, "Quadrature")
.def(py::init<const xt::xtensor<double,3>&>(),
"Quadrature",
py::arg("x"))
.def(py::init<
const xt::xtensor<double,3>&,
const xt::xtensor<double,2>&,
const xt::xtensor<double,1>&>(),
"Quadrature",
py::arg("x"),
py::arg("xi"),
py::arg("w"))
.def("update_x",
&GooseFEM::Element::Hex8::Quadrature::update_x,
"Update the nodal positions")
.def("nelem",
&GooseFEM::Element::Hex8::Quadrature::nelem,
"Number of elements")
.def("nne",
&GooseFEM::Element::Hex8::Quadrature::nne,
"Number of nodes per element")
.def("ndim",
&GooseFEM::Element::Hex8::Quadrature::ndim,
"Number of dimensions")
.def("nip",
&GooseFEM::Element::Hex8::Quadrature::nip,
"Number of integration points")
.def("DV",
py::overload_cast<size_t>(&GooseFEM::Element::Hex8::Quadrature::DV, py::const_),
"Integration point volume (qtensor)")
.def("DV",
py::overload_cast<>(&GooseFEM::Element::Hex8::Quadrature::DV, py::const_),
"Integration point volume (qscalar)")
.def("GradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Hex8::Quadrature::GradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("GradN_vector_T",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Hex8::Quadrature::GradN_vector_T, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("SymGradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Hex8::Quadrature::SymGradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("Int_N_scalar_NT_dV",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::Element::Hex8::Quadrature::Int_N_scalar_NT_dV, py::const_),
"Integration, returns 'elemmat'",
py::arg("qscalar"))
.def("Int_gradN_dot_tensor2_dV",
py::overload_cast<const xt::xtensor<double,4>&>(
&GooseFEM::Element::Hex8::Quadrature::Int_gradN_dot_tensor2_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("Int_gradN_dot_tensor4_dot_gradNT_dV",
py::overload_cast<const xt::xtensor<double,6>&>(
&GooseFEM::Element::Hex8::Quadrature::Int_gradN_dot_tensor4_dot_gradNT_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("__repr__",
[](const GooseFEM::Element::Hex8::Quadrature&){
return "<GooseFEM.Element.Hex8.Quadrature>"; });
}
// -------------------------------------------------------------------------------------------------
void init_ElementHex8Gauss(py::module& m)
{
m.def("nip",
&GooseFEM::Element::Hex8::Gauss::nip,
"Return number of integration point");
m.def("xi",
&GooseFEM::Element::Hex8::Gauss::xi,
"Return integration point coordinates");
m.def("w",
&GooseFEM::Element::Hex8::Gauss::w,
"Return integration point weights");
}
// -------------------------------------------------------------------------------------------------
void init_ElementHex8Nodal(py::module& m)
{
m.def("nip",
&GooseFEM::Element::Hex8::Nodal::nip,
"Return number of integration point");
m.def("xi",
&GooseFEM::Element::Hex8::Nodal::xi,
"Return integration point coordinates");
m.def("w",
&GooseFEM::Element::Hex8::Nodal::w,
"Return integration point weights");
}
// =================================================================================================
diff --git a/python/ElementQuad4.hpp b/python/ElementQuad4.hpp
index aadc58b..7b8c9ba 100644
--- a/python/ElementQuad4.hpp
+++ b/python/ElementQuad4.hpp
@@ -1,149 +1,144 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_ElementQuad4(py::module& m)
{
py::class_<GooseFEM::Element::Quad4::Quadrature>(m, "Quadrature")
.def(py::init<const xt::xtensor<double,3>&>(),
"Quadrature",
py::arg("x"))
.def(py::init<
const xt::xtensor<double,3>&,
const xt::xtensor<double,2>&,
const xt::xtensor<double,1>&>(),
"Quadrature",
py::arg("x"),
py::arg("xi"),
py::arg("w"))
.def("update_x",
&GooseFEM::Element::Quad4::Quadrature::update_x,
"Update the nodal positions")
.def("nelem",
&GooseFEM::Element::Quad4::Quadrature::nelem,
"Number of elements")
.def("nne",
&GooseFEM::Element::Quad4::Quadrature::nne,
"Number of nodes per element")
.def("ndim",
&GooseFEM::Element::Quad4::Quadrature::ndim,
"Number of dimensions")
.def("nip",
&GooseFEM::Element::Quad4::Quadrature::nip,
"Number of integration points")
.def("DV",
py::overload_cast<size_t>(&GooseFEM::Element::Quad4::Quadrature::DV, py::const_),
"Integration point volume (qtensor)")
.def("DV",
py::overload_cast<>(&GooseFEM::Element::Quad4::Quadrature::DV, py::const_),
"Integration point volume (qscalar)")
.def("GradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::Quadrature::GradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("GradN_vector_T",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::Quadrature::GradN_vector_T, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("SymGradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::Quadrature::SymGradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("Int_N_scalar_NT_dV",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::Element::Quad4::Quadrature::Int_N_scalar_NT_dV, py::const_),
"Integration, returns 'elemmat'",
py::arg("qscalar"))
.def("Int_gradN_dot_tensor2_dV",
py::overload_cast<const xt::xtensor<double,4>&>(
&GooseFEM::Element::Quad4::Quadrature::Int_gradN_dot_tensor2_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("Int_gradN_dot_tensor4_dot_gradNT_dV",
py::overload_cast<const xt::xtensor<double,6>&>(
&GooseFEM::Element::Quad4::Quadrature::Int_gradN_dot_tensor4_dot_gradNT_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("__repr__",
[](const GooseFEM::Element::Quad4::Quadrature&){
return "<GooseFEM.Element.Quad4.Quadrature>"; });
}
// -------------------------------------------------------------------------------------------------
void init_ElementQuad4Gauss(py::module& m)
{
m.def("nip",
&GooseFEM::Element::Quad4::Gauss::nip,
"Return number of integration point");
m.def("xi",
&GooseFEM::Element::Quad4::Gauss::xi,
"Return integration point coordinates");
m.def("w",
&GooseFEM::Element::Quad4::Gauss::w,
"Return integration point weights");
}
// -------------------------------------------------------------------------------------------------
void init_ElementQuad4Nodal(py::module& m)
{
m.def("nip",
&GooseFEM::Element::Quad4::Nodal::nip,
"Return number of integration point");
m.def("xi",
&GooseFEM::Element::Quad4::Nodal::xi,
"Return integration point coordinates");
m.def("w",
&GooseFEM::Element::Quad4::Nodal::w,
"Return integration point weights");
}
// =================================================================================================
diff --git a/python/ElementQuad4Axisymmetric.hpp b/python/ElementQuad4Axisymmetric.hpp
index e252bb0..97e54fe 100644
--- a/python/ElementQuad4Axisymmetric.hpp
+++ b/python/ElementQuad4Axisymmetric.hpp
@@ -1,111 +1,106 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_ElementQuad4Axisymmetric(py::module& m)
{
py::class_<GooseFEM::Element::Quad4::QuadratureAxisymmetric>(m, "QuadratureAxisymmetric")
.def(py::init<const xt::xtensor<double,3>&>(),
"QuadratureAxisymmetric",
py::arg("x"))
.def(py::init<
const xt::xtensor<double,3>&,
const xt::xtensor<double,2>&,
const xt::xtensor<double,1>&>(),
"QuadratureAxisymmetric",
py::arg("x"),
py::arg("xi"),
py::arg("w"))
.def("update_x",
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::update_x,
"Update the nodal positions")
.def("nelem",
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::nelem,
"Number of elements")
.def("nne",
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::nne,
"Number of nodes per element")
.def("ndim",
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::ndim,
"Number of dimensions")
.def("nip",
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::nip,
"Number of integration points")
.def("DV",
py::overload_cast<size_t>(&GooseFEM::Element::Quad4::QuadratureAxisymmetric::DV, py::const_),
"Integration point volume (qtensor)")
.def("DV",
py::overload_cast<>(&GooseFEM::Element::Quad4::QuadratureAxisymmetric::DV, py::const_),
"Integration point volume (qscalar)")
.def("GradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::GradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("GradN_vector_T",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::GradN_vector_T, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("SymGradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::SymGradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("Int_N_scalar_NT_dV",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::Int_N_scalar_NT_dV, py::const_),
"Integration, returns 'elemmat'",
py::arg("qscalar"))
.def("Int_gradN_dot_tensor2_dV",
py::overload_cast<const xt::xtensor<double,4>&>(
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::Int_gradN_dot_tensor2_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("Int_gradN_dot_tensor4_dot_gradNT_dV",
py::overload_cast<const xt::xtensor<double,6>&>(
&GooseFEM::Element::Quad4::QuadratureAxisymmetric::Int_gradN_dot_tensor4_dot_gradNT_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("__repr__",
[](const GooseFEM::Element::Quad4::QuadratureAxisymmetric&){
return "<GooseFEM.Element.Quad4.QuadratureAxisymmetric>"; });
}
// =================================================================================================
diff --git a/python/ElementQuad4Planar.hpp b/python/ElementQuad4Planar.hpp
index 9876bd7..05d6b0e 100644
--- a/python/ElementQuad4Planar.hpp
+++ b/python/ElementQuad4Planar.hpp
@@ -1,111 +1,106 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_ElementQuad4Planar(py::module& m)
{
py::class_<GooseFEM::Element::Quad4::QuadraturePlanar>(m, "QuadraturePlanar")
.def(py::init<const xt::xtensor<double,3>&>(),
"QuadraturePlanar",
py::arg("x"))
.def(py::init<
const xt::xtensor<double,3>&,
const xt::xtensor<double,2>&,
const xt::xtensor<double,1>&>(),
"QuadraturePlanar",
py::arg("x"),
py::arg("xi"),
py::arg("w"))
.def("update_x",
&GooseFEM::Element::Quad4::QuadraturePlanar::update_x,
"Update the nodal positions")
.def("nelem",
&GooseFEM::Element::Quad4::QuadraturePlanar::nelem,
"Number of elements")
.def("nne",
&GooseFEM::Element::Quad4::QuadraturePlanar::nne,
"Number of nodes per element")
.def("ndim",
&GooseFEM::Element::Quad4::QuadraturePlanar::ndim,
"Number of dimensions")
.def("nip",
&GooseFEM::Element::Quad4::QuadraturePlanar::nip,
"Number of integration points")
.def("DV",
py::overload_cast<size_t>(&GooseFEM::Element::Quad4::QuadraturePlanar::DV, py::const_),
"Integration point volume (qtensor)")
.def("DV",
py::overload_cast<>(&GooseFEM::Element::Quad4::QuadraturePlanar::DV, py::const_),
"Integration point volume (qscalar)")
.def("GradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::QuadraturePlanar::GradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("GradN_vector_T",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::QuadraturePlanar::GradN_vector_T, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("SymGradN_vector",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::Element::Quad4::QuadraturePlanar::SymGradN_vector, py::const_),
"Dyadic product, returns 'qtensor'",
py::arg("elemvec"))
.def("Int_N_scalar_NT_dV",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::Element::Quad4::QuadraturePlanar::Int_N_scalar_NT_dV, py::const_),
"Integration, returns 'elemmat'",
py::arg("qscalar"))
.def("Int_gradN_dot_tensor2_dV",
py::overload_cast<const xt::xtensor<double,4>&>(
&GooseFEM::Element::Quad4::QuadraturePlanar::Int_gradN_dot_tensor2_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("Int_gradN_dot_tensor4_dot_gradNT_dV",
py::overload_cast<const xt::xtensor<double,6>&>(
&GooseFEM::Element::Quad4::QuadraturePlanar::Int_gradN_dot_tensor4_dot_gradNT_dV, py::const_),
"Integration, returns 'elemvec'",
py::arg("qtensor"))
.def("__repr__",
[](const GooseFEM::Element::Quad4::QuadraturePlanar&){
return "<GooseFEM.Element.Quad4.QuadraturePlanar>"; });
}
// =================================================================================================
diff --git a/python/Matrix.hpp b/python/Matrix.hpp
new file mode 100644
index 0000000..f79a971
--- /dev/null
+++ b/python/Matrix.hpp
@@ -0,0 +1,79 @@
+/* =================================================================================================
+
+(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
+
+================================================================================================= */
+
+#include <Eigen/Eigen>
+#include <pybind11/pybind11.h>
+#include <pybind11/eigen.h>
+#include <pyxtensor/pyxtensor.hpp>
+#include "../include/GooseFEM/GooseFEM.h"
+
+// =================================================================================================
+
+namespace py = pybind11;
+
+// =================================================================================================
+
+void init_Matrix(py::module& m)
+{
+
+py::class_<GooseFEM::Matrix<>>(m, "Matrix")
+
+ .def(py::init<
+ const xt::xtensor<size_t,2>&,
+ const xt::xtensor<size_t,2>&>(),
+ "Sparse matrix",
+ py::arg("conn"),
+ py::arg("dofs"))
+
+ .def("nelem",
+ &GooseFEM::Matrix<>::nelem,
+ "Number of element")
+
+ .def("nne",
+ &GooseFEM::Matrix<>::nne,
+ "Number of nodes per element")
+
+ .def("nnode",
+ &GooseFEM::Matrix<>::nnode,
+ "Number of nodes")
+
+ .def("ndim",
+ &GooseFEM::Matrix<>::ndim,
+ "Number of dimensions")
+
+ .def("ndof",
+ &GooseFEM::Matrix<>::ndof,
+ "Number of degrees-of-freedom")
+
+ .def("assemble",
+ &GooseFEM::Matrix<>::assemble,
+ "Assemble matrix from 'elemmat",
+ py::arg("elemmat"))
+
+ .def("dofs",
+ &GooseFEM::Matrix<>::dofs,
+ "Return degrees-of-freedom")
+
+ .def("Solve",
+ py::overload_cast<const xt::xtensor<double,1>&>(
+ &GooseFEM::Matrix<>::Solve),
+ "Solve",
+ py::arg("b"))
+
+ .def("Solve",
+ py::overload_cast<const xt::xtensor<double,2>&>(
+ &GooseFEM::Matrix<>::Solve),
+ "Solve",
+ py::arg("b"))
+
+ .def("__repr__",
+ [](const GooseFEM::Matrix<>&){
+ return "<GooseFEM.Matrix>"; });
+
+}
+
+// =================================================================================================
+
diff --git a/python/MatrixDiagonal.hpp b/python/MatrixDiagonal.hpp
new file mode 100644
index 0000000..1e818d3
--- /dev/null
+++ b/python/MatrixDiagonal.hpp
@@ -0,0 +1,97 @@
+/* =================================================================================================
+
+(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
+
+================================================================================================= */
+
+#include <pybind11/pybind11.h>
+#include <pyxtensor/pyxtensor.hpp>
+#include "../include/GooseFEM/GooseFEM.h"
+
+// =================================================================================================
+
+namespace py = pybind11;
+
+// =================================================================================================
+
+void init_MatrixDiagonal(py::module& m)
+{
+
+py::class_<GooseFEM::MatrixDiagonal>(m, "MatrixDiagonal")
+
+ .def(py::init<
+ const xt::xtensor<size_t,2>&,
+ const xt::xtensor<size_t,2>&>(),
+ "Diagonal matrix",
+ py::arg("conn"),
+ py::arg("dofs"))
+
+ .def("nelem",
+ &GooseFEM::MatrixDiagonal::nelem,
+ "Number of element")
+
+ .def("nne",
+ &GooseFEM::MatrixDiagonal::nne,
+ "Number of nodes per element")
+
+ .def("nnode",
+ &GooseFEM::MatrixDiagonal::nnode,
+ "Number of nodes")
+
+ .def("ndim",
+ &GooseFEM::MatrixDiagonal::ndim,
+ "Number of dimensions")
+
+ .def("ndof",
+ &GooseFEM::MatrixDiagonal::ndof,
+ "Number of degrees-of-freedom")
+
+ .def("set",
+ &GooseFEM::MatrixDiagonal::set,
+ "Set matrix components",
+ py::arg("A"))
+
+ .def("assemble",
+ &GooseFEM::MatrixDiagonal::assemble,
+ "Assemble matrix from 'elemmat",
+ py::arg("elemmat"))
+
+ .def("dofs",
+ &GooseFEM::MatrixDiagonal::dofs,
+ "Return degrees-of-freedom")
+
+ .def("AsDiagonal", &GooseFEM::MatrixDiagonal::AsDiagonal,
+ "Return as diagonal matrix (column)")
+
+ .def("Dot",
+ py::overload_cast<const xt::xtensor<double,1>&>(
+ &GooseFEM::MatrixDiagonal::Dot, py::const_),
+ "Dot product 'b_i = A_ij * x_j",
+ py::arg("x"))
+
+ .def("Dot",
+ py::overload_cast<const xt::xtensor<double,2>&>(
+ &GooseFEM::MatrixDiagonal::Dot, py::const_),
+ "Dot product 'b_i = A_ij * x_j",
+ py::arg("x"))
+
+ .def("Solve",
+ py::overload_cast<const xt::xtensor<double,1>&>(
+ &GooseFEM::MatrixDiagonal::Solve),
+ "Solve",
+ py::arg("b"))
+
+ .def("Solve",
+ py::overload_cast<const xt::xtensor<double,2>&>(
+ &GooseFEM::MatrixDiagonal::Solve),
+ "Solve",
+ py::arg("b"))
+
+ .def("__repr__",
+ [](const GooseFEM::MatrixDiagonal&){
+ return "<GooseFEM.MatrixDiagonal>"; });
+
+}
+
+// =================================================================================================
+
diff --git a/python/MatrixDiagonalPartitioned.hpp b/python/MatrixDiagonalPartitioned.hpp
index 2e08896..1b5311c 100644
--- a/python/MatrixDiagonalPartitioned.hpp
+++ b/python/MatrixDiagonalPartitioned.hpp
@@ -1,153 +1,148 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_MatrixDiagonalPartitioned(py::module& m)
{
py::class_<GooseFEM::MatrixDiagonalPartitioned>(m, "MatrixDiagonalPartitioned")
.def(py::init<
const xt::xtensor<size_t,2>&,
const xt::xtensor<size_t,2>&,
const xt::xtensor<size_t,1>&>(),
"Diagonal, partitioned, matrix",
py::arg("conn"),
py::arg("dofs"),
py::arg("iip"))
.def("nelem",
&GooseFEM::MatrixDiagonalPartitioned::nelem,
"Number of element")
.def("nne",
&GooseFEM::MatrixDiagonalPartitioned::nne,
"Number of nodes per element")
.def("nnode",
&GooseFEM::MatrixDiagonalPartitioned::nnode,
"Number of nodes")
.def("ndim",
&GooseFEM::MatrixDiagonalPartitioned::ndim,
"Number of dimensions")
.def("ndof",
&GooseFEM::MatrixDiagonalPartitioned::ndof,
"Number of degrees-of-freedom")
.def("nnu",
&GooseFEM::MatrixDiagonalPartitioned::nnu,
"Number of unknown degrees-of-freedom")
.def("nnp",
&GooseFEM::MatrixDiagonalPartitioned::nnp,
"Number of prescribed degrees-of-freedom")
.def("assemble",
&GooseFEM::MatrixDiagonalPartitioned::assemble,
"Assemble matrix from 'elemmat",
py::arg("elemmat"))
.def("dofs",
&GooseFEM::MatrixDiagonalPartitioned::dofs,
"Return degrees-of-freedom")
.def("iiu",
&GooseFEM::MatrixDiagonalPartitioned::iiu,
"Return unknown degrees-of-freedom")
.def("iip",
&GooseFEM::MatrixDiagonalPartitioned::iip,
"Return prescribed degrees-of-freedom")
.def("AsDiagonal", &GooseFEM::MatrixDiagonalPartitioned::AsDiagonal,
"Return as diagonal matrix (column)")
.def("Dot",
py::overload_cast<const xt::xtensor<double,1>&>(
&GooseFEM::MatrixDiagonalPartitioned::Dot, py::const_),
"Dot product 'b_i = A_ij * x_j",
py::arg("x"))
.def("Dot_u",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixDiagonalPartitioned::Dot_u, py::const_),
"Dot product 'b_i = A_ij * x_j (b_u = A_uu * x_u + A_up * x_p == A_uu * x_u)",
py::arg("x_u"),
py::arg("x_p"))
.def("Dot_p",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixDiagonalPartitioned::Dot_p, py::const_),
"Dot product 'b_i = A_ij * x_j (b_p = A_pu * x_u + A_pp * x_p == A_pp * x_p)",
py::arg("x_u"),
py::arg("x_p"))
.def("Solve",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixDiagonalPartitioned::Solve),
"Solve",
py::arg("b"),
py::arg("x"))
.def("Solve",
py::overload_cast<const xt::xtensor<double,2>&, const xt::xtensor<double,2>&>(
&GooseFEM::MatrixDiagonalPartitioned::Solve),
"Solve",
py::arg("b"),
py::arg("x"))
.def("Solve_u",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixDiagonalPartitioned::Solve_u),
"Solve_u",
py::arg("b_u"),
py::arg("x_p"))
.def("Reaction",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixDiagonalPartitioned::Reaction, py::const_),
"Reaction",
py::arg("x"),
py::arg("b"))
.def("Reaction",
py::overload_cast<const xt::xtensor<double,2>&, const xt::xtensor<double,2>&>(
&GooseFEM::MatrixDiagonalPartitioned::Reaction, py::const_),
"Reaction",
py::arg("x"),
py::arg("b"))
.def("Reaction_p",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixDiagonalPartitioned::Reaction_p, py::const_),
"Reaction_p",
py::arg("x_u"),
py::arg("x_p"))
.def("__repr__",
[](const GooseFEM::MatrixDiagonalPartitioned&){
return "<GooseFEM.MatrixDiagonalPartitioned>"; });
}
// =================================================================================================
diff --git a/python/MatrixPartitioned.hpp b/python/MatrixPartitioned.hpp
index 30345ce..c9cfe94 100644
--- a/python/MatrixPartitioned.hpp
+++ b/python/MatrixPartitioned.hpp
@@ -1,130 +1,127 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_MatrixPartitioned(py::module& m)
{
py::class_<GooseFEM::MatrixPartitioned<>>(m, "MatrixPartitioned")
.def(py::init<
const xt::xtensor<size_t,2>&,
const xt::xtensor<size_t,2>&,
const xt::xtensor<size_t,1>&>(),
"Sparse, partitioned, matrix",
py::arg("conn"),
py::arg("dofs"),
py::arg("iip"))
.def("nelem",
&GooseFEM::MatrixPartitioned<>::nelem,
"Number of element")
.def("nne",
&GooseFEM::MatrixPartitioned<>::nne,
"Number of nodes per element")
.def("nnode",
&GooseFEM::MatrixPartitioned<>::nnode,
"Number of nodes")
.def("ndim",
&GooseFEM::MatrixPartitioned<>::ndim,
"Number of dimensions")
.def("ndof",
&GooseFEM::MatrixPartitioned<>::ndof,
"Number of degrees-of-freedom")
.def("nnu",
&GooseFEM::MatrixPartitioned<>::nnu,
"Number of unknown degrees-of-freedom")
.def("nnp",
&GooseFEM::MatrixPartitioned<>::nnp,
"Number of prescribed degrees-of-freedom")
.def("assemble",
&GooseFEM::MatrixPartitioned<>::assemble,
"Assemble matrix from 'elemmat",
py::arg("elemmat"))
.def("dofs",
&GooseFEM::MatrixPartitioned<>::dofs,
"Return degrees-of-freedom")
.def("iiu",
&GooseFEM::MatrixPartitioned<>::iiu,
"Return unknown degrees-of-freedom")
.def("iip",
&GooseFEM::MatrixPartitioned<>::iip,
"Return prescribed degrees-of-freedom")
.def("Solve",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixPartitioned<>::Solve),
"Solve",
py::arg("b"),
py::arg("x"))
.def("Solve",
py::overload_cast<const xt::xtensor<double,2>&, const xt::xtensor<double,2>&>(
&GooseFEM::MatrixPartitioned<>::Solve),
"Solve",
py::arg("b"),
py::arg("x"))
.def("Solve_u",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixPartitioned<>::Solve_u),
"Solve_u",
py::arg("b_u"),
py::arg("x_p"))
.def("Reaction",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixPartitioned<>::Reaction, py::const_),
"Reaction",
py::arg("x"),
py::arg("b"))
.def("Reaction",
py::overload_cast<const xt::xtensor<double,2>&, const xt::xtensor<double,2>&>(
&GooseFEM::MatrixPartitioned<>::Reaction, py::const_),
"Reaction",
py::arg("x"),
py::arg("b"))
.def("Reaction_p",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
&GooseFEM::MatrixPartitioned<>::Reaction_p, py::const_),
"Reaction_p",
py::arg("x_u"),
py::arg("x_p"))
.def("__repr__",
[](const GooseFEM::MatrixPartitioned<>&){
return "<GooseFEM.MatrixPartitioned>"; });
}
// =================================================================================================
diff --git a/python/MatrixPartitioned.hpp b/python/MatrixPartitionedTyings.hpp
similarity index 54%
copy from python/MatrixPartitioned.hpp
copy to python/MatrixPartitionedTyings.hpp
index 30345ce..ed15013 100644
--- a/python/MatrixPartitioned.hpp
+++ b/python/MatrixPartitionedTyings.hpp
@@ -1,130 +1,128 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
-void init_MatrixPartitioned(py::module& m)
+void init_MatrixPartitionedTyings(py::module& m)
{
-py::class_<GooseFEM::MatrixPartitioned<>>(m, "MatrixPartitioned")
+py::class_<GooseFEM::MatrixPartitionedTyings<>>(m, "MatrixPartitionedTyings")
.def(py::init<
const xt::xtensor<size_t,2>&,
const xt::xtensor<size_t,2>&,
- const xt::xtensor<size_t,1>&>(),
+ const Eigen::SparseMatrix<double>&,
+ const Eigen::SparseMatrix<double>&>(),
"Sparse, partitioned, matrix",
py::arg("conn"),
py::arg("dofs"),
- py::arg("iip"))
+ py::arg("Cdu"),
+ py::arg("Cdp"))
.def("nelem",
- &GooseFEM::MatrixPartitioned<>::nelem,
+ &GooseFEM::MatrixPartitionedTyings<>::nelem,
"Number of element")
.def("nne",
- &GooseFEM::MatrixPartitioned<>::nne,
+ &GooseFEM::MatrixPartitionedTyings<>::nne,
"Number of nodes per element")
.def("nnode",
- &GooseFEM::MatrixPartitioned<>::nnode,
+ &GooseFEM::MatrixPartitionedTyings<>::nnode,
"Number of nodes")
.def("ndim",
- &GooseFEM::MatrixPartitioned<>::ndim,
+ &GooseFEM::MatrixPartitionedTyings<>::ndim,
"Number of dimensions")
.def("ndof",
- &GooseFEM::MatrixPartitioned<>::ndof,
+ &GooseFEM::MatrixPartitionedTyings<>::ndof,
"Number of degrees-of-freedom")
.def("nnu",
- &GooseFEM::MatrixPartitioned<>::nnu,
+ &GooseFEM::MatrixPartitionedTyings<>::nnu,
"Number of unknown degrees-of-freedom")
.def("nnp",
- &GooseFEM::MatrixPartitioned<>::nnp,
+ &GooseFEM::MatrixPartitionedTyings<>::nnp,
"Number of prescribed degrees-of-freedom")
+ .def("nni",
+ &GooseFEM::MatrixPartitionedTyings<>::nni,
+ "Number of independent degrees-of-freedom")
+
+ .def("nnd",
+ &GooseFEM::MatrixPartitionedTyings<>::nnd,
+ "Number of dependent degrees-of-freedom")
+
.def("assemble",
- &GooseFEM::MatrixPartitioned<>::assemble,
+ &GooseFEM::MatrixPartitionedTyings<>::assemble,
"Assemble matrix from 'elemmat",
py::arg("elemmat"))
.def("dofs",
- &GooseFEM::MatrixPartitioned<>::dofs,
+ &GooseFEM::MatrixPartitionedTyings<>::dofs,
"Return degrees-of-freedom")
.def("iiu",
- &GooseFEM::MatrixPartitioned<>::iiu,
+ &GooseFEM::MatrixPartitionedTyings<>::iiu,
"Return unknown degrees-of-freedom")
.def("iip",
- &GooseFEM::MatrixPartitioned<>::iip,
+ &GooseFEM::MatrixPartitionedTyings<>::iip,
"Return prescribed degrees-of-freedom")
+ .def("iii",
+ &GooseFEM::MatrixPartitionedTyings<>::iii,
+ "Return independent degrees-of-freedom")
+
+ .def("iid",
+ &GooseFEM::MatrixPartitionedTyings<>::iid,
+ "Return dependent degrees-of-freedom")
+
.def("Solve",
py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
- &GooseFEM::MatrixPartitioned<>::Solve),
+ &GooseFEM::MatrixPartitionedTyings<>::Solve),
"Solve",
py::arg("b"),
py::arg("x"))
.def("Solve",
py::overload_cast<const xt::xtensor<double,2>&, const xt::xtensor<double,2>&>(
- &GooseFEM::MatrixPartitioned<>::Solve),
+ &GooseFEM::MatrixPartitionedTyings<>::Solve),
"Solve",
py::arg("b"),
py::arg("x"))
.def("Solve_u",
- py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
- &GooseFEM::MatrixPartitioned<>::Solve_u),
+ py::overload_cast<
+ const xt::xtensor<double,1>&,
+ const xt::xtensor<double,1>&,
+ const xt::xtensor<double,1>&>(
+ &GooseFEM::MatrixPartitionedTyings<>::Solve_u),
"Solve_u",
py::arg("b_u"),
- py::arg("x_p"))
-
- .def("Reaction",
- py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
- &GooseFEM::MatrixPartitioned<>::Reaction, py::const_),
- "Reaction",
- py::arg("x"),
- py::arg("b"))
-
- .def("Reaction",
- py::overload_cast<const xt::xtensor<double,2>&, const xt::xtensor<double,2>&>(
- &GooseFEM::MatrixPartitioned<>::Reaction, py::const_),
- "Reaction",
- py::arg("x"),
- py::arg("b"))
-
- .def("Reaction_p",
- py::overload_cast<const xt::xtensor<double,1>&, const xt::xtensor<double,1>&>(
- &GooseFEM::MatrixPartitioned<>::Reaction_p, py::const_),
- "Reaction_p",
- py::arg("x_u"),
+ py::arg("b_d"),
py::arg("x_p"))
.def("__repr__",
- [](const GooseFEM::MatrixPartitioned<>&){
- return "<GooseFEM.MatrixPartitioned>"; });
+ [](const GooseFEM::MatrixPartitionedTyings<>&){
+ return "<GooseFEM.MatrixPartitionedTyings>"; });
}
// =================================================================================================
diff --git a/python/Mesh.hpp b/python/Mesh.hpp
index 98da07c..eae3d68 100644
--- a/python/Mesh.hpp
+++ b/python/Mesh.hpp
@@ -1,95 +1,100 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_Mesh(py::module& m)
{
+// -------------------------------------------------------------------------------------------------
+
+py::enum_<GooseFEM::Mesh::ElementType>(m, "ElementType", "ElementType")
+ .value("Tri3", GooseFEM::Mesh::ElementType::Tri3)
+ .value("Quad4", GooseFEM::Mesh::ElementType::Quad4)
+ .value("Hex8", GooseFEM::Mesh::ElementType::Hex8)
+ .export_values();
+
+// -------------------------------------------------------------------------------------------------
+
py::class_<GooseFEM::Mesh::Renumber>(m, "Renumber")
.def(py::init<const xt::xarray<size_t>&>(),
"Class to renumber to the lowest possible indices. Use ``Renumber(...).get()`` to get the renumbered result",
py::arg("dofs"))
.def("get",
&GooseFEM::Mesh::Renumber::get,
"Get result of renumbering")
.def("index",
&GooseFEM::Mesh::Renumber::index,
"Get index list to apply renumbering. Apply renumbering using ``index[dofs]``")
.def("__repr__",
[](const GooseFEM::Mesh::Renumber&){ return "<GooseFEM.Mesh.Renumber>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::Mesh::Reorder>(m, "Reorder")
.def(py::init([](xt::xtensor<size_t,1>& a)
{ return new GooseFEM::Mesh::Reorder({a}); }))
.def(py::init([](xt::xtensor<size_t,1>& a, xt::xtensor<size_t,1>& b)
{ return new GooseFEM::Mesh::Reorder({a,b}); }))
.def(py::init([](xt::xtensor<size_t,1>& a, xt::xtensor<size_t,1>& b, xt::xtensor<size_t,1>& c)
{ return new GooseFEM::Mesh::Reorder({a,b,c}); }))
.def(py::init([](xt::xtensor<size_t,1>& a, xt::xtensor<size_t,1>& b, xt::xtensor<size_t,1>& c, xt::xtensor<size_t,1>& d)
{ return new GooseFEM::Mesh::Reorder({a,b,c,d}); }))
.def("get",
&GooseFEM::Mesh::Reorder::get,
"Reorder matrix (e.g. ``dofs``)")
.def("index",
&GooseFEM::Mesh::Reorder::index,
"Get index list to apply renumbering. Apply renumbering using ``index[dofs]``")
.def("__repr__",
[](const GooseFEM::Mesh::Reorder &){ return "<GooseFEM.Mesh.Reorder>"; });
// -------------------------------------------------------------------------------------------------
m.def("dofs",
&GooseFEM::Mesh::dofs,
"List with DOF-numbers (in sequential order)",
py::arg("nnode"),
py::arg("ndim"));
m.def("renumber",
&GooseFEM::Mesh::renumber,
"Renumber to lowest possible indices. Use ``GooseFEM.Mesh.Renumber`` for advanced functionality",
py::arg("dofs"));
m.def("coordination",
&GooseFEM::Mesh::coordination,
"Coordination number of each node (number of elements connected to each node)",
py::arg("conn"));
m.def("elem2node",
&GooseFEM::Mesh::elem2node,
"Element-numbers connected to each node",
py::arg("conn"));
}
// =================================================================================================
diff --git a/python/MeshHex8.hpp b/python/MeshHex8.hpp
index da2c29a..3e6040a 100644
--- a/python/MeshHex8.hpp
+++ b/python/MeshHex8.hpp
@@ -1,770 +1,770 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_MeshHex8(py::module& m)
{
py::class_<GooseFEM::Mesh::Hex8::Regular>(m, "Regular")
.def(py::init<size_t,size_t,size_t,double>(),
"Mesh with nx*ny*nz 'pixels' and edge size h",
py::arg("nx"),
py::arg("ny"),
py::arg("nz"),
py::arg("h")=1.)
.def("nelem",
&GooseFEM::Mesh::Hex8::Regular::nelem)
.def("nnode",
&GooseFEM::Mesh::Hex8::Regular::nnode)
.def("nne",
&GooseFEM::Mesh::Hex8::Regular::nne)
.def("ndim",
&GooseFEM::Mesh::Hex8::Regular::ndim)
.def("coor",
&GooseFEM::Mesh::Hex8::Regular::coor)
.def("conn",
&GooseFEM::Mesh::Hex8::Regular::conn)
+ .def("getElementType",
+ &GooseFEM::Mesh::Hex8::Regular::getElementType)
+
.def("nodesFront",
&GooseFEM::Mesh::Hex8::Regular::nodesFront)
.def("nodesBack",
&GooseFEM::Mesh::Hex8::Regular::nodesBack)
.def("nodesLeft",
&GooseFEM::Mesh::Hex8::Regular::nodesLeft)
.def("nodesRight",
&GooseFEM::Mesh::Hex8::Regular::nodesRight)
.def("nodesBottom",
&GooseFEM::Mesh::Hex8::Regular::nodesBottom)
.def("nodesTop",
&GooseFEM::Mesh::Hex8::Regular::nodesTop)
.def("nodesFrontFace",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontFace)
.def("nodesBackFace",
&GooseFEM::Mesh::Hex8::Regular::nodesBackFace)
.def("nodesLeftFace",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftFace)
.def("nodesRightFace",
&GooseFEM::Mesh::Hex8::Regular::nodesRightFace)
.def("nodesBottomFace",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomFace)
.def("nodesTopFace",
&GooseFEM::Mesh::Hex8::Regular::nodesTopFace)
.def("nodesFrontBottomEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontBottomEdge)
.def("nodesFrontTopEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontTopEdge)
.def("nodesFrontLeftEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontLeftEdge)
.def("nodesFrontRightEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontRightEdge)
.def("nodesBackBottomEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackBottomEdge)
.def("nodesBackTopEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackTopEdge)
.def("nodesBackLeftEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackLeftEdge)
.def("nodesBackRightEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackRightEdge)
.def("nodesBottomLeftEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomLeftEdge)
.def("nodesBottomRightEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomRightEdge)
.def("nodesTopLeftEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopLeftEdge)
.def("nodesTopRightEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopRightEdge)
.def("nodesBottomFrontEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomFrontEdge)
.def("nodesBottomBackEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomBackEdge)
.def("nodesTopFrontEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopFrontEdge)
.def("nodesTopBackEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopBackEdge)
.def("nodesLeftBottomEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBottomEdge)
.def("nodesLeftFrontEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftFrontEdge)
.def("nodesLeftBackEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBackEdge)
.def("nodesLeftTopEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftTopEdge)
.def("nodesRightBottomEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBottomEdge)
.def("nodesRightTopEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightTopEdge)
.def("nodesRightFrontEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightFrontEdge)
.def("nodesRightBackEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBackEdge)
.def("nodesFrontBottomOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontBottomOpenEdge)
.def("nodesFrontTopOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontTopOpenEdge)
.def("nodesFrontLeftOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontLeftOpenEdge)
.def("nodesFrontRightOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontRightOpenEdge)
.def("nodesBackBottomOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackBottomOpenEdge)
.def("nodesBackTopOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackTopOpenEdge)
.def("nodesBackLeftOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackLeftOpenEdge)
.def("nodesBackRightOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBackRightOpenEdge)
.def("nodesBottomLeftOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomLeftOpenEdge)
.def("nodesBottomRightOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomRightOpenEdge)
.def("nodesTopLeftOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopLeftOpenEdge)
.def("nodesTopRightOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopRightOpenEdge)
.def("nodesBottomFrontOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomFrontOpenEdge)
.def("nodesBottomBackOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomBackOpenEdge)
.def("nodesTopFrontOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopFrontOpenEdge)
.def("nodesTopBackOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesTopBackOpenEdge)
.def("nodesLeftBottomOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBottomOpenEdge)
.def("nodesLeftFrontOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftFrontOpenEdge)
.def("nodesLeftBackOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBackOpenEdge)
.def("nodesLeftTopOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftTopOpenEdge)
.def("nodesRightBottomOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBottomOpenEdge)
.def("nodesRightTopOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightTopOpenEdge)
.def("nodesRightFrontOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightFrontOpenEdge)
.def("nodesRightBackOpenEdge",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBackOpenEdge)
.def("nodesFrontBottomLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontBottomLeftCorner)
.def("nodesFrontBottomRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontBottomRightCorner)
.def("nodesFrontTopLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontTopLeftCorner)
.def("nodesFrontTopRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontTopRightCorner)
.def("nodesBackBottomLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackBottomLeftCorner)
.def("nodesBackBottomRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackBottomRightCorner)
.def("nodesBackTopLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackTopLeftCorner)
.def("nodesBackTopRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackTopRightCorner)
.def("nodesFrontLeftBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontLeftBottomCorner)
.def("nodesBottomFrontLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomFrontLeftCorner)
.def("nodesBottomLeftFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomLeftFrontCorner)
.def("nodesLeftFrontBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftFrontBottomCorner)
.def("nodesLeftBottomFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBottomFrontCorner)
.def("nodesFrontRightBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontRightBottomCorner)
.def("nodesBottomFrontRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomFrontRightCorner)
.def("nodesBottomRightFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomRightFrontCorner)
.def("nodesRightFrontBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightFrontBottomCorner)
.def("nodesRightBottomFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBottomFrontCorner)
.def("nodesFrontLeftTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontLeftTopCorner)
.def("nodesTopFrontLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopFrontLeftCorner)
.def("nodesTopLeftFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopLeftFrontCorner)
.def("nodesLeftFrontTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftFrontTopCorner)
.def("nodesLeftTopFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftTopFrontCorner)
.def("nodesFrontRightTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesFrontRightTopCorner)
.def("nodesTopFrontRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopFrontRightCorner)
.def("nodesTopRightFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopRightFrontCorner)
.def("nodesRightFrontTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightFrontTopCorner)
.def("nodesRightTopFrontCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightTopFrontCorner)
.def("nodesBackLeftBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackLeftBottomCorner)
.def("nodesBottomBackLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomBackLeftCorner)
.def("nodesBottomLeftBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomLeftBackCorner)
.def("nodesLeftBackBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBackBottomCorner)
.def("nodesLeftBottomBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBottomBackCorner)
.def("nodesBackRightBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackRightBottomCorner)
.def("nodesBottomBackRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomBackRightCorner)
.def("nodesBottomRightBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBottomRightBackCorner)
.def("nodesRightBackBottomCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBackBottomCorner)
.def("nodesRightBottomBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBottomBackCorner)
.def("nodesBackLeftTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackLeftTopCorner)
.def("nodesTopBackLeftCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopBackLeftCorner)
.def("nodesTopLeftBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopLeftBackCorner)
.def("nodesLeftBackTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftBackTopCorner)
.def("nodesLeftTopBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesLeftTopBackCorner)
.def("nodesBackRightTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesBackRightTopCorner)
.def("nodesTopBackRightCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopBackRightCorner)
.def("nodesTopRightBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesTopRightBackCorner)
.def("nodesRightBackTopCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightBackTopCorner)
.def("nodesRightTopBackCorner",
&GooseFEM::Mesh::Hex8::Regular::nodesRightTopBackCorner)
-
.def("nodesPeriodic",
&GooseFEM::Mesh::Hex8::Regular::nodesPeriodic)
.def("nodesOrigin",
&GooseFEM::Mesh::Hex8::Regular::nodesOrigin)
.def("dofs",
&GooseFEM::Mesh::Hex8::Regular::dofs)
.def("dofsPeriodic",
&GooseFEM::Mesh::Hex8::Regular::dofsPeriodic)
.def("__repr__",
[](const GooseFEM::Mesh::Hex8::Regular &){ return "<GooseFEM.Mesh.Hex8.Regular>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::Mesh::Hex8::FineLayer>(m, "FineLayer")
.def(py::init<size_t,size_t,size_t,double,size_t>(),
"Mesh with nx*ny*nz 'pixels' and edge size h",
py::arg("nx"),
py::arg("ny"),
py::arg("nz"),
py::arg("h")=1.,
py::arg("nfine")=1)
.def("nelem",
&GooseFEM::Mesh::Hex8::FineLayer::nelem)
.def("nnode",
&GooseFEM::Mesh::Hex8::FineLayer::nnode)
.def("nne",
&GooseFEM::Mesh::Hex8::FineLayer::nne)
.def("ndim",
&GooseFEM::Mesh::Hex8::FineLayer::ndim)
.def("shape",
&GooseFEM::Mesh::Hex8::FineLayer::shape)
.def("coor",
&GooseFEM::Mesh::Hex8::FineLayer::coor)
.def("conn",
&GooseFEM::Mesh::Hex8::FineLayer::conn)
+ .def("getElementType",
+ &GooseFEM::Mesh::Hex8::FineLayer::getElementType)
+
.def("elementsMiddleLayer",
&GooseFEM::Mesh::Hex8::FineLayer::elementsMiddleLayer)
.def("nodesFront",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFront)
.def("nodesBack",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBack)
.def("nodesLeft",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeft)
.def("nodesRight",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRight)
.def("nodesBottom",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottom)
.def("nodesTop",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTop)
.def("nodesFrontFace",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontFace)
.def("nodesBackFace",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackFace)
.def("nodesLeftFace",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftFace)
.def("nodesRightFace",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightFace)
.def("nodesBottomFace",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomFace)
.def("nodesTopFace",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopFace)
.def("nodesFrontBottomEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontBottomEdge)
.def("nodesFrontTopEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontTopEdge)
.def("nodesFrontLeftEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontLeftEdge)
.def("nodesFrontRightEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontRightEdge)
.def("nodesBackBottomEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackBottomEdge)
.def("nodesBackTopEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackTopEdge)
.def("nodesBackLeftEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackLeftEdge)
.def("nodesBackRightEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackRightEdge)
.def("nodesBottomLeftEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomLeftEdge)
.def("nodesBottomRightEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomRightEdge)
.def("nodesTopLeftEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopLeftEdge)
.def("nodesTopRightEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopRightEdge)
.def("nodesBottomFrontEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomFrontEdge)
.def("nodesBottomBackEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomBackEdge)
.def("nodesTopFrontEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopFrontEdge)
.def("nodesTopBackEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopBackEdge)
.def("nodesLeftBottomEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBottomEdge)
.def("nodesLeftFrontEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftFrontEdge)
.def("nodesLeftBackEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBackEdge)
.def("nodesLeftTopEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftTopEdge)
.def("nodesRightBottomEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBottomEdge)
.def("nodesRightTopEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightTopEdge)
.def("nodesRightFrontEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightFrontEdge)
.def("nodesRightBackEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBackEdge)
.def("nodesFrontBottomOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontBottomOpenEdge)
.def("nodesFrontTopOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontTopOpenEdge)
.def("nodesFrontLeftOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontLeftOpenEdge)
.def("nodesFrontRightOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontRightOpenEdge)
.def("nodesBackBottomOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackBottomOpenEdge)
.def("nodesBackTopOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackTopOpenEdge)
.def("nodesBackLeftOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackLeftOpenEdge)
.def("nodesBackRightOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackRightOpenEdge)
.def("nodesBottomLeftOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomLeftOpenEdge)
.def("nodesBottomRightOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomRightOpenEdge)
.def("nodesTopLeftOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopLeftOpenEdge)
.def("nodesTopRightOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopRightOpenEdge)
.def("nodesBottomFrontOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomFrontOpenEdge)
.def("nodesBottomBackOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomBackOpenEdge)
.def("nodesTopFrontOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopFrontOpenEdge)
.def("nodesTopBackOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopBackOpenEdge)
.def("nodesLeftBottomOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBottomOpenEdge)
.def("nodesLeftFrontOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftFrontOpenEdge)
.def("nodesLeftBackOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBackOpenEdge)
.def("nodesLeftTopOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftTopOpenEdge)
.def("nodesRightBottomOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBottomOpenEdge)
.def("nodesRightTopOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightTopOpenEdge)
.def("nodesRightFrontOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightFrontOpenEdge)
.def("nodesRightBackOpenEdge",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBackOpenEdge)
.def("nodesFrontBottomLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontBottomLeftCorner)
.def("nodesFrontBottomRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontBottomRightCorner)
.def("nodesFrontTopLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontTopLeftCorner)
.def("nodesFrontTopRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontTopRightCorner)
.def("nodesBackBottomLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackBottomLeftCorner)
.def("nodesBackBottomRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackBottomRightCorner)
.def("nodesBackTopLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackTopLeftCorner)
.def("nodesBackTopRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackTopRightCorner)
.def("nodesFrontLeftBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontLeftBottomCorner)
.def("nodesBottomFrontLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomFrontLeftCorner)
.def("nodesBottomLeftFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomLeftFrontCorner)
.def("nodesLeftFrontBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftFrontBottomCorner)
.def("nodesLeftBottomFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBottomFrontCorner)
.def("nodesFrontRightBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontRightBottomCorner)
.def("nodesBottomFrontRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomFrontRightCorner)
.def("nodesBottomRightFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomRightFrontCorner)
.def("nodesRightFrontBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightFrontBottomCorner)
.def("nodesRightBottomFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBottomFrontCorner)
.def("nodesFrontLeftTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontLeftTopCorner)
.def("nodesTopFrontLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopFrontLeftCorner)
.def("nodesTopLeftFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopLeftFrontCorner)
.def("nodesLeftFrontTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftFrontTopCorner)
.def("nodesLeftTopFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftTopFrontCorner)
.def("nodesFrontRightTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesFrontRightTopCorner)
.def("nodesTopFrontRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopFrontRightCorner)
.def("nodesTopRightFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopRightFrontCorner)
.def("nodesRightFrontTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightFrontTopCorner)
.def("nodesRightTopFrontCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightTopFrontCorner)
.def("nodesBackLeftBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackLeftBottomCorner)
.def("nodesBottomBackLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomBackLeftCorner)
.def("nodesBottomLeftBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomLeftBackCorner)
.def("nodesLeftBackBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBackBottomCorner)
.def("nodesLeftBottomBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBottomBackCorner)
.def("nodesBackRightBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackRightBottomCorner)
.def("nodesBottomBackRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomBackRightCorner)
.def("nodesBottomRightBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBottomRightBackCorner)
.def("nodesRightBackBottomCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBackBottomCorner)
.def("nodesRightBottomBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBottomBackCorner)
.def("nodesBackLeftTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackLeftTopCorner)
.def("nodesTopBackLeftCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopBackLeftCorner)
.def("nodesTopLeftBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopLeftBackCorner)
.def("nodesLeftBackTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftBackTopCorner)
.def("nodesLeftTopBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesLeftTopBackCorner)
.def("nodesBackRightTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesBackRightTopCorner)
.def("nodesTopBackRightCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopBackRightCorner)
.def("nodesTopRightBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesTopRightBackCorner)
.def("nodesRightBackTopCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightBackTopCorner)
.def("nodesRightTopBackCorner",
&GooseFEM::Mesh::Hex8::FineLayer::nodesRightTopBackCorner)
.def("nodesPeriodic",
&GooseFEM::Mesh::Hex8::FineLayer::nodesPeriodic)
.def("nodesOrigin",
&GooseFEM::Mesh::Hex8::FineLayer::nodesOrigin)
.def("dofs",
&GooseFEM::Mesh::Hex8::FineLayer::dofs)
.def("dofsPeriodic",
&GooseFEM::Mesh::Hex8::FineLayer::dofsPeriodic)
.def("__repr__",
[](const GooseFEM::Mesh::Hex8::FineLayer &){ return "<GooseFEM.Mesh.Hex8.FineLayer>"; });
}
// =================================================================================================
diff --git a/python/MeshQuad4.hpp b/python/MeshQuad4.hpp
index 070f937..3ab9c4d 100644
--- a/python/MeshQuad4.hpp
+++ b/python/MeshQuad4.hpp
@@ -1,326 +1,327 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_MeshQuad4(py::module& m)
{
py::class_<GooseFEM::Mesh::Quad4::Regular>(m, "Regular")
.def(py::init<size_t,size_t,double>(),
"Regular mesh: 'nx' pixels in horizontal direction, 'ny' in vertical direction, edge size 'h'",
py::arg("nx"),
py::arg("ny"),
py::arg("h")=1.)
.def("coor",
&GooseFEM::Mesh::Quad4::Regular::coor)
.def("conn",
&GooseFEM::Mesh::Quad4::Regular::conn)
.def("nelem",
&GooseFEM::Mesh::Quad4::Regular::nelem)
.def("nnode",
&GooseFEM::Mesh::Quad4::Regular::nnode)
.def("nne",
&GooseFEM::Mesh::Quad4::Regular::nne)
.def("ndim",
&GooseFEM::Mesh::Quad4::Regular::ndim)
.def("nelx",
&GooseFEM::Mesh::Quad4::Regular::nelx)
.def("nely",
&GooseFEM::Mesh::Quad4::Regular::nely)
.def("h",
&GooseFEM::Mesh::Quad4::Regular::h)
+ .def("getElementType",
+ &GooseFEM::Mesh::Quad4::Regular::getElementType)
+
.def("nodesBottomEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesBottomEdge)
.def("nodesTopEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesTopEdge)
.def("nodesLeftEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesLeftEdge)
.def("nodesRightEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesRightEdge)
.def("nodesBottomOpenEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesBottomOpenEdge)
.def("nodesTopOpenEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesTopOpenEdge)
.def("nodesLeftOpenEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesLeftOpenEdge)
.def("nodesRightOpenEdge",
&GooseFEM::Mesh::Quad4::Regular::nodesRightOpenEdge)
.def("nodesBottomLeftCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesBottomLeftCorner)
.def("nodesBottomRightCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesBottomRightCorner)
.def("nodesTopLeftCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesTopLeftCorner)
.def("nodesTopRightCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesTopRightCorner)
.def("nodesLeftBottomCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesLeftBottomCorner)
.def("nodesLeftTopCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesLeftTopCorner)
.def("nodesRightBottomCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesRightBottomCorner)
.def("nodesRightTopCorner",
&GooseFEM::Mesh::Quad4::Regular::nodesRightTopCorner)
.def("dofs",
&GooseFEM::Mesh::Quad4::Regular::dofs)
.def("nodesPeriodic",
&GooseFEM::Mesh::Quad4::Regular::nodesPeriodic)
.def("nodesOrigin",
&GooseFEM::Mesh::Quad4::Regular::nodesOrigin)
.def("dofsPeriodic",
&GooseFEM::Mesh::Quad4::Regular::dofsPeriodic)
.def("elementMatrix",
&GooseFEM::Mesh::Quad4::Regular::elementMatrix)
.def("__repr__",
[](const GooseFEM::Mesh::Quad4::Regular&){ return "<GooseFEM.Mesh.Quad4.Regular>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::Mesh::Quad4::FineLayer>(m, "FineLayer")
.def(py::init<size_t,size_t,double,size_t>(),
"FineLayer mesh: 'nx' pixels in horizontal direction (length 'Lx'), idem in vertical direction",
py::arg("nx"),
py::arg("ny"),
py::arg("h")=1.,
py::arg("nfine")=1)
.def("coor",
&GooseFEM::Mesh::Quad4::FineLayer::coor)
.def("conn",
&GooseFEM::Mesh::Quad4::FineLayer::conn)
.def("nelem",
&GooseFEM::Mesh::Quad4::FineLayer::nelem)
.def("nnode",
&GooseFEM::Mesh::Quad4::FineLayer::nnode)
.def("nne",
&GooseFEM::Mesh::Quad4::FineLayer::nne)
.def("ndim",
&GooseFEM::Mesh::Quad4::FineLayer::ndim)
.def("nelx",
&GooseFEM::Mesh::Quad4::FineLayer::nelx)
.def("nely",
&GooseFEM::Mesh::Quad4::FineLayer::nely)
.def("h",
&GooseFEM::Mesh::Quad4::FineLayer::h)
+ .def("getElementType",
+ &GooseFEM::Mesh::Quad4::FineLayer::getElementType)
+
.def("elementsMiddleLayer",
&GooseFEM::Mesh::Quad4::FineLayer::elementsMiddleLayer)
.def("nodesBottomEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesBottomEdge)
.def("nodesTopEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesTopEdge)
.def("nodesLeftEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesLeftEdge)
.def("nodesRightEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesRightEdge)
.def("nodesBottomOpenEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesBottomOpenEdge)
.def("nodesTopOpenEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesTopOpenEdge)
.def("nodesLeftOpenEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesLeftOpenEdge)
.def("nodesRightOpenEdge",
&GooseFEM::Mesh::Quad4::FineLayer::nodesRightOpenEdge)
.def("nodesBottomLeftCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesBottomLeftCorner)
.def("nodesBottomRightCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesBottomRightCorner)
.def("nodesTopLeftCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesTopLeftCorner)
.def("nodesTopRightCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesTopRightCorner)
.def("nodesLeftBottomCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesLeftBottomCorner)
.def("nodesLeftTopCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesLeftTopCorner)
.def("nodesRightBottomCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesRightBottomCorner)
.def("nodesRightTopCorner",
&GooseFEM::Mesh::Quad4::FineLayer::nodesRightTopCorner)
.def("dofs",
&GooseFEM::Mesh::Quad4::FineLayer::dofs)
.def("nodesPeriodic",
&GooseFEM::Mesh::Quad4::FineLayer::nodesPeriodic)
.def("nodesOrigin",
&GooseFEM::Mesh::Quad4::FineLayer::nodesOrigin)
.def("dofsPeriodic",
&GooseFEM::Mesh::Quad4::FineLayer::dofsPeriodic)
.def("__repr__",
[](const GooseFEM::Mesh::Quad4::FineLayer&){ return "<GooseFEM.Mesh.Quad4.FineLayer>"; }
);
}
// =================================================================================================
void init_MeshQuad4Map(py::module& m)
{
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::Mesh::Quad4::Map::RefineRegular>(m, "RefineRegular")
.def(py::init<const GooseFEM::Mesh::Quad4::Regular &, size_t, size_t>(),
"Refine a regular mesh",
py::arg("mesh"),
py::arg("nx"),
py::arg("ny"))
.def("getCoarseMesh",
&GooseFEM::Mesh::Quad4::Map::RefineRegular::getCoarseMesh)
.def("getFineMesh",
&GooseFEM::Mesh::Quad4::Map::RefineRegular::getFineMesh)
.def("getMap",
&GooseFEM::Mesh::Quad4::Map::RefineRegular::getMap)
.def("mapToCoarse",
py::overload_cast<const xt::xtensor<double,1>&>(
&GooseFEM::Mesh::Quad4::Map::RefineRegular::mapToCoarse, py::const_))
.def("mapToCoarse",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::Mesh::Quad4::Map::RefineRegular::mapToCoarse, py::const_))
.def("mapToCoarse",
py::overload_cast<const xt::xtensor<double,4>&>(
&GooseFEM::Mesh::Quad4::Map::RefineRegular::mapToCoarse, py::const_))
.def("mapToFine",
py::overload_cast<const xt::xtensor<double,1>&>(
&GooseFEM::Mesh::Quad4::Map::RefineRegular::mapToFine, py::const_))
.def("mapToFine",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::Mesh::Quad4::Map::RefineRegular::mapToFine, py::const_))
.def("mapToFine",
py::overload_cast<const xt::xtensor<double,4>&>(
&GooseFEM::Mesh::Quad4::Map::RefineRegular::mapToFine, py::const_))
.def("__repr__",
[](const GooseFEM::Mesh::Quad4::Map::RefineRegular &){
return "<GooseFEM.Mesh.Quad4.Map.RefineRegular>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::Mesh::Quad4::Map::FineLayer2Regular>(m, "FineLayer2Regular")
.def(py::init<const GooseFEM::Mesh::Quad4::FineLayer &>(),
"Map a FineLayer mesh to a Regular mesh",
py::arg("mesh"))
.def("getRegularMesh",
&GooseFEM::Mesh::Quad4::Map::FineLayer2Regular::getRegularMesh)
.def("getFineLayerMesh",
&GooseFEM::Mesh::Quad4::Map::FineLayer2Regular::getFineLayerMesh)
.def("getMap",
&GooseFEM::Mesh::Quad4::Map::FineLayer2Regular::getMap)
.def("getMapFraction",
&GooseFEM::Mesh::Quad4::Map::FineLayer2Regular::getMapFraction)
.def("mapToRegular",
py::overload_cast<const xt::xtensor<double,1>&>(
&GooseFEM::Mesh::Quad4::Map::FineLayer2Regular::mapToRegular, py::const_))
.def("mapToRegular",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::Mesh::Quad4::Map::FineLayer2Regular::mapToRegular, py::const_))
.def("mapToRegular",
py::overload_cast<const xt::xtensor<double,4>&>(
&GooseFEM::Mesh::Quad4::Map::FineLayer2Regular::mapToRegular, py::const_))
.def("__repr__",
[](const GooseFEM::Mesh::Quad4::Map::FineLayer2Regular &){
return "<GooseFEM.Mesh.Quad4.Map.FineLayer2Regular>"; });
// -------------------------------------------------------------------------------------------------
}
// =================================================================================================
diff --git a/python/MeshTri3.hpp b/python/MeshTri3.hpp
index 1648394..b77fe6f 100644
--- a/python/MeshTri3.hpp
+++ b/python/MeshTri3.hpp
@@ -1,133 +1,145 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_MeshTri3(py::module& m)
{
py::class_<GooseFEM::Mesh::Tri3::Regular>(m, "Regular")
.def(
py::init<size_t,size_t,double>(),
"Regular mesh: 'nx' pixels in horizontal direction, 'ny' in vertical direction, edge size 'h'",
py::arg("nx"),
py::arg("ny"),
py::arg("h")=1.)
.def("coor",
&GooseFEM::Mesh::Tri3::Regular::coor)
.def("conn",
&GooseFEM::Mesh::Tri3::Regular::conn)
.def("nelem",
&GooseFEM::Mesh::Tri3::Regular::nelem)
.def("nnode",
&GooseFEM::Mesh::Tri3::Regular::nnode)
.def("nne",
&GooseFEM::Mesh::Tri3::Regular::nne)
.def("ndim",
&GooseFEM::Mesh::Tri3::Regular::ndim)
+ .def("getElementType",
+ &GooseFEM::Mesh::Tri3::Regular::getElementType)
+
.def("nodesBottomEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesBottomEdge)
.def("nodesTopEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesTopEdge)
.def("nodesLeftEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesLeftEdge)
.def("nodesRightEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesRightEdge)
.def("nodesBottomOpenEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesBottomOpenEdge)
.def("nodesTopOpenEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesTopOpenEdge)
.def("nodesLeftOpenEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesLeftOpenEdge)
.def("nodesRightOpenEdge",
&GooseFEM::Mesh::Tri3::Regular::nodesRightOpenEdge)
.def("nodesBottomLeftCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesBottomLeftCorner)
.def("nodesBottomRightCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesBottomRightCorner)
.def("nodesTopLeftCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesTopLeftCorner)
.def("nodesTopRightCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesTopRightCorner)
.def("nodesLeftBottomCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesLeftBottomCorner)
.def("nodesLeftTopCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesLeftTopCorner)
.def("nodesRightBottomCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesRightBottomCorner)
.def("nodesRightTopCorner",
&GooseFEM::Mesh::Tri3::Regular::nodesRightTopCorner)
.def("nodesPeriodic",
&GooseFEM::Mesh::Tri3::Regular::nodesPeriodic)
.def("nodesOrigin",
&GooseFEM::Mesh::Tri3::Regular::nodesOrigin)
.def("dofs",
&GooseFEM::Mesh::Tri3::Regular::dofs)
.def("dofsPeriodic",
&GooseFEM::Mesh::Tri3::Regular::dofsPeriodic)
.def("__repr__",
[](const GooseFEM::Mesh::Tri3::Regular&){ return "<GooseFEM.Mesh.Tri3.Regular>"; });
// -------------------------------------------------------------------------------------------------
m.def("getOrientation",
&GooseFEM::Mesh::Tri3::getOrientation,
"Get the orientation of each element",
py::arg("coor"),
py::arg("conn"));
-m.def("retriangulate",
- &GooseFEM::Mesh::Tri3::retriangulate,
- "Re-triangulate existing mesh",
+m.def("setOrientation",
+ py::overload_cast<
+ const xt::xtensor<double,2>&,
+ const xt::xtensor<size_t,2>&,
+ int>(&GooseFEM::Mesh::Tri3::setOrientation),
+ "Set the orientation of each element",
py::arg("coor"),
py::arg("conn"),
- py::arg("orientation")=-1);
-
+ py::arg("orientation"));
+
+m.def("setOrientation",
+ py::overload_cast<
+ const xt::xtensor<double,2>&,
+ const xt::xtensor<size_t,2>&,
+ const xt::xtensor<int,1>&,
+ int>(&GooseFEM::Mesh::Tri3::setOrientation),
+ "Set the orientation of each element",
+ py::arg("coor"),
+ py::arg("conn"),
+ py::arg("val"),
+ py::arg("orientation"));
}
// =================================================================================================
diff --git a/python/ParaView.hpp b/python/ParaView.hpp
index 4ad07e7..345e7f7 100644
--- a/python/ParaView.hpp
+++ b/python/ParaView.hpp
@@ -1,214 +1,220 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#define GOOSEFEM_NO_HIGHFIVE
#include "../include/GooseFEM/GooseFEM.h"
#include "../include/GooseFEM/ParaView.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_ParaViewHDF5(py::module& m)
{
m.def("as3d", &GooseFEM::ParaView::HDF5::as3d);
// -------------------------------------------------------------------------------------------------
py::enum_<GooseFEM::ParaView::HDF5::ElementType>(m, "ElementType", "ElementType")
.value("Triangle", GooseFEM::ParaView::HDF5::ElementType::Triangle)
.value("Quadrilateral", GooseFEM::ParaView::HDF5::ElementType::Quadrilateral)
.value("Hexahedron", GooseFEM::ParaView::HDF5::ElementType::Hexahedron)
.export_values();
// -------------------------------------------------------------------------------------------------
py::enum_<GooseFEM::ParaView::HDF5::AttributeType>(m, "AttributeType", "AttributeType")
.value("Cell", GooseFEM::ParaView::HDF5::AttributeType::Cell)
.value("Node", GooseFEM::ParaView::HDF5::AttributeType::Node)
.export_values();
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::ParaView::HDF5::Connectivity>(m, "Connectivity")
.def(py::init<
const std::string&,
const std::string&,
GooseFEM::ParaView::HDF5::ElementType,
const std::vector<size_t>&>(),
"Connectivity",
py::arg("fname"),
py::arg("dataset"),
py::arg("ElementType"),
py::arg("shape"))
+ .def(py::init<
+ const std::string&,
+ const std::string&,
+ GooseFEM::Mesh::ElementType,
+ const std::vector<size_t>&>(),
+ "Connectivity",
+ py::arg("fname"),
+ py::arg("dataset"),
+ py::arg("ElementType"),
+ py::arg("shape"))
+
.def("nelem",
&GooseFEM::ParaView::HDF5::Connectivity::nelem)
.def("nne",
&GooseFEM::ParaView::HDF5::Connectivity::nne)
.def("shape",
&GooseFEM::ParaView::HDF5::Connectivity::shape)
.def("fname",
&GooseFEM::ParaView::HDF5::Connectivity::fname)
.def("xdmf",
&GooseFEM::ParaView::HDF5::Connectivity::xdmf,
py::arg("indent")=4)
.def("__repr__",
[](const GooseFEM::ParaView::HDF5::Connectivity &){
return "<GooseFEM.ParaView.HDF5.Connectivity>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::ParaView::HDF5::Coordinates>(m, "Coordinates")
.def(py::init<
const std::string&,
const std::string&,
const std::vector<size_t>&>(),
"Coordinates",
py::arg("fname"),
py::arg("dataset"),
py::arg("shape"))
.def("nnode", &GooseFEM::ParaView::HDF5::Coordinates::nnode)
.def("ndim", &GooseFEM::ParaView::HDF5::Coordinates::ndim)
.def("shape", &GooseFEM::ParaView::HDF5::Coordinates::shape)
.def("fname", &GooseFEM::ParaView::HDF5::Coordinates::fname)
.def("xdmf", &GooseFEM::ParaView::HDF5::Coordinates::xdmf, py::arg("indent")=4)
.def("__repr__",
[](const GooseFEM::ParaView::HDF5::Coordinates &){
return "<GooseFEM.ParaView.HDF5.Coordinates>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::ParaView::HDF5::Attribute>(m, "Attribute")
.def(py::init<
const std::string&,
const std::string&,
const std::string&, GooseFEM::ParaView::HDF5::AttributeType,
const std::vector<size_t>&>(),
"Attribute",
py::arg("fname"),
py::arg("dataset"),
py::arg("name"),
py::arg("AttributeType"),
py::arg("shape"))
.def("shape",
&GooseFEM::ParaView::HDF5::Attribute::shape)
.def("fname",
&GooseFEM::ParaView::HDF5::Attribute::fname)
.def("xdmf",
&GooseFEM::ParaView::HDF5::Attribute::xdmf,
py::arg("indent")=4)
.def("__repr__",
[](const GooseFEM::ParaView::HDF5::Attribute &){
return "<GooseFEM.ParaView.HDF5.Attribute>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::ParaView::HDF5::Mesh>(m, "Mesh")
.def(py::init<
const GooseFEM::ParaView::HDF5::Connectivity&,
const GooseFEM::ParaView::HDF5::Coordinates&>(),
"Mesh",
py::arg("conn"),
py::arg("coor"))
.def("push_back",
py::overload_cast<const GooseFEM::ParaView::HDF5::Attribute&>(
&GooseFEM::ParaView::HDF5::Mesh::push_back))
.def("xdmf",
&GooseFEM::ParaView::HDF5::Mesh::xdmf,
py::arg("indent")=4)
.def("write",
&GooseFEM::ParaView::HDF5::Mesh::write,
py::arg("fname"),
py::arg("indent")=4)
.def("__repr__",
[](const GooseFEM::ParaView::HDF5::Mesh &){
return "<GooseFEM.ParaView.HDF5.Mesh>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::ParaView::HDF5::Increment>(m, "Increment")
.def(py::init<
const GooseFEM::ParaView::HDF5::Connectivity&,
const GooseFEM::ParaView::HDF5::Coordinates&>(),
"Increment",
py::arg("conn"),
py::arg("coor"))
.def("push_back",
py::overload_cast<const GooseFEM::ParaView::HDF5::Connectivity&>(
&GooseFEM::ParaView::HDF5::Increment::push_back))
.def("push_back",
py::overload_cast<const GooseFEM::ParaView::HDF5::Coordinates&>(
&GooseFEM::ParaView::HDF5::Increment::push_back))
.def("push_back",
py::overload_cast<const GooseFEM::ParaView::HDF5::Attribute&>(
&GooseFEM::ParaView::HDF5::Increment::push_back))
.def("xdmf",
&GooseFEM::ParaView::HDF5::Increment::xdmf,
py::arg("indent")=4)
.def("__repr__",
[](const GooseFEM::ParaView::HDF5::Increment &){
return "<GooseFEM.ParaView.HDF5.Increment>"; });
// -------------------------------------------------------------------------------------------------
py::class_<GooseFEM::ParaView::HDF5::TimeSeries>(m, "TimeSeries")
.def(py::init<>(),
"TimeSeries")
.def("push_back",
&GooseFEM::ParaView::HDF5::TimeSeries::push_back)
.def("xdmf",
&GooseFEM::ParaView::HDF5::TimeSeries::xdmf,
py::arg("indent")=4)
.def("write",
&GooseFEM::ParaView::HDF5::TimeSeries::write,
py::arg("fname"),
py::arg("indent")=4)
.def("__repr__",
[](const GooseFEM::ParaView::HDF5::TimeSeries &){
return "<GooseFEM.ParaView.HDF5.TimeSeries>"; });
}
diff --git a/python/Vector.hpp b/python/Vector.hpp
index cab2cb0..8b95be7 100644
--- a/python/Vector.hpp
+++ b/python/Vector.hpp
@@ -1,107 +1,102 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_Vector(py::module& m)
{
py::class_<GooseFEM::Vector>(m, "Vector")
.def(py::init<const xt::xtensor<size_t,2> &, const xt::xtensor<size_t,2> &>(),
"Switch between dofval/nodevec/elemvec",
py::arg("conn"),
py::arg("dofs"))
.def("nelem",
&GooseFEM::Vector::nelem,
"Number of element")
.def("nne",
&GooseFEM::Vector::nne,
"Number of nodes per element")
.def("nnode",
&GooseFEM::Vector::nnode,
"Number of nodes")
.def("ndim",
&GooseFEM::Vector::ndim,
"Number of dimensions")
.def("ndof",
&GooseFEM::Vector::ndof,
"Number of degrees-of-freedom")
.def("dofs",
&GooseFEM::Vector::dofs,
"Return degrees-of-freedom")
.def("AsDofs",
py::overload_cast<const xt::xtensor<double,2>&>(&GooseFEM::Vector::AsDofs, py::const_),
"Set 'dofval",
py::arg("nodevec"))
.def("AsDofs",
py::overload_cast<const xt::xtensor<double,3>&>(&GooseFEM::Vector::AsDofs, py::const_),
"Set 'dofval",
py::arg("elemvec"))
.def("AsNode",
py::overload_cast<const xt::xtensor<double,1>&>(&GooseFEM::Vector::AsNode, py::const_),
"Set 'nodevec",
py::arg("dofval"))
.def("AsNode",
py::overload_cast<const xt::xtensor<double,3>&>(&GooseFEM::Vector::AsNode, py::const_),
"Set 'nodevec",
py::arg("elemvec"))
.def("AsElement",
py::overload_cast<const xt::xtensor<double,1>&>(&GooseFEM::Vector::AsElement, py::const_),
"Set 'elemvec",
py::arg("dofval"))
.def("AsElement",
py::overload_cast<const xt::xtensor<double,2>&>(&GooseFEM::Vector::AsElement, py::const_),
"Set 'elemvec",
py::arg("nodevec"))
.def("AssembleDofs",
py::overload_cast<const xt::xtensor<double,2>&>(&GooseFEM::Vector::AssembleDofs, py::const_),
"Assemble 'dofval'",
py::arg("nodevec"))
.def("AssembleDofs",
py::overload_cast<const xt::xtensor<double,3>&>(&GooseFEM::Vector::AssembleDofs, py::const_),
"Assemble 'dofval'",
py::arg("elemvec"))
.def("AssembleNode",
py::overload_cast<const xt::xtensor<double,3>&>(&GooseFEM::Vector::AssembleNode, py::const_),
"Assemble 'nodevec'",
py::arg("elemvec"))
.def("__repr__",
[](const GooseFEM::Vector&){ return "<GooseFEM.Vector>"; });
}
// =================================================================================================
diff --git a/python/VectorPartitioned.hpp b/python/VectorPartitioned.hpp
index 0cf650a..3792030 100644
--- a/python/VectorPartitioned.hpp
+++ b/python/VectorPartitioned.hpp
@@ -1,219 +1,214 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
-#include <Eigen/Eigen>
-
#include <pybind11/pybind11.h>
-#include <pybind11/eigen.h>
-
#include <pyxtensor/pyxtensor.hpp>
-
#include "../include/GooseFEM/GooseFEM.h"
// =================================================================================================
namespace py = pybind11;
// =================================================================================================
void init_VectorPartitioned(py::module& m)
{
py::class_<GooseFEM::VectorPartitioned>(m, "VectorPartitioned")
.def(py::init<
const xt::xtensor<size_t,2>&,
const xt::xtensor<size_t,2>&,
const xt::xtensor<size_t,1>&>(),
"Switch between dofval/nodevec/elemvec",
py::arg("conn"),
py::arg("dofs"),
py::arg("iip"))
.def("nelem",
&GooseFEM::VectorPartitioned::nelem,
"Number of element")
.def("nne",
&GooseFEM::VectorPartitioned::nne,
"Number of nodes per element")
.def("nnode",
&GooseFEM::VectorPartitioned::nnode,
"Number of nodes")
.def("ndim",
&GooseFEM::VectorPartitioned::ndim,
"Number of dimensions")
.def("ndof",
&GooseFEM::VectorPartitioned::ndof,
"Number of degrees-of-freedom")
.def("nnu",
&GooseFEM::VectorPartitioned::nnu,
"Number of unknown degrees-of-freedom")
.def("nnp",
&GooseFEM::VectorPartitioned::nnp,
"Number of prescribed degrees-of-freedom")
.def("dofs",
&GooseFEM::VectorPartitioned::dofs,
"Return degrees-of-freedom")
.def("iiu",
&GooseFEM::VectorPartitioned::iiu,
"Return unknown degrees-of-freedom")
.def("iip",
&GooseFEM::VectorPartitioned::iip,
"Return prescribed degrees-of-freedom")
.def("AsDofs",
py::overload_cast<const xt::xtensor<double,1>&,const xt::xtensor<double,1>&>(
&GooseFEM::VectorPartitioned::AsDofs, py::const_),
"Set 'dofval",
py::arg("dofval_u"),
py::arg("dofval_p"))
.def("AsDofs",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::VectorPartitioned::AsDofs, py::const_),
"Set 'dofval",
py::arg("nodevec"))
.def("AsDofs",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::VectorPartitioned::AsDofs, py::const_),
"Set 'dofval",
py::arg("elemvec"))
.def("AsDofs_u",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::VectorPartitioned::AsDofs_u, py::const_),
"Set 'dofval",
py::arg("nodevec"))
.def("AsDofs_u",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::VectorPartitioned::AsDofs_u, py::const_),
"Set 'dofval",
py::arg("elemvec"))
.def("AsDofs_p",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::VectorPartitioned::AsDofs_p, py::const_),
"Set 'dofval",
py::arg("nodevec"))
.def("AsDofs_p",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::VectorPartitioned::AsDofs_p, py::const_),
"Set 'dofval",
py::arg("elemvec"))
.def("AsNode",
py::overload_cast<const xt::xtensor<double,1>&,const xt::xtensor<double,1>&>(
&GooseFEM::VectorPartitioned::AsNode, py::const_),
"Set 'nodevec",
py::arg("dofval_u"),
py::arg("dofval_p"))
.def("AsNode",
py::overload_cast<const xt::xtensor<double,1>&>(
&GooseFEM::VectorPartitioned::AsNode, py::const_),
"Set 'nodevec",
py::arg("dofval"))
.def("AsNode",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::VectorPartitioned::AsNode, py::const_),
"Set 'nodevec",
py::arg("elemvec"))
.def("AsElement",
py::overload_cast<const xt::xtensor<double,1>&,const xt::xtensor<double,1>&>(
&GooseFEM::VectorPartitioned::AsElement, py::const_),
"Set 'elemvec",
py::arg("dofval_u"),
py::arg("dofval_p"))
.def("AsElement",
py::overload_cast<const xt::xtensor<double,1>&>(
&GooseFEM::VectorPartitioned::AsElement, py::const_),
"Set 'elemvec",
py::arg("dofval"))
.def("AsElement",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::VectorPartitioned::AsElement, py::const_),
"Set 'elemvec",
py::arg("nodevec"))
.def("AssembleDofs",
py::overload_cast<const xt::xtensor<double,2>&>(
- &GooseFEM::VectorPartitioned::AssembleDofs , py::const_),
+ &GooseFEM::VectorPartitioned::AssembleDofs, py::const_),
"Assemble 'dofval'",
py::arg("nodevec"))
.def("AssembleDofs",
py::overload_cast<const xt::xtensor<double,3>&>(
- &GooseFEM::VectorPartitioned::AssembleDofs , py::const_),
+ &GooseFEM::VectorPartitioned::AssembleDofs, py::const_),
"Assemble 'dofval'",
py::arg("elemvec"))
.def("AssembleDofs_u",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::VectorPartitioned::AssembleDofs_u, py::const_),
"Assemble 'dofval'",
py::arg("nodevec"))
.def("AssembleDofs_u",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::VectorPartitioned::AssembleDofs_u, py::const_),
"Assemble 'dofval'",
py::arg("elemvec"))
.def("AssembleDofs_p",
py::overload_cast<const xt::xtensor<double,2>&>(
&GooseFEM::VectorPartitioned::AssembleDofs_p, py::const_),
"Assemble 'dofval'",
py::arg("nodevec"))
.def("AssembleDofs_p",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::VectorPartitioned::AssembleDofs_p, py::const_),
"Assemble 'dofval'",
py::arg("elemvec"))
.def("AssembleNode",
py::overload_cast<const xt::xtensor<double,3>&>(
&GooseFEM::VectorPartitioned::AssembleNode, py::const_),
"Assemble 'nodevec'",
py::arg("elemvec"))
.def("Copy",
&GooseFEM::VectorPartitioned::Copy,
"Copy")
.def("Copy_u",
&GooseFEM::VectorPartitioned::Copy_u,
"Copy iiu")
.def("Copy_p",
&GooseFEM::VectorPartitioned::Copy_p,
"Copy iip")
.def("__repr__", [](
const GooseFEM::VectorPartitioned&){ return "<GooseFEM.VectorPartitioned>"; });
}
// =================================================================================================
diff --git a/python/VectorPartitionedTyings.hpp b/python/VectorPartitionedTyings.hpp
new file mode 100644
index 0000000..e9e940f
--- /dev/null
+++ b/python/VectorPartitionedTyings.hpp
@@ -0,0 +1,122 @@
+/* =================================================================================================
+
+(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
+
+================================================================================================= */
+
+#include <pybind11/pybind11.h>
+#include <pyxtensor/pyxtensor.hpp>
+#include "../include/GooseFEM/GooseFEM.h"
+
+// =================================================================================================
+
+namespace py = pybind11;
+
+// =================================================================================================
+
+void init_VectorPartitionedTyings(py::module& m)
+{
+
+py::class_<GooseFEM::VectorPartitionedTyings>(m, "VectorPartitionedTyings")
+
+ .def(py::init<
+ const xt::xtensor<size_t,2>&,
+ const xt::xtensor<size_t,2>&,
+ const Eigen::SparseMatrix<double>&,
+ const Eigen::SparseMatrix<double>&,
+ const Eigen::SparseMatrix<double>&>(),
+ "Switch between dofval/nodevec/elemvec",
+ py::arg("conn"),
+ py::arg("dofs"),
+ py::arg("Cdu"),
+ py::arg("Cdp"),
+ py::arg("Cdi"))
+
+ .def("nelem",
+ &GooseFEM::VectorPartitionedTyings::nelem,
+ "Number of element")
+
+ .def("nne",
+ &GooseFEM::VectorPartitionedTyings::nne,
+ "Number of nodes per element")
+
+ .def("nnode",
+ &GooseFEM::VectorPartitionedTyings::nnode,
+ "Number of nodes")
+
+ .def("ndim",
+ &GooseFEM::VectorPartitionedTyings::ndim,
+ "Number of dimensions")
+
+ .def("ndof",
+ &GooseFEM::VectorPartitionedTyings::ndof,
+ "Number of degrees-of-freedom")
+
+ .def("nnu",
+ &GooseFEM::VectorPartitionedTyings::nnu,
+ "Number of unknown degrees-of-freedom")
+
+ .def("nnp",
+ &GooseFEM::VectorPartitionedTyings::nnp,
+ "Number of prescribed degrees-of-freedom")
+
+ .def("nni",
+ &GooseFEM::VectorPartitionedTyings::nni,
+ "Number of independent degrees-of-freedom")
+
+ .def("nnd",
+ &GooseFEM::VectorPartitionedTyings::nnd,
+ "Number of dependent degrees-of-freedom")
+
+ .def("dofs",
+ &GooseFEM::VectorPartitionedTyings::dofs,
+ "Return degrees-of-freedom")
+
+ .def("iiu",
+ &GooseFEM::VectorPartitionedTyings::iiu,
+ "Return unknown degrees-of-freedom")
+
+ .def("iip",
+ &GooseFEM::VectorPartitionedTyings::iip,
+ "Return prescribed degrees-of-freedom")
+
+ .def("iii",
+ &GooseFEM::VectorPartitionedTyings::iii,
+ "Return independent degrees-of-freedom")
+
+ .def("iid",
+ &GooseFEM::VectorPartitionedTyings::iid,
+ "Return dependent degrees-of-freedom")
+
+ .def("AsDofs_i",
+ &GooseFEM::VectorPartitionedTyings::AsDofs_i,
+ "Set 'dofval",
+ py::arg("nodevec"))
+
+ .def("AsNode",
+ &GooseFEM::VectorPartitionedTyings::AsNode,
+ "Set 'nodevec",
+ py::arg("dofval"))
+
+ .def("AsElement",
+ &GooseFEM::VectorPartitionedTyings::AsElement,
+ "Set 'elemvec",
+ py::arg("nodevec"))
+
+ .def("AssembleDofs",
+ &GooseFEM::VectorPartitionedTyings::AssembleDofs,
+ "Assemble 'dofval'",
+ py::arg("elemvec"))
+
+ .def("AssembleNode",
+ &GooseFEM::VectorPartitionedTyings::AssembleNode,
+ "Assemble 'nodevec'",
+ py::arg("elemvec"))
+
+ .def("__repr__", [](
+ const GooseFEM::VectorPartitionedTyings&){ return "<GooseFEM.VectorPartitionedTyings>"; });
+
+}
+
+// =================================================================================================
+
diff --git a/python/main.cpp b/python/main.cpp
index 34f9be6..1bb9f14 100644
--- a/python/main.cpp
+++ b/python/main.cpp
@@ -1,132 +1,140 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#include <Eigen/Eigen>
#include <pybind11/pybind11.h>
#include <pybind11/eigen.h>
#include <pyxtensor/pyxtensor.hpp>
#define GOOSEFEM_ENABLE_ASSERT
#include "../include/GooseFEM/GooseFEM.h"
namespace py = pybind11;
#include "Vector.hpp"
#include "VectorPartitioned.hpp"
+#include "VectorPartitionedTyings.hpp"
+#include "Matrix.hpp"
#include "MatrixPartitioned.hpp"
+#include "MatrixPartitionedTyings.hpp"
+#include "MatrixDiagonal.hpp"
#include "MatrixDiagonalPartitioned.hpp"
#include "Element.hpp"
#include "ElementQuad4.hpp"
#include "ElementQuad4Planar.hpp"
#include "ElementQuad4Axisymmetric.hpp"
#include "ElementHex8.hpp"
#include "Mesh.hpp"
#include "MeshTri3.hpp"
#include "MeshQuad4.hpp"
#include "MeshHex8.hpp"
#include "ParaView.hpp"
// =================================================================================================
PYBIND11_MODULE(GooseFEM, m) {
// -------------------------------------------------------------------------------------------------
// GooseFEM
// -------------------------------------------------------------------------------------------------
m.doc() = "Some simple finite element meshes and operations";
init_Vector(m);
init_VectorPartitioned(m);
+init_VectorPartitionedTyings(m);
+init_Matrix(m);
init_MatrixPartitioned(m);
+init_MatrixPartitionedTyings(m);
+init_MatrixDiagonal(m);
init_MatrixDiagonalPartitioned(m);
// -------------------------------------------------------------------------------------------------
// GooseFEM.Element
// -------------------------------------------------------------------------------------------------
py::module mElement = m.def_submodule("Element", "Generic element routines");
init_Element(mElement);
// -------------------------------------------------------------------------------------------------
// GooseFEM.Element.Quad4
// -------------------------------------------------------------------------------------------------
py::module mElementQuad4 = mElement.def_submodule("Quad4", "Linear quadrilateral elements (2D)");
py::module mElementQuad4Gauss = mElementQuad4.def_submodule("Gauss", "Gauss quadrature");
py::module mElementQuad4Nodal = mElementQuad4.def_submodule("Nodal", "Nodal quadrature");
init_ElementQuad4(mElementQuad4);
init_ElementQuad4Planar(mElementQuad4);
init_ElementQuad4Axisymmetric(mElementQuad4);
init_ElementQuad4Gauss(mElementQuad4Gauss);
init_ElementQuad4Nodal(mElementQuad4Nodal);
// -------------------------------------------------------------------------------------------------
// GooseFEM.Element.Hex8
// -------------------------------------------------------------------------------------------------
py::module mElementHex8 = mElement.def_submodule("Hex8", "Linear hexahedron (brick) elements (3D)");
py::module mElementHex8Gauss = mElementHex8.def_submodule("Gauss", "Gauss quadrature");
py::module mElementHex8Nodal = mElementHex8.def_submodule("Nodal", "Nodal quadrature");
init_ElementHex8(mElementHex8);
init_ElementHex8Gauss(mElementHex8Gauss);
init_ElementHex8Nodal(mElementHex8Nodal);
// -------------------------------------------------------------------------------------------------
// GooseFEM.Mesh
// -------------------------------------------------------------------------------------------------
py::module mMesh = m.def_submodule("Mesh", "Generic mesh routines");
init_Mesh(mMesh);
// -------------------------------------------------------------------------------------------------
// GooseFEM.Mesh.Tri3
// -------------------------------------------------------------------------------------------------
py::module mMeshTri3 = mMesh.def_submodule("Tri3", "Linear triangular elements (2D)");
init_MeshTri3(mMeshTri3);
// -------------------------------------------------------------------------------------------------
// GooseFEM.Mesh.Quad4
// -------------------------------------------------------------------------------------------------
py::module mMeshQuad4 = mMesh.def_submodule("Quad4", "Linear quadrilateral elements (2D)");
init_MeshQuad4(mMeshQuad4);
py::module mMeshQuad4Map = mMeshQuad4.def_submodule("Map", "Map mesh objects");
init_MeshQuad4Map(mMeshQuad4Map);
// -------------------------------------------------------------------------------------------------
// GooseFEM.Mesh.Hex8
// -------------------------------------------------------------------------------------------------
py::module mMeshHex8 = mMesh.def_submodule("Hex8", "Linear hexahedron (brick) elements (3D)");
init_MeshHex8(mMeshHex8);
// -------------------------------------------------------------------------------------------------
// GooseFEM.ParaView
// -------------------------------------------------------------------------------------------------
py::module mParaView = m.def_submodule("ParaView", "ParaView output files");
py::module mParaViewHDF5 = mParaView.def_submodule("HDF5", "ParaView/HDF5 support using XDMF files");
init_ParaViewHDF5(mParaViewHDF5);
// =================================================================================================
}