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Element.h
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rGOOSEFEM GooseFEM
Element.h
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/**
Convenience methods for integration point data.
\file Element.h
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_ELEMENT_H
#define GOOSEFEM_ELEMENT_H
#include "config.h"
#include "Allocate.h"
namespace
GooseFEM
{
namespace
Element
{
/**
Convert nodal vector with ("nodevec", shape:``[nnode, ndim]``) to nodal vector stored per element
("elemvec", shape: ``[nelem, nne, ndim]``).
\param conn Connectivity.
\param nodevec "nodevec".
\return "elemvec".
*/
inline
xt
::
xtensor
<
double
,
3
>
asElementVector
(
const
xt
::
xtensor
<
size_t
,
2
>&
conn
,
const
xt
::
xtensor
<
double
,
2
>&
nodevec
);
/**
Assemble nodal vector stored per element ("elemvec", shape ``[nelem, nne, ndim]``) to nodal vector
("nodevec", shape ``[nnode, ndim]``).
\param conn Connectivity.
\param elemvec "elemvec".
\return "nodevec".
*/
inline
xt
::
xtensor
<
double
,
2
>
assembleNodeVector
(
const
xt
::
xtensor
<
size_t
,
2
>&
conn
,
const
xt
::
xtensor
<
double
,
3
>&
elemvec
);
/**
Check that DOFs leave no holes.
\param dofs DOFs ("nodevec")
\return ``true`` if there are no holds.
*/
template
<
class
E
>
inline
bool
isSequential
(
const
E
&
dofs
);
/**
Check that all of the matrices stored per elemmat (shape: ``[nelem, nne * ndim, nne * ndim]``)
are diagonal.
\param elemmat Element-vectors ("elemmat")
\return ``true`` if all element matrices are diagonal.
*/
bool
isDiagonal
(
const
xt
::
xtensor
<
double
,
3
>&
elemmat
);
/**
Base quadrature-class.
This class does not have a specific element-type in mind, it is used mostly internally
to derive from such that common methods do not have to be reimplementation.
\tparam ne Number of nodes per element.
\tparam nd Number of dimensions for node vectors.
\tparam td Number of dimensions for integration point tensors.
*/
template
<
size_t
ne
,
size_t
nd
,
size_t
td
>
class
QuadratureBase
{
public:
QuadratureBase
()
=
default
;
/**
Constructor
*/
QuadratureBase
(
size_t
nelem
,
size_t
nip
);
/**
Number of elements.
\return Scalar.
*/
size_t
nelem
()
const
;
/**
Number of nodes per element.
\return Scalar.
*/
size_t
nne
()
const
;
/**
Number of dimensions for node vectors.
\return Scalar.
*/
size_t
ndim
()
const
;
/**
Number of dimensions for integration point tensors.
\return Scalar.
*/
size_t
tdim
()
const
;
/**
Number of integration points.
\return Scalar.
*/
size_t
nip
()
const
;
/**
Convert "qscalar" to "qtensor" of certain rank.
Fully allocated output passed as reference, use AsTensor to allocate and return data.
\param qscalar A "qscalar".
\param qtensor A "qtensor".
*/
template
<
size_t
rank
=
0
,
class
T
>
void
asTensor
(
const
xt
::
xtensor
<
T
,
2
>&
qscalar
,
xt
::
xtensor
<
T
,
2
+
rank
>&
qtensor
)
const
;
/**
Convert "qscalar" to "qtensor" of certain rank.
\param "qscalar".
\return "qtensor".
*/
template
<
size_t
rank
=
0
,
class
T
>
xt
::
xtensor
<
T
,
2
+
rank
>
AsTensor
(
const
xt
::
xtensor
<
T
,
2
>&
qscalar
)
const
;
/**
Convert "qscalar" to "qtensor" of certain rank.
\param rank Tensor rank.
\param qscalar A "qscalar".
\return "qtensor".
*/
template
<
class
T
>
xt
::
xarray
<
T
>
AsTensor
(
size_t
rank
,
const
xt
::
xtensor
<
T
,
2
>&
qscalar
)
const
;
/**
Get the shape of a "qtensor" of a certain rank
(0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
Default: rank = 0, a.k.a. scalar.
\returns Shape as `std::array`.
*/
template
<
size_t
rank
=
0
>
std
::
array
<
size_t
,
2
+
rank
>
ShapeQtensor
()
const
;
/**
Get the shape of a "qtensor" of a certain rank
(0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
\param rank The tensor rank.
\returns Shape as `std::vector`.
*/
std
::
vector
<
size_t
>
ShapeQtensor
(
size_t
rank
)
const
;
/**
Get the shape of a "qscalar" (a "qtensor" of rank 0)
\returns Shape as `std::vector`.
*/
std
::
vector
<
size_t
>
ShapeQscalar
()
const
;
/**
Get an allocated `xt::xtensor` to store a "qtensor" of a certain rank
(0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
Default: rank = 0, a.k.a. scalar.
Note: the container is not (zero-)initialised.
\returns `xt::xtensor` container of the correct shape (and rank).
*/
template
<
size_t
rank
=
0
,
class
T
>
xt
::
xtensor
<
T
,
2
+
rank
>
AllocateQtensor
()
const
;
/**
Get an allocated and initialised `xt::xtensor` to store a "qtensor" of a certain rank
(0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
Default: rank = 0, a.k.a. scalar.
\param val The value to which to initialise all items.
\returns `xt::xtensor` container of the correct shape (and rank).
*/
template
<
size_t
rank
=
0
,
class
T
>
xt
::
xtensor
<
T
,
2
+
rank
>
AllocateQtensor
(
T
val
)
const
;
/**
Get an allocated `xt::xarray` to store a "qtensor" of a certain rank
(0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
Note: the container is not (zero-)initialised.
\param rank The tensor rank.
\returns `xt::xarray` container of the correct shape.
*/
template
<
class
T
>
xt
::
xarray
<
T
>
AllocateQtensor
(
size_t
rank
)
const
;
/**
Get an allocated and initialised `xt::xarray` to store a "qtensor" of a certain rank
(0 = scalar, 1, vector, 2 = 2nd-order tensor, etc.).
\param rank The tensor rank.
\param val The value to which to initialise all items.
\returns `xt::xtensor` container of the correct shape (and rank).
*/
template
<
class
T
>
xt
::
xarray
<
T
>
AllocateQtensor
(
size_t
rank
,
T
val
)
const
;
/**
Get an allocated `xt::xtensor` to store a "qscalar" (a "qtensor" of rank 0).
Note: the container is not (zero-)initialised.
\returns `xt::xarray` container of the correct shape.
*/
template
<
class
T
>
xt
::
xtensor
<
T
,
2
>
AllocateQscalar
()
const
;
/**
Get an allocated and initialised `xt::xarray` to store a "qscalar" (a "qtensor" of rank 0).
\param val The value to which to initialise all items.
\returns `xt::xtensor` container of the correct shape (and rank).
*/
template
<
class
T
>
xt
::
xtensor
<
T
,
2
>
AllocateQscalar
(
T
val
)
const
;
protected:
/**
Wrapper of constructor, for derived classes.
*/
void
initQuadratureBase
(
size_t
nelem
,
size_t
nip
);
protected:
size_t
m_nelem
;
///< Number of elements.
size_t
m_nip
;
///< Number of integration points per element.
constexpr
static
size_t
m_nne
=
ne
;
///< Number of nodes per element.
constexpr
static
size_t
m_ndim
=
nd
;
///< Number of dimensions for nodal vectors.
constexpr
static
size_t
m_tdim
=
td
;
///< Number of dimensions for integration point tensors.
};
}
// namespace Element
}
// namespace GooseFEM
#include "Element.hpp"
#endif
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