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diff --git a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/CMakeLists.txt b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/CMakeLists.txt
index 0aafb9a..bfd2cc0 100644
--- a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/CMakeLists.txt
+++ b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/CMakeLists.txt
@@ -1,68 +1,68 @@
cmake_minimum_required(VERSION 3.1)
# define a project name
project(example)
# define empty list of libraries to link
set(PROJECT_LIBS "")
# set optimization level
set(CMAKE_BUILD_TYPE Release)
# set C++ standard
set(CMAKE_CXX_STANDARD 14)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
set(CMAKE_CXX_EXTENSIONS OFF)
# add optimization options: switch on/off assertions
option(ASSERT "Switch on assertions" OFF)
if(NOT ASSERT)
add_definitions(-DNDEBUG)
endif()
# set warnings on
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wall -Wextra -pedantic")
# OpenMP settings
option(OPENMP "Switch on parallelization" ON)
if(OPENMP)
if (NOT "${CMAKE_CXX_COMPILER_ID}" STREQUAL "AppleClang")
find_package(OpenMP)
if(OPENMP_FOUND)
set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} ${OpenMP_C_FLAGS}")
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
endif()
endif()
else()
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-unknown-pragmas")
endif()
# load pkg-config
find_package(PkgConfig)
# load HDF5
find_package(HDF5 COMPONENTS CXX REQUIRED)
include_directories(${HDF5_INCLUDE_DIRS})
set(PROJECT_LIBS ${PROJECT_LIBS} ${HDF5_LIBS} ${HDF5_LIBRARIES})
# load header-only modules using pkg-config
# - eigen3
pkg_check_modules(EIGEN3 REQUIRED eigen3)
include_directories(SYSTEM ${EIGEN3_INCLUDE_DIRS})
# - cppmat
pkg_check_modules(CPPMAT REQUIRED cppmat)
include_directories(${CPPMAT_INCLUDE_DIRS})
# - GooseFEM
pkg_check_modules(GOOSEFEM REQUIRED GooseFEM)
include_directories(${GOOSEFEM_INCLUDE_DIRS})
-# - GooseMaterial
-pkg_check_modules(GOOSEMATERIAL REQUIRED GooseMaterial)
-include_directories(${GOOSEMATERIAL_INCLUDE_DIRS})
+# - ElastoPlasticQPot
+pkg_check_modules(ELASTOPLASTICQPOT REQUIRED ElastoPlasticQPot)
+include_directories(${ELASTOPLASTICQPOT_INCLUDE_DIRS})
# - HDF5pp
pkg_check_modules(HDF5PP REQUIRED HDF5pp)
include_directories(${HDF5PP_INCLUDE_DIRS})
# create executable
add_executable(${PROJECT_NAME} main.cpp)
# link libraries
target_link_libraries(${PROJECT_NAME} ${PROJECT_LIBS})
diff --git a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/example.svg b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/example.svg
index 04560d6..15cf70b 100644
--- a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/example.svg
+++ b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/example.svg
@@ -1,12239 +1,12239 @@
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diff --git a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/main.cpp b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/main.cpp
index 50ae9d1..8b4b9ff 100644
--- a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/main.cpp
+++ b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/main.cpp
@@ -1,214 +1,228 @@
#include <Eigen/Eigen>
#include <cppmat/cppmat.h>
#include <GooseFEM/GooseFEM.h>
-#include <GooseMaterial/GooseMaterial.h>
+#include <ElastoPlasticQPot/ElastoPlasticQPot.h>
#include <HDF5pp.h>
// -------------------------------------------------------------------------------------------------
-// introduce aliases
-using ColD = GooseFEM::ColD;
-using T2 = cppmat::cartesian2d::tensor2<double>;
-using Mat = GooseMaterial::AmorphousSolid::LinearStrain::Elastic::Cartesian2d::Material;
+namespace GF = GooseFEM;
+namespace Elem = GooseFEM::Element::Quad4;
+namespace Mat = ElastoPlasticQPot::Cartesian2d;
-// =================================================================================================
+using T2 = cppmat::cartesian2d::tensor2<double>;
-class Material
+// -------------------------------------------------------------------------------------------------
+
+class Geometry : public GooseFEM::Dynamics::Geometry
{
-public:
+private:
- // class variables
- // ---------------
+ // dimensions
+ size_t m_nnode;
+ size_t m_ndim;
+ size_t m_nelem;
+ size_t m_nne;
+ size_t m_nip;
- // strain(-rate), stress, mass density, background damping [mandatory]
- cppmat::matrix<double> eps, epsdot, sig, rho, alpha;
+ // mesh
+ GF::MatS m_conn;
+ GF::MatD m_coor;
+ GF::MatD m_u;
+ GF::MatD m_v;
+ GF::MatD m_a;
- // mesh dimensions
- size_t nelem, nne=4, ndim=2, nip=4;
+ // vector-definition: transform nodal vectors <-> DOF values
+ GF::Vector m_vec;
- // constitutive response [customize]
- std::vector<Mat> material;
+ // mass matrix (diagonal)
+ GF::MatrixDiagonal m_M;
- // class functions
- // ---------------
+ // numerical quadrature
+ Elem::Quadrature m_quad;
- // constructor [customize]
- Material(size_t nelem, size_t nhard);
+ // material definition
+ Mat::Matrix m_mat;
- // compute stress for a certain element "e" and integration point "k" [mandatory]
- void updated_eps (size_t e, size_t k);
- void updated_epsdot(size_t e, size_t k);
+public:
- // post process variables / functions [customize]
- // - potential energy
- cppmat::matrix<double> Epot;
- // - compute potential energy
- void post();
-};
+ // constructor
+ Geometry(size_t nx);
-// -------------------------------------------------------------------------------------------------
+ // apply update in macroscopic deformation gradient
+ void add_dFbar(const T2 &dFbar);
-Material::Material(size_t _nelem, size_t _nhard)
-{
- // copy from input [customize]
- nelem = _nelem;
+ // compute total kinetic and potential energy
+ double Ekin() const;
+ double Epot() const;
- // allocate symmetric tensors and scalars per element, per integration point [mandatory]
- eps .resize({nelem,nip,3});
- epsdot.resize({nelem,nip,3});
- sig .resize({nelem,nip,3});
- rho .resize({nelem,nne });
- alpha .resize({nelem,nne });
+ // return mesh
+ GF::MatS conn() const { return m_conn; }
+ GF::MatD coor() const { return m_coor; }
- // set mass-density and background damping [customize]
- rho .setConstant(1.0);
- alpha.setConstant(0.0);
+ // return nodal vectors
+ GF::MatD u() const { return m_u; }
+ GF::MatD v() const { return m_v; }
+ GF::MatD a() const { return m_a; }
- // post variables [customize]
- Epot.resize({nelem,nip});
+ // return DOF values
+ GF::ColD dofs_v() const { return m_vec.asDofs(m_v); }
+ GF::ColD dofs_a() const { return m_vec.asDofs(m_a); }
- // constitutive response per element (per integration post) [customize]
- for ( size_t e = 0 ; e < nelem ; ++e )
- {
- if ( e < _nhard )
- {
- Mat mat = Mat(100.,10.);
- material.push_back(mat);
- }
- else
- {
- Mat mat = Mat(100.,1.);
- material.push_back(mat);
- }
- }
-}
+ // overwrite nodal vectors
+ void set_u(const GF::MatD &nodevec) { m_u = nodevec; };
+
+ // overwrite nodal vectors, reconstructed from DOF values
+ void set_v(const GF::ColD &dofval) { m_v = m_vec.asNode(dofval); };
+ void set_a(const GF::ColD &dofval) { m_a = m_vec.asNode(dofval); };
+
+ // solve for DOF-accelerations
+ GF::ColD solve();
+};
// -------------------------------------------------------------------------------------------------
-void Material::updated_eps(size_t e, size_t k)
+inline Geometry::Geometry(size_t nx)
{
- // local views of the global arrays (speeds up indexing, and increases readability)
- cppmat::cartesian2d::tensor2s<double> Eps, Sig;
+ // get mesh
+ GF::Mesh::Quad4::Regular mesh(nx,nx,1.);
+
+ // vector-definition
+ m_vec = GF::Vector(mesh.conn(), mesh.dofsPeriodic());
+
+ // quadrature
+ m_quad = Elem::Quadrature(m_vec.asElement(mesh.coor()));
+
+ // dimensions, connectivity, and coordinates
+ m_nnode = mesh.nnode();
+ m_ndim = mesh.ndim();
+ m_nelem = mesh.nelem();
+ m_nne = mesh.nne();
+ m_nip = m_quad.nip();
+ m_conn = mesh.conn();
+ m_coor = mesh.coor();
+
+ // zero-initialize displacement, velocity, acceleration
+ m_u = GF::MatD::Zero(m_nnode, m_ndim);
+ m_v = GF::MatD::Zero(m_nnode, m_ndim);
+ m_a = GF::MatD::Zero(m_nnode, m_ndim);
+
+ // material definition
+ // - allocate
+ m_mat = Mat::Matrix({m_nelem, m_nip});
+ // - phase indicators
+ cppmat::matrix<size_t> Ihard = cppmat::matrix<size_t>::Zero({m_nelem, m_nip});
+ cppmat::matrix<size_t> Isoft = cppmat::matrix<size_t>::Ones({m_nelem, m_nip});
+ // - set hard indicator
+ for ( size_t e = 0 ; e < nx*nx/4 ; ++e )
+ for ( size_t k = 0 ; k < m_nip ; ++k )
+ Ihard(e,k) = 1;
+ // - set soft indicator
+ Isoft -= Ihard;
+ // - set material definition
+ m_mat.setElastic(Ihard, 100., 10.);
+ m_mat.setElastic(Isoft, 100., 1.);
+ // - check that all points have been set (not strictly needed)
+ m_mat.check();
+
+ // mass matrix
+ // - nodal quadrature
+ Elem::Quadrature q(m_vec.asElement(m_coor), Elem::Nodal::xi(), Elem::Nodal::w());
+ // - set density
+ GF::ArrD rho = GF::ArrD::Constant({m_nelem, m_nip}, 1.0);
+ // - allocate mass matrix
+ m_M = GF::MatrixDiagonal(m_conn, mesh.dofsPeriodic());
+ // - compute (constant hereafter)
+ m_M.assemble( q.int_N_scalar_NT_dV(rho) );
+}
- // point to correct position in matrix of tensors
- Eps.map(&eps(e,k));
+// -------------------------------------------------------------------------------------------------
- // compute stress
- Sig = material[e].stress(Eps);
+inline GF::ColD Geometry::solve()
+{
+ GF::ArrD Eps = m_quad.symGradN_vector( m_vec.asElement(m_u) );
+ GF::ArrD Sig = m_mat.stress(Eps);
+ GF::ColD F = m_vec.assembleDofs( m_quad.int_gradN_dot_tensor2_dV(Sig) );
- // copy to matrix of tensors
- std::copy(Sig.begin(), Sig.end(), &sig(e,k));
+ return m_M.solve( -F );
}
// -------------------------------------------------------------------------------------------------
-void Material::updated_epsdot(size_t e, size_t k)
+inline void Geometry::add_dFbar(const T2 &dFbar)
{
+ for ( size_t i = 0 ; i < m_nnode ; ++i )
+ for ( size_t j = 0 ; j < m_ndim ; ++j )
+ for ( size_t k = 0 ; k < m_ndim ; ++k )
+ m_u(i,j) += dFbar(j,k) * ( m_coor(i,k) - m_coor(0,k) );
}
// -------------------------------------------------------------------------------------------------
-void Material::post()
+inline double Geometry::Ekin() const
{
-#pragma omp parallel
-{
- // local views of the global arrays (speeds up indexing, and increases readability)
- cppmat::cartesian2d::tensor2s<double> Eps;
+ GF::ColD V = m_vec.asDofs(m_v);
+ GF::ColD M = m_M.asDiagonal();
- // loop over all elements / integration points
- #pragma omp for
- for ( size_t e = 0 ; e < nelem ; ++e )
- {
- for ( size_t k = 0 ; k < nip ; ++k )
- {
- // point to correct position in matrix of tensors
- Eps.map(&eps(e,k));
-
- // compute energy
- Epot(e,k) = material[e].energy(Eps);
- }
- }
-}
+ return 0.5 * M.dot(V.cwiseProduct(V));
}
-// =================================================================================================
+// -------------------------------------------------------------------------------------------------
+
+inline double Geometry::Epot() const
+{
+ GF::ArrD Eps = m_quad.symGradN_vector( m_vec.asElement(m_u) );
+ GF::ArrD E = m_mat.energy(Eps);
-// introduce aliases
-using Mesh = GooseFEM::Mesh::Quad4::Regular;
-using Element = GooseFEM::Dynamics::Diagonal::SmallStrain::Quad4<Material>;
-using Simulation = GooseFEM::Dynamics::Diagonal::Periodic<Element>;
+ return E.average(m_quad.dV(),false);
+}
-// =================================================================================================
+// -------------------------------------------------------------------------------------------------
int main()
{
// set simulation parameters
double T = 60. ; // total time
double dt = 1.e-2; // time increment
size_t nx = 40 ; // number of elements in both directions
double gamma = .05 ; // displacement step
- // class which provides the mesh
- Mesh mesh(nx,nx,1.);
- // extract information
- size_t nodeOrigin = mesh.nodesOrigin();
- size_t nelem = mesh.nelem();
- size_t nhard = nx*nx/4;
-
- // simulation class
- Simulation sim = Simulation(
- std::make_unique<Element>(std::make_unique<Material>(nelem,nhard),nelem),
- mesh.coor(),
- mesh.conn(),
- mesh.dofsPeriodic(),
- dt
- );
+ // define geometry
+ Geometry geometry(nx);
// define update in macroscopic deformation gradient
- T2 dFbar(0.);
+ T2 dFbar = T2::Zero();
dFbar(0,1) = gamma;
- // update the displacement according to the macroscopic deformation gradient update
- for ( size_t i = 0 ; i < sim.nnode ; ++i )
- for ( size_t j = 0 ; j < sim.ndim ; ++j )
- for ( size_t k = 0 ; k < sim.ndim ; ++k )
- sim.u(i,j) += dFbar(j,k) * ( sim.x(i,k) - sim.x(nodeOrigin,k) );
-
- // process updates for displacement dependent variables
- sim.updated_u();
+ // update displacement
+ geometry.add_dFbar(dFbar);
// output variables
- ColD Epot(static_cast<int>(T/dt)); Epot.setZero();
- ColD Ekin(static_cast<int>(T/dt)); Ekin.setZero();
- ColD t (static_cast<int>(T/dt)); t .setZero();
+ GF::ColD Epot(static_cast<int>(T/dt)); Epot.setZero();
+ GF::ColD Ekin(static_cast<int>(T/dt)); Ekin.setZero();
+ GF::ColD t (static_cast<int>(T/dt)); t .setZero();
// loop over increments
for ( size_t inc = 0 ; inc < static_cast<size_t>(Epot.size()) ; ++inc )
{
// - compute increment
- sim.Verlet();
-
- // - store time
- t(inc) = sim.t;
-
- // - store total kinetic energy
- for ( size_t i = 0 ; i < sim.ndof ; ++i )
- Ekin(inc) += .5 * sim.M(i) * std::pow(sim.V(i),2.);
+ GF::Dynamics::Verlet(geometry, dt);
- // - store total potential energy
- sim.elem->mat->post();
- Epot(inc) = sim.elem->mat->Epot.average(sim.elem->vol) * sim.elem->vol.sum();
+ // - store output
+ t (inc) = static_cast<double>(inc) * dt;
+ Ekin(inc) = geometry.Ekin();
+ Epot(inc) = geometry.Epot();
}
// write to output file
H5p::File f = H5p::File("example.hdf5","w");
- f.write("/global/Epot",Epot );
- f.write("/global/Ekin",Ekin );
- f.write("/global/t" ,t );
- f.write("/mesh/coor" ,mesh.coor());
- f.write("/mesh/conn" ,mesh.conn());
- f.write("/mesh/disp" ,sim.u );
+ f.write("/global/Epot",Epot );
+ f.write("/global/Ekin",Ekin );
+ f.write("/global/t" ,t );
+ f.write("/mesh/conn" ,geometry.conn());
+ f.write("/mesh/coor" ,geometry.coor());
+ f.write("/mesh/disp" ,geometry.u() );
return 0;
}
diff --git a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/plot.py b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/plot.py
index e83c20c..5e4d8b4 100644
--- a/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/plot.py
+++ b/docs/examples/DynamicsDiagonal/Periodic/laminate/no_damping/Verlet/plot.py
@@ -1,52 +1,52 @@
-import sys,os,re
+import sys, os, re
import h5py
-import numpy as np
+import numpy as np
import matplotlib.pyplot as plt
-import goosempl as gplt
-import matplotlib as mpl
+import goosempl as gplt
+import matplotlib as mpl
plt.style.use(['goose','goose-latex'])
# --------------------------------------------------------------------------------------------------
name = 'example.hdf5'
f = h5py.File(name,'r')
-fig = plt.figure(figsize=(20,10))
-fig.set_tight_layout(True)
+fig, axes = plt.subplots(figsize=(20,10), ncols=2)
# --------------------------------------------------------------------------------------------------
-ax = fig.add_subplot(1,2,1)
+ax = axes[0]
t = f['/global/t' ][:]
E = f['/global/Ekin'][:] + f['/global/Epot'][:]; ax.plot(t,E,color='k',label=r'$E_\mathrm{pot} + E_\mathrm{kin}$')
E = f['/global/Epot'][:] ; ax.plot(t,E,color='r',label=r'$E_\mathrm{pot}$')
E = f['/global/Ekin'][:] ; ax.plot(t,E,color='b',label=r'$E_\mathrm{kin}$')
-plt.legend(loc='lower right')
+ax.legend(loc='lower right')
-plt.xlabel(r'$t$')
-plt.ylabel(r'$E$')
+ax.set_xlabel(r'$t$')
+ax.set_ylabel(r'$E$')
# --------------------------------------------------------------------------------------------------
-ax = fig.add_subplot(1,2,2)
+ax = axes[1]
coor = f['/mesh/coor'][:]
conn = f['/mesh/conn'][:]
u = f['/mesh/disp'][:]
+
im = gplt.patch(coor=coor+u,conn=conn)
Lx = np.max(coor[:,0])-np.min(coor[:,0])
Ly = np.max(coor[:,1])-np.min(coor[:,1])
-plt.xlim([-0.1*Lx,1.3*Lx])
-plt.ylim([-0.1*Ly,1.3*Ly])
+ax.set_xlim([-0.1*Lx,1.3*Lx])
+ax.set_ylim([-0.1*Ly,1.3*Ly])
ax.set_aspect('equal')
plt.savefig(re.sub(r'(.*)(\.hdf5)',r'\1.svg',name))
plt.show()
diff --git a/src/GooseFEM/Dynamics.h b/src/GooseFEM/Dynamics.h
index 77a62ef..115ddae 100644
--- a/src/GooseFEM/Dynamics.h
+++ b/src/GooseFEM/Dynamics.h
@@ -1,70 +1,70 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_DYNAMICS_H
#define GOOSEFEM_DYNAMICS_H
// -------------------------------------------------------------------------------------------------
#include "GooseFEM.h"
// ======================================= GooseFEM::Dynamics =======================================
namespace GooseFEM {
namespace Dynamics {
// -------------------------------------------------------------------------------------------------
class Geometry
{
public:
// solve for DOF-accelerations [ndof]
- virtual ColD solve() const { return ColD(); };
+ virtual ColD solve() { return ColD(); };
// reset residuals, check for convergence
virtual void reset() { return; }
virtual bool stop(double tol) { UNUSED(tol); return false; };
// process time-step
virtual void timestep(double dt) { UNUSED(dt); return; };
// return nodal vectors [nnode, ndim]
virtual MatD u() const { return MatD(); };
virtual MatD v() const { return MatD(); };
virtual MatD a() const { return MatD(); };
// return DOF values [ndof]
virtual ColD dofs_v() const { return ColD(); };
virtual ColD dofs_a() const { return ColD(); };
// overwrite nodal vectors [nnode, ndim]
virtual void set_u(const MatD &nodevec) { UNUSED(nodevec); return; };
// overwrite nodal vectors, reconstructed from DOF values [ndof]
virtual void set_v(const ColD &dofval) { UNUSED(dofval); return; };
virtual void set_a(const ColD &dofval) { UNUSED(dofval); return; };
};
// -------------------------------------------------------------------------------------------------
// evaluate one time step
inline void Verlet(Geometry &geometry, double dt);
// evaluate one time step
inline void velocityVerlet(Geometry &geometry, double dt);
// iterate until all nodes have come to a rest
inline size_t quasiStaticVelocityVerlet(Geometry &geometry, double dt, double tol);
// -------------------------------------------------------------------------------------------------
}} // namespace ...
// =================================================================================================
#endif
diff --git a/src/GooseFEM/ElementQuad4.cpp b/src/GooseFEM/ElementQuad4.cpp
index 56299e8..9c463ec 100644
--- a/src/GooseFEM/ElementQuad4.cpp
+++ b/src/GooseFEM/ElementQuad4.cpp
@@ -1,644 +1,644 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_ELEMENTQUAD4_CPP
#define GOOSEFEM_ELEMENTQUAD4_CPP
// -------------------------------------------------------------------------------------------------
#include "ElementQuad4.h"
// =================================== GooseFEM::Element::Quad4 ====================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// ================================ GooseFEM::Element::Quad4::Gauss ================================
namespace Gauss {
// --------------------------------- number of integration points ----------------------------------
inline size_t nip()
{
return 4;
}
// ----------------------- integration point coordinates (local coordinates) -----------------------
-inline ArrD coordinates()
+inline ArrD xi()
{
size_t nip = 4;
size_t ndim = 2;
ArrD xi({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;
}
// ----------------------------------- integration point weights -----------------------------------
-inline ArrD weights()
+inline ArrD w()
{
size_t nip = 4;
ArrD w({nip});
w(0) = 1.;
w(1) = 1.;
w(2) = 1.;
w(3) = 1.;
return w;
}
// -------------------------------------------------------------------------------------------------
}
// ================================ GooseFEM::Element::Quad4::Nodal ================================
namespace Nodal {
// --------------------------------- number of integration points ----------------------------------
inline size_t nip()
{
return 4;
}
// ----------------------- integration point coordinates (local coordinates) -----------------------
-inline ArrD coordinates()
+inline ArrD xi()
{
size_t nip = 4;
size_t ndim = 2;
ArrD xi({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;
}
// ----------------------------------- integration point weights -----------------------------------
-inline ArrD weights()
+inline ArrD w()
{
size_t nip = 4;
ArrD w({nip});
w(0) = 1.;
w(1) = 1.;
w(2) = 1.;
w(3) = 1.;
return w;
}
// -------------------------------------------------------------------------------------------------
}
// =================================================================================================
// ------------------------------------------ constructor ------------------------------------------
inline Quadrature::Quadrature(const ArrD &x, const ArrD &xi, const ArrD &w)
: m_x(x), m_w(w), m_xi(xi)
{
// check input
assert( m_x.ndim() == 3 ); // shape: [nelem, nne, ndim]
assert( m_x.shape(1) == m_nne ); // number of nodes per element
assert( m_x.shape(2) == m_ndim ); // number of dimensions
// extract number of elements
m_nelem = m_x.shape(0);
// integration scheme
// - default
if ( m_w.size() == 0 and m_xi.size() == 0 )
{
m_nip = Gauss::nip();
- m_xi = Gauss::coordinates();
- m_w = Gauss::weights();
+ m_xi = Gauss::xi();
+ m_w = Gauss::w();
}
// - input
else if ( m_w.size() > 0 and m_xi.size() > 0 )
{
m_nip = m_w.size();
}
// - unknown
else
{
throw std::runtime_error("Input integration point coordinates and weights");
}
// check input
assert( m_xi.ndim() == 2 ); // shape: [nip, ndim]
assert( m_xi.shape(0) == m_nip ); // number of integration points
assert( m_xi.shape(1) == m_ndim ); // number of dimensions
assert( m_w .ndim() == 1 ); // shape: [nip]
assert( m_w .size() == m_nip ); // number of integration points
// allocate arrays
// - shape functions
m_N.resize({m_nip,m_nne});
// - shape function gradients in local coordinates
m_dNxi.resize({m_nip,m_nne,m_ndim});
// - shape function gradients in global coordinates
m_dNx.resize({m_nelem,m_nip,m_nne,m_ndim});
// - integration point volume
m_vol.resize({m_nelem,m_nip});
// shape functions
for ( size_t k = 0 ; k < m_nip ; ++k )
{
m_N(k,0) = .25 * (1.-m_xi(k,0)) * (1.-m_xi(k,1));
m_N(k,1) = .25 * (1.+m_xi(k,0)) * (1.-m_xi(k,1));
m_N(k,2) = .25 * (1.+m_xi(k,0)) * (1.+m_xi(k,1));
m_N(k,3) = .25 * (1.-m_xi(k,0)) * (1.+m_xi(k,1));
}
// shape function gradients in local coordinates
for ( size_t k = 0 ; k < m_nip ; ++k )
{
m_dNxi(k,0,0) = -.25*(1.-m_xi(k,1)); m_dNxi(k,0,1) = -.25*(1.-m_xi(k,0));
m_dNxi(k,1,0) = +.25*(1.-m_xi(k,1)); m_dNxi(k,1,1) = -.25*(1.+m_xi(k,0));
m_dNxi(k,2,0) = +.25*(1.+m_xi(k,1)); m_dNxi(k,2,1) = +.25*(1.+m_xi(k,0));
m_dNxi(k,3,0) = -.25*(1.+m_xi(k,1)); m_dNxi(k,3,1) = +.25*(1.-m_xi(k,0));
}
// compute the shape function gradients, based on "x"
compute_dN();
}
// -------------------------------------- integration volume ---------------------------------------
inline ArrD Quadrature::dV() const
{
return m_vol;
}
// ---------------------------- integration volume per tensor-component ----------------------------
inline ArrD Quadrature::dV(size_t ncomp) const
{
ArrD out = ArrD::Zero({m_nelem, m_nip, ncomp});
#pragma omp parallel for
for ( size_t e = 0 ; e < m_nelem ; ++e )
for ( size_t k = 0 ; k < m_nip ; ++k )
for ( size_t i = 0 ; i < ncomp ; ++i )
out(e,k,i) = m_vol(e,k);
return out;
}
// -------------------------------------- number of elements ---------------------------------------
inline size_t Quadrature::nelem() const
{
return m_nelem;
}
// ---------------------------------- number of nodes per element ----------------------------------
inline size_t Quadrature::nne() const
{
return m_nne;
}
// ------------------------------------- number of dimensions --------------------------------------
inline size_t Quadrature::ndim() const
{
return m_ndim;
}
// --------------------------------- number of integration points ----------------------------------
inline size_t Quadrature::nip() const
{
return m_nip;
}
// --------------------------------------- update positions ----------------------------------------
inline void Quadrature::update_x(const ArrD &x)
{
// check input
assert( x.ndim() == 3 ); // shape: [nelem, nne, ndim]
assert( x.shape(0) == m_nelem ); // number of elements
assert( x.shape(1) == m_nne ); // number of nodes per element
assert( x.shape(2) == m_ndim ); // number of dimensions
assert( x.size() == m_x.size() ); // total number of components (redundant)
// update positions
- std::copy(x.begin(), x.end(), m_x.begin());
+ m_x.setCopy(x.begin(), x.end());
// update the shape function gradients for the new "x"
compute_dN();
}
// ------------------------ shape function gradients in global coordinates -------------------------
inline void Quadrature::compute_dN()
{
#pragma omp parallel
{
// intermediate quantities and local views
double Jdet, w, vol;
cppmat::tiny::matrix2<double,m_nne,m_ndim> dNx;
cppmat::view::matrix2<double,m_nne,m_ndim> dNxi, x;
cppmat::cartesian2d::tensor2<double> J, Jinv;
// loop over all elements (in parallel)
#pragma omp for
for ( size_t e = 0 ; e < m_nelem ; ++e )
{
// alias
x.setMap(&m_x(e)); // nodal positions
// loop over integration points
for ( size_t k = 0 ; k < m_nip ; ++k )
{
// - alias
dNxi.setMap(&m_dNxi( k)); // shape function gradients (local coordinates)
vol = m_vol (e,k); // volume
w = m_w ( k); // weight factor
// - Jacobian (loops unrolled for efficiency)
// J(i,j) += dNxi(m,i) * xe(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
Jdet = J.det();
Jinv = J.inv();
// - integration point volume
vol = w * Jdet;
// - 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);
}
// - copy to matrix: shape function gradients (global coordinates)
std::copy(dNx.begin(), dNx.end(), m_dNx.item(e,k));
// - copy to matrix: integration point volume
m_vol(e,k) = vol;
}
}
} // #pragma omp parallel
}
// ------------------- dyadic product "qtensor(i,j) = dNdx(m,i) * elemvec(m,j)" --------------------
template<class T>
inline ArrD Quadrature::gradN_vector(const ArrD &elemvec) const
{
// check input
assert( elemvec.ndim() == 3 ); // shape: [nelem, nne, ndim]
assert( elemvec.shape(0) == m_nelem ); // number of elements
assert( elemvec.shape(1) == m_nne ); // number of nodes per element
assert( elemvec.shape(2) == m_ndim ); // number of dimensions
// temporary tensor, to deduce size of the output
T dummytensor;
size_t tdim = dummytensor.size();
// zero-initialize output: matrix of tensors
ArrD qtensor = ArrD::Zero({m_nelem, m_nip, tdim});
#pragma omp parallel
{
// intermediate quantities and local views
T gradu;
cppmat::view::matrix2<double,m_nne,m_ndim> dNx, u;
// loop over all elements (in parallel)
#pragma omp for
for ( size_t e = 0 ; e < m_nelem ; ++e )
{
// alias
u.setMap(&elemvec(e)); // element vector (e.g. nodal displacements)
// loop over all integration points in element "e"
for ( size_t k = 0 ; k < m_nip ; ++k )
{
// - alias
dNx.setMap(&m_dNx(e,k)); // shape function gradients (global coordinates)
// - evaluate dyadic product (loops unrolled for efficiency)
// gradu(i,j) += dNx(m,i) * ue(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);
// - copy resulting integration point tensor
std::copy(gradu.begin(), gradu.end(), qtensor.item(e,k));
}
}
} // #pragma omp parallel
return qtensor;
}
// ---------------------------------- transpose of "GradN_vector" ----------------------------------
template<class T>
inline ArrD Quadrature::gradN_vector_T(const ArrD &elemvec) const
{
// check input
assert( elemvec.ndim() == 3 ); // shape: [nelem, nne, ndim]
assert( elemvec.shape(0) == m_nelem ); // number of elements
assert( elemvec.shape(1) == m_nne ); // number of nodes per element
assert( elemvec.shape(2) == m_ndim ); // number of dimensions
// temporary tensor, to deduce size of the output
T dummytensor;
size_t tdim = dummytensor.size();
// zero-initialize output: matrix of tensors
ArrD qtensor = ArrD::Zero({m_nelem, m_nip, tdim});
#pragma omp parallel
{
// intermediate quantities and local views
T gradu;
cppmat::view::matrix2<double,m_nne,m_ndim> dNx, u;
// loop over all elements (in parallel)
#pragma omp for
for ( size_t e = 0 ; e < m_nelem ; ++e )
{
// alias
u.setMap(&elemvec(e)); // element vector (e.g. nodal displacements)
// loop over all integration points in element "e"
for ( size_t k = 0 ; k < m_nip ; ++k )
{
// - alias
dNx.setMap(&m_dNx(e,k)); // shape function gradients (global coordinates)
// - evaluate dyadic product (loops unrolled for efficiency)
// gradu(j,i) += dNx(m,i) * ue(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);
// - copy resulting integration point tensor
std::copy(gradu.begin(), gradu.end(), qtensor.item(e,k));
}
}
} // #pragma omp parallel
return qtensor;
}
// ------------------------------- symmetric part of "GradN_vector" --------------------------------
template<class T>
inline ArrD Quadrature::symGradN_vector(const ArrD &elemvec) const
{
// check input
assert( elemvec.ndim() == 3 ); // shape: [nelem, nne, ndim]
assert( elemvec.shape(0) == m_nelem ); // number of elements
assert( elemvec.shape(1) == m_nne ); // number of nodes per element
assert( elemvec.shape(2) == m_ndim ); // number of dimensions
// temporary tensor, to deduce size of the output
T dummytensor;
size_t tdim = dummytensor.size();
// zero-initialize output: matrix of tensors
ArrD qtensor = ArrD::Zero({m_nelem, m_nip, tdim});
#pragma omp parallel
{
// intermediate quantities and local views
T eps;
cppmat::cartesian2d::tensor2<double> gradu;
cppmat::view::matrix2<double,m_nne,m_ndim> dNx, u;
// loop over all elements (in parallel)
#pragma omp for
for ( size_t e = 0 ; e < m_nelem ; ++e )
{
// alias
u.setMap(&elemvec(e)); // element vector (e.g. nodal displacements)
// loop over all integration points in element "e"
for ( size_t k = 0 ; k < m_nip ; ++k )
{
// - alias
dNx.setMap(&m_dNx(e,k)); // shape function gradients (global coordinates)
// - evaluate dyadic product (loops unrolled for efficiency)
// gradu(i,j) += dNx(m,i) * ue(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);
// - symmetrize (loops unrolled for efficiency)
// eps(i,j) = .5 * ( gradu(i,j) + gradu(j,i) )
eps(0,0) = gradu(0,0);
eps(0,1) = .5 * ( gradu(0,1) + gradu(1,0) );
eps(1,0) = eps (0,1);
eps(1,1) = gradu(1,1);
// - copy resulting integration point tensor
std::copy(eps.begin(), eps.end(), qtensor.item(e,k));
}
}
} // #pragma omp parallel
return qtensor;
}
// ------- scalar product "elemmat(m*ndim+i,n*ndim+i) = N(m) * qscalar * N(n)"; for all "i" --------
inline ArrD Quadrature::int_N_scalar_NT_dV(const ArrD &qscalar) const
{
// check input
assert( qscalar.ndim() == 2 ); // shape: [nelem, nip]
assert( qscalar.shape(0) == m_nelem ); // number of elements
assert( qscalar.shape(1) == m_nip ); // number of integration points
// zero-initialize: matrix of matrices
ArrD elemmat = ArrD::Zero({m_nelem, m_nne*m_ndim, m_nne*m_ndim});
#pragma omp parallel
{
// intermediate quantities and local views
cppmat::tiny::matrix2<double,m_nne*m_ndim,m_nne*m_ndim> M;
cppmat::view::vector<double,m_nne> N;
double rho, vol;
// loop over all elements (in parallel)
#pragma omp for
for ( size_t e = 0 ; e < m_nelem ; ++e )
{
// zero-initialize (e.g. mass matrix)
M.setZero();
// loop over all integration points in element "e"
for ( size_t k = 0 ; k < m_nip ; ++k )
{
// - alias
N.setMap(&m_N( k)); // shape functions
vol = m_vol (e,k); // integration point volume
rho = qscalar(e,k); // integration point scalar (e.g. density)
// - 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;
}
}
}
// copy result to element matrix
std::copy(M.begin(), M.end(), elemmat.item(e));
}
} // #pragma omp parallel
return elemmat;
}
// ------------ integral of dot product "elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV" ------------
template<class T>
inline ArrD Quadrature::int_gradN_dot_tensor2_dV(const ArrD &qtensor) const
{
#ifndef NDEBUG
// dummy variable
T tmp;
// check input
assert( qtensor.ndim() == 3 ); // shape: [nelem, nip, #tensor-components]
assert( qtensor.shape(0) == m_nelem ); // number of elements
assert( qtensor.shape(1) == m_nip ); // number of integration points
assert( qtensor.shape(2) == tmp.size() ); // tensor dimensions
#endif
// zero-initialize output: matrix of vectors
ArrD elemvec = ArrD::Zero({m_nelem, m_nne, m_ndim});
#pragma omp parallel
{
// intermediate quantities and local views
cppmat::view::matrix2<double,m_nne,m_ndim> dNx;
cppmat::tiny::matrix2<double,m_nne,m_ndim> f;
double vol;
T sig;
// loop over all elements (in parallel)
#pragma omp for
for ( size_t e = 0 ; e < m_nelem ; ++e )
{
// zero-initialize (e.g. nodal force)
f.setZero();
// loop over all integration points in element "e"
for ( size_t k = 0 ; k < m_nip ; ++k )
{
// - alias
dNx.setMap(&m_dNx (e,k)); // shape function gradients (global coordinates)
sig.setMap(&qtensor(e,k)); // integration point tensor (e.g. stress)
vol = m_vol (e,k); // integration point volume
// - evaluate dot product, and assemble (loops partly unrolled for efficiency)
// f(m,j) += dNdx(m,i) * sig(i,j) * dV;
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;
}
}
// copy result to element vector
std::copy(f.begin(), f.end(), elemvec.item(e));
}
} // #pragma omp parallel
return elemvec;
}
// ---------------------- wrappers with default storage (no template needed) -----------------------
inline ArrD Quadrature::gradN_vector(const ArrD &elemvec) const
{
return gradN_vector<cppmat::cartesian2d::tensor2<double>>(elemvec);
}
// -------------------------------------------------------------------------------------------------
inline ArrD Quadrature::gradN_vector_T(const ArrD &elemvec) const
{
return gradN_vector_T<cppmat::cartesian2d::tensor2<double>>(elemvec);
}
// -------------------------------------------------------------------------------------------------
inline ArrD Quadrature::symGradN_vector(const ArrD &elemvec) const
{
return symGradN_vector<cppmat::cartesian2d::tensor2s<double>>(elemvec);
}
// -------------------------------------------------------------------------------------------------
inline ArrD Quadrature::int_gradN_dot_tensor2_dV(const ArrD &qtensor) const
{
assert( qtensor.ndim() == 3 ); // shape: [nelem, nip, #tensor-components]
if ( qtensor.shape(2) == m_ndim*m_ndim )
return int_gradN_dot_tensor2_dV<cppmat::view::cartesian2d::tensor2<double>>(qtensor);
else if ( qtensor.shape(2) == (m_ndim+1)*m_ndim/2 )
return int_gradN_dot_tensor2_dV<cppmat::view::cartesian2d::tensor2s<double>>(qtensor);
else
throw std::runtime_error("assert: qtensor.shape(2) == 4 or qtensor.shape(2) == 3");
}
// -------------------------------------------------------------------------------------------------
inline ArrD Quadrature::int_gradN_dot_tensor2s_dV(const ArrD &qtensor) const
{
return int_gradN_dot_tensor2_dV<cppmat::view::cartesian2d::tensor2s<double>>(qtensor);
}
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/src/GooseFEM/ElementQuad4.h b/src/GooseFEM/ElementQuad4.h
index ce1e140..5c1d72d 100644
--- a/src/GooseFEM/ElementQuad4.h
+++ b/src/GooseFEM/ElementQuad4.h
@@ -1,124 +1,125 @@
/* =================================================================================================
(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 "GooseFEM.h"
// =================================== GooseFEM::Element::Quad4 ====================================
namespace GooseFEM {
namespace Element {
namespace Quad4 {
// ================================ GooseFEM::Element::Quad4::Gauss ================================
namespace Gauss {
-inline size_t nip(); // number of integration points
-inline ArrD coordinates(); // integration point coordinates (local coordinates)
-inline ArrD weights(); // integration point weights
+inline size_t nip(); // number of integration points
+inline ArrD xi(); // integration point coordinates (local coordinates)
+inline ArrD w(); // integration point weights
}
// ================================ GooseFEM::Element::Quad4::Nodal ================================
namespace Nodal {
-inline size_t nip(); // number of integration points
-inline ArrD coordinates(); // integration point coordinates (local coordinates)
-inline ArrD weights(); // integration point weights
+inline size_t nip(); // number of integration points
+inline ArrD xi(); // integration point coordinates (local coordinates)
+inline ArrD w(); // integration point weights
}
// =================================================================================================
// ------------------------------------------ quadrature -------------------------------------------
class Quadrature
{
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
ArrD m_x; // nodal positions stored per element [nelem, nne, ndim]
ArrD m_w; // weight of each integration point [nip]
ArrD m_xi; // local coordinate of each integration point [nip, ndim]
ArrD m_N; // shape functions [nip, nne]
ArrD m_dNxi; // shape function gradients w.r.t. local coordinate [nip, nne, ndim]
ArrD m_dNx; // shape function gradients w.r.t. global coordinate [nelem, nip, nne, ndim]
ArrD m_vol; // integration point volume [nelem, nip]
private:
// compute "vol" and "dNdx" based on current "x"
void compute_dN();
public:
// convention:
// "elemmat" - matrices stored per element - ArrD - [nelem, nne*ndim, nne*ndim]
// "elemvec" - nodal vectors stored per element - ArrD - [nelem, nne, ndim]
// "qtensor" - integration point tensor - ArrD - [nelem, nip, #tensor-components]
// "qscalar" - integration point scalar - ArrD - [nelem, nip]
//
// alias:
// T2 = cppmat::cartesian2d::tensor2<double> - #tensor-components = 4
// T2s = cppmat::cartesian2d::tensor2s<double> - #tensor-components = 3
// vT2 = cppmat::view::cartesian2d::tensor2<double> - #tensor-components = 4
// vT2s = cppmat::view::cartesian2d::tensor2s<double> - #tensor-components = 3
// constructor: integration point coordinates and weights are optional (default: Gauss)
+ Quadrature(){};
Quadrature(const ArrD &x, const ArrD &xi=ArrD(), const ArrD &w=ArrD());
// update the nodal positions (shape of "x" should match the earlier definition)
void update_x(const ArrD &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 integration volume
ArrD dV() const; // returns: qscalar
ArrD dV(size_t ncomp) const; // returns: qtensor (same volume per tensor-component)
// dyadic product "qtensor(i,j) += dNdx(m,i) * elemvec(m,j)", its transpose and its symmetric part
// - allow template (e.g. T2/T2s, or higher dimensional tensors)
template<class T> ArrD gradN_vector (const ArrD &elemvec) const; // returns: qtensor
template<class T> ArrD gradN_vector_T (const ArrD &elemvec) const; // returns: qtensor
template<class T> ArrD symGradN_vector(const ArrD &elemvec) const; // returns: qtensor
// - default template
ArrD gradN_vector (const ArrD &elemvec) const; // template: T2
ArrD gradN_vector_T (const ArrD &elemvec) const; // template: T2
ArrD symGradN_vector(const ArrD &elemvec) const; // template: T2s
// integral of the scalar product "elemmat(m*ndim+i,n*ndim+i) += N(m) * qscalar * N(n) * dV"
ArrD int_N_scalar_NT_dV(const ArrD &qscalar) const; // returns: elemmat
// integral of the dot product "elemvec(m,j) += dNdx(m,i) * qtensor(i,j) * dV"
// - allow template (e.g. vT2/vT2s, or higher dimensional tensors)
template<class T> ArrD int_gradN_dot_tensor2_dV(const ArrD &qtensor) const; // returns: elemvec
// - default template
ArrD int_gradN_dot_tensor2_dV (const ArrD &qtensor) const; // template: vT2/vT2s (auto-select)
ArrD int_gradN_dot_tensor2s_dV(const ArrD &qtensor) const; // template: vT2s
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
diff --git a/src/GooseFEM/MatrixDiagonal.cpp b/src/GooseFEM/MatrixDiagonal.cpp
index 002cc3a..d524d97 100644
--- a/src/GooseFEM/MatrixDiagonal.cpp
+++ b/src/GooseFEM/MatrixDiagonal.cpp
@@ -1,405 +1,409 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXDIAGONAL_CPP
#define GOOSEFEM_MATRIXDIAGONAL_CPP
// -------------------------------------------------------------------------------------------------
#include "MatrixDiagonal.h"
// =========================================== GooseFEM ============================================
namespace GooseFEM {
// ------------------------------------------ constructor ------------------------------------------
inline MatrixDiagonal::MatrixDiagonal(const MatS &conn, const MatS &dofs, const ColS &iip) :
m_conn(conn), m_dofs(dofs), m_iip(iip)
{
// extract mesh dimensions
m_nelem = static_cast<size_t>(m_conn.rows());
m_nne = static_cast<size_t>(m_conn.cols());
m_nnode = static_cast<size_t>(m_dofs.rows());
m_ndim = static_cast<size_t>(m_dofs.cols());
m_ndof = static_cast<size_t>(m_dofs.maxCoeff() + 1);
m_nnp = static_cast<size_t>(m_iip .size());
m_nnu = m_ndof - m_nnp;
// check consistency
assert( m_conn.maxCoeff() + 1 == m_nnode );
assert( m_ndof <= m_nnode * m_ndim );
// reorder DOFs such that they can be used for partitioning; renumber such that
// "iiu" -> beginning
// "iip" -> end
// (otherwise preserving the order)
// this array can be used to assemble to/from partitioned arrays
m_part = Mesh::reorder(m_dofs, m_iip, "end");
// extract unknown DOFs
// - allocate
m_iiu.conservativeResize(m_nnu);
// - set
#pragma omp parallel for
for ( size_t n = 0 ; n < m_nnode ; ++n )
for ( size_t i = 0 ; i < m_ndim ; ++i )
if ( m_part(n,i) < m_nnu )
m_iiu(m_part(n,i)) = m_dofs(n,i);
// allocate matrix and its inverse
m_data.conservativeResize(m_ndof);
m_inv .conservativeResize(m_ndof);
}
// ---------------------------------------- index operator -----------------------------------------
inline double& MatrixDiagonal::operator[](size_t i)
{
m_change = true;
return m_data[i];
}
// ---------------------------------------- index operator -----------------------------------------
inline const double& MatrixDiagonal::operator[](size_t i) const
{
return m_data[i];
}
// ---------------------------------------- index operator -----------------------------------------
inline double& MatrixDiagonal::operator()(size_t a)
{
m_change = true;
return m_data[a];
}
// ---------------------------------------- index operator -----------------------------------------
inline const double& MatrixDiagonal::operator()(size_t a) const
{
return m_data[a];
}
// ---------------------------------------- index operator -----------------------------------------
inline double& MatrixDiagonal::operator()(size_t a, size_t b)
{
assert( a == b );
+ UNUSED(b);
+
m_change = true;
return m_data[a];
}
// ---------------------------------------- index operator -----------------------------------------
inline const double& MatrixDiagonal::operator()(size_t a, size_t b) const
{
assert( a == b );
+ UNUSED(b);
+
return m_data[a];
}
// -------------------------------------- number of elements ---------------------------------------
inline size_t MatrixDiagonal::nelem() const
{
return m_nelem;
}
// ---------------------------------- number of nodes per element ----------------------------------
inline size_t MatrixDiagonal::nne() const
{
return m_nne;
}
// ---------------------------------------- number of nodes ----------------------------------------
inline size_t MatrixDiagonal::nnode() const
{
return m_nnode;
}
// ------------------------------------- number of dimensions --------------------------------------
inline size_t MatrixDiagonal::ndim() const
{
return m_ndim;
}
// ---------------------------------------- number of DOFs -----------------------------------------
inline size_t MatrixDiagonal::ndof() const
{
return m_ndof;
}
// ------------------------------------ number of unknown DOFs -------------------------------------
inline size_t MatrixDiagonal::nnu() const
{
return m_nnu;
}
// ----------------------------------- number of prescribed DOFs -----------------------------------
inline size_t MatrixDiagonal::nnp() const
{
return m_nnp;
}
// -------------------------------------- return unknown DOFs --------------------------------------
inline ColS MatrixDiagonal::iiu() const
{
return m_iiu;
}
// ------------------------------------ return prescribed DOFs -------------------------------------
inline ColS MatrixDiagonal::iip() const
{
return m_iip;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot(const ColD &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// compute product
return m_data.cwiseProduct(b);
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_u(const ColD &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// allocate output
ColD c_u(m_nnu);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnu ; ++i )
c_u(i) = m_data(m_iiu(i)) * b(m_iiu(i));
return c_u;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_u(const ColD &b_u, const ColD &b_p) const
{
// suppress warning
UNUSED(b_p);
// check input
assert( static_cast<size_t>(b_u.size()) == m_nnu );
assert( static_cast<size_t>(b_p.size()) == m_nnp );
// allocate output
ColD c_u(m_nnu);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnu ; ++i )
c_u(i) = m_data(m_iiu(i)) * b_u(i);
return c_u;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_p(const ColD &b) const
{
// check input
assert( static_cast<size_t>(b.size()) == m_ndof );
// allocate output
ColD c_p(m_nnp);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnp ; ++i )
c_p(i) = m_data(m_iip(i)) * b(m_iip(i));
return c_p;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD MatrixDiagonal::dot_p(const ColD &b_u, const ColD &b_p) const
{
// suppress warning
UNUSED(b_u);
// check input
assert( static_cast<size_t>(b_u.size()) == m_nnu );
assert( static_cast<size_t>(b_p.size()) == m_nnp );
// allocate output
ColD c_p(m_nnp);
// compute product
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnp ; ++i )
c_p(i) = m_data(m_iip(i)) * b_p(i);
return c_p;
}
// ------------------------ check structure of matrices stored per element -------------------------
inline void MatrixDiagonal::check_diagonal(const ArrD &elemmat) const
{
// check input
assert( elemmat.ndim() == 3 );
assert( elemmat.shape(0) == m_nelem );
assert( elemmat.shape(1) == m_nne*m_ndim );
assert( elemmat.shape(2) == m_nne*m_ndim );
// get numerical precision
double eps = std::numeric_limits<double>::epsilon();
// loop over all entries
#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 )
for ( size_t n = 0 ; n < m_nne ; ++n )
for ( size_t j = 0 ; j < m_ndim ; ++j )
if ( m*m_ndim+i != n*m_ndim+j )
if ( std::abs(elemmat(e,m*m_ndim+i,n*m_ndim+j)) > eps )
throw std::runtime_error("Element matrices are not diagonal");
}
// ----------------------------- assemble matrices stored per element ------------------------------
inline void MatrixDiagonal::assemble(const ArrD &elemmat)
{
// check input
assert( elemmat.ndim() == 3 );
assert( elemmat.shape(0) == m_nelem );
assert( elemmat.shape(1) == m_nne*m_ndim );
assert( elemmat.shape(2) == m_nne*m_ndim );
// zero-initialize matrix
m_data.setZero();
// temporarily disable parallelization by Eigen
Eigen::setNbThreads(1);
// start threads (all variables declared in this scope are local to each thread)
#pragma omp parallel
{
// zero-initialize matrix
ColD t_mat = ColD::Zero(m_ndof);
// assemble
#pragma omp 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 )
t_mat(m_dofs(m_conn(e,m),i)) += elemmat(e,m*m_ndim+i,m*m_ndim+i);
// reduce: combine result obtained on the different threads
#pragma omp critical
m_data += t_mat;
}
// reset automatic parallelization by Eigen
Eigen::setNbThreads(0);
// signal change
m_change = true;
}
// ------------------------------------- solve: Mat * u = rhs --------------------------------------
inline ColD MatrixDiagonal::solve(const ColD &rhs, const ColD &u_p)
{
// suppress warning
UNUSED(u_p);
// check input
assert( static_cast<size_t>(u_p.size()) == m_nnp );
assert( static_cast<size_t>(rhs.size()) == m_ndof );
// invert if needed
if ( m_change ) m_inv = m_data.cwiseInverse();
// reset signal
m_change = false;
// solve
ColD u = m_inv.cwiseProduct(rhs);
// set prescribed DOFs
for ( size_t i = 0 ; i < m_nnp ; ++i )
u(m_iip(i)) = u_p(i);
return u;
}
// ------------------------------------- solve: Mat * u = rhs --------------------------------------
inline ColD MatrixDiagonal::solve_u(const ColD &rhs_u, const ColD &u_p)
{
// suppress warning
UNUSED(u_p);
// check input
assert( static_cast<size_t>(u_p .size()) == m_nnp );
assert( static_cast<size_t>(rhs_u.size()) == m_nnu );
// invert if needed
if ( m_change ) m_inv = m_data.cwiseInverse();
// reset signal
m_change = false;
// allocate output
ColD u_u(m_nnu);
// solve
#pragma omp parallel for
for ( size_t i = 0 ; i < m_nnu ; ++i )
u_u(i) = m_inv(m_iiu(i)) * rhs_u(i);
return u_u;
}
// ----------------------------------- return as diagonal matrix -----------------------------------
inline ColD MatrixDiagonal::asDiagonal() const
{
return m_data;
}
// --------------------------------------- c_i = A_ij * b_j ----------------------------------------
inline ColD operator* (const MatrixDiagonal &A, const ColD &b)
{
return A.dot(b);
}
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/src/GooseFEM/MatrixDiagonal.h b/src/GooseFEM/MatrixDiagonal.h
index 784d91b..97b4be7 100644
--- a/src/GooseFEM/MatrixDiagonal.h
+++ b/src/GooseFEM/MatrixDiagonal.h
@@ -1,133 +1,134 @@
/* =================================================================================================
(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 "GooseFEM.h"
// =========================================== GooseFEM ============================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
class MatrixDiagonal
{
private:
// data
ColD m_data; // the diagonal matrix (not-partitioned)
ColD m_inv; // inverse of "m_data", can be re-used to solve different right-hand-sides
bool m_change=false; // signal changes to data compare to the last inverse
// information
MatS m_conn; // connectivity [nelem, nne ]
MatS m_dofs; // DOF-numbers per node [nnode, ndim]
MatS m_part; // DOF-numbers per node, after partitioning [nnode, ndim]
ColS m_iiu; // DOF-numbers that are unknown [nnu]
ColS 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
public:
// constructor
+ MatrixDiagonal(){};
MatrixDiagonal(const MatS &conn, const MatS &dofs, const ColS &iip=ColS());
// index operators: access plain storage
double& operator[](size_t i);
const double& operator[](size_t i) const;
// index operators: access using matrix indices
double& operator()(size_t a);
const double& operator()(size_t a) const;
double& operator()(size_t a, size_t b);
const double& operator()(size_t a, size_t b) const;
// 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
ColS iiu() const; // unknown DOFs
ColS iip() const; // prescribed DOFs
// product: c_i = A_ij * b_j
ColD dot (const ColD &b ) const; // c = A * b
ColD dot_u(const ColD &b ) const; // c_u = A_uu * b_u + A_up * b_p
ColD dot_u(const ColD &b_u, const ColD &b_p) const; // c_u = A_uu * b_u + A_up * b_p
ColD dot_p(const ColD &b ) const; // c_p = A_pu * b_u + A_pp * b_p
ColD dot_p(const ColD &b_u, const ColD &b_p) const; // c_p = A_pu * b_u + A_pp * b_p
// check structure of the matrices stored per element [nelem, nne*ndim, nne*ndim]
void check_diagonal(const ArrD &elemmat) const;
// assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
// WARNING: ignores any off-diagonal terms
void assemble(const ArrD &elemmat);
// set matrix components from externally assembled object
void set (const ColD &matrix ) const; // diagonal [ndof]
void set_uu(const ColD &matrix_uu) const; // diagonal [nnu]
void set_pp(const ColD &matrix_pp) const; // diagonal [nnp]
// solve
// ("u_p" is useless as all cross-terms are zero, it is here for aesthetics)
ColD solve (const ColD &rhs , const ColD &u_p=ColD()); // [ndof] -> [ndof]
ColD solve_u(const ColD &rhs_u, const ColD &u_p=ColD()); // [nnu] -> [nnu]
// get the right-hand-side of prescribed DOFs: [nnu], [nnp] -> [nnp]
// ("u_u" is useless as all cross-terms are zero, it is here for aesthetics)
ColD rhs_p(const ColD &u_u, const ColD &u_p) const;
// return (sub-)matrix as diagonal matrix (column)
ColD asDiagonal () const; // [ndpf]
ColD asDiagonal_uu() const; // [nnu]
ColD asDiagonal_pp() const; // [nnp]
// return (sub-)matrix as sparse matrix
SpMatD asSparse () const; // [ndof,ndof]
SpMatD asSparse_uu() const; // [nnu ,nnu ]
SpMatD asSparse_up() const; // [nnu ,nnp ]
SpMatD asSparse_pu() const; // [nnp ,nnu ]
SpMatD asSparse_pp() const; // [nnp ,nnp ]
// return (sub-)matrix as dense matrix
MatD asDense () const; // [ndof,ndof]
MatD asDense_uu() const; // [nnu ,nnu ]
MatD asDense_up() const; // [nnu ,nnp ]
MatD asDense_pu() const; // [nnp ,nnu ]
MatD asDense_pp() const; // [nnp ,nnp ]
};
// -------------------------------------------------------------------------------------------------
// matrix/column product: '[ndof,ndof]' * [ndof] -> [ndof]
inline ColD operator* (const MatrixDiagonal &A, const ColD &b);
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif
diff --git a/src/GooseFEM/Vector.h b/src/GooseFEM/Vector.h
index 67c33bd..61d2353 100644
--- a/src/GooseFEM/Vector.h
+++ b/src/GooseFEM/Vector.h
@@ -1,97 +1,98 @@
/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_VECTOR_H
#define GOOSEFEM_VECTOR_H
// -------------------------------------------------------------------------------------------------
#include "GooseFEM.h"
// =========================================== GooseFEM ============================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
class Vector
{
private:
// information
MatS m_conn; // connectivity [nelem, nne ]
MatS m_dofs; // DOF-numbers per node [nnode, ndim]
MatS m_part; // DOF-numbers per node, after partitioning [nnode, ndim]
ColS m_iiu; // DOF-numbers that are unknown [nnu]
ColS 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
public:
// notation:
// "nodevec" - nodal vectors - MatD - [nnode, ndim]
// "elemvec" - nodal vectors stored per element - ArrD - [nelem, nne, ndim]
// "dofval" - DOF values - ColD - [ndof]
// "dofval_u" - DOF values (Unknown) - ColD - [nnu]
// "dofval_p" - DOF values (Prescribed) - ColD - [nnp]
// constructor
+ Vector(){};
Vector(const MatS &conn, const MatS &dofs, const ColS &iip=ColS());
// 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
ColS iiu() const; // unknown DOFs
ColS iip() const; // prescribed DOFs
// convert vectors (overwrite entries that occur more that once)
ColD asDofs (const ColD &dofval_u, const ColD &dofval_p) const;
ColD asDofs (const MatD &nodevec ) const;
ColD asDofs (const ArrD &elemvec ) const;
ColD asDofs_u (const MatD &nodevec ) const;
ColD asDofs_u (const ArrD &elemvec ) const;
ColD asDofs_p (const MatD &nodevec ) const;
ColD asDofs_p (const ArrD &elemvec ) const;
MatD asNode (const ColD &dofval ) const;
MatD asNode (const ColD &dofval_u, const ColD &dofval_p) const;
MatD asNode (const ArrD &elemvec ) const;
ArrD asElement(const ColD &dofval ) const;
ArrD asElement(const ColD &dofval_u, const ColD &dofval_p) const;
ArrD asElement(const MatD &nodevec ) const;
// assemble vectors (adds entries that occur more that once)
ColD assembleDofs (const MatD &nodevec) const;
ColD assembleDofs (const ArrD &elemvec) const;
ColD assembleDofs_u(const MatD &nodevec) const;
ColD assembleDofs_u(const ArrD &elemvec) const;
ColD assembleDofs_p(const MatD &nodevec) const;
ColD assembleDofs_p(const ArrD &elemvec) const;
MatD assembleNode (const ArrD &elemvec) const;
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#endif

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