pbat::fem::Mesh< TElement, Dims, TScalar, TIndex > Struct Template Reference

A generic stateful finite element mesh representation. More...

#include <Mesh.h>

Public Types
using	ElementType = TElement
	Underlying finite element type.
using	ScalarType = TScalar
	Floating point type.
using	IndexType = TIndex
	Index type.
using	NodeMatrix
	Node positions matrix type.
using	ElementMatrix
	Element indices matrix type.

Public Member Functions
template<class TDerivedV, class TDerivedC>
	Mesh (Eigen::MatrixBase< TDerivedV > const &V, Eigen::DenseBase< TDerivedC > const &C)
	Constructs a finite element mesh given some input geometric mesh.
template<class TDerivedV, class TDerivedC>
void	Construct (Eigen::MatrixBase< TDerivedV > const &V, Eigen::DenseBase< TDerivedC > const &C)
	Constructs a finite element mesh given some input geometric mesh.
template<int QuadratureOrder>
auto	QuadraturePoints () const -> Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic >
	Compute quadrature points in domain space on this mesh.
template<int QuadratureOrder, int kPoints = TElement::template QuadratureType<QuadratureOrder, ScalarType>::kPoints>
auto	QuadratureWeights () const -> Eigen::Vector< ScalarType, kPoints >
	Obtain quadrature weights on the reference element of this mesh.
void	Serialize (io::Archive &archive) const
	Serialize to HDF5 group.
void	Deserialize (io::Archive const &archive)
	Deserialize from HDF5 group.
template<int QuadratureOrder>
Eigen::Matrix< TScalar, Eigen::Dynamic, Eigen::Dynamic >	QuadraturePoints () const
template<int QuadratureOrder, int kPoints>
Eigen::Vector< TScalar, kPoints >	QuadratureWeights () const

Public Attributes
NodeMatrix	X
	kDims x |# nodes| nodal positions
ElementMatrix	E
	|Element::Nodes| x |# elements| element nodal indices

Static Public Attributes
static int constexpr	kDims = Dims
	Embedding dimensions of the mesh.
static int constexpr	kOrder = ElementType::kOrder
	Shape function order.
static int constexpr	kNodesPerElement = ElementType::kNodes
	Number of nodes per element.

Detailed Description

template<CElement TElement, int Dims, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>
struct pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >

A generic stateful finite element mesh representation.

Template Parameters

TElement	Type satisfying concept CElement
Dims	Embedding dimensions of the mesh
TScalar	Floating point type, defaults to Scalar
TIndex	Index type, defaults to Index

Member Typedef Documentation

ElementMatrix

template<CElement TElement, int Dims, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

using pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::ElementMatrix

Initial value:

 
        Eigen::Matrix<IndexType, kNodesPerElement, Eigen::Dynamic>

Element indices matrix type.

NodeMatrix

template<CElement TElement, int Dims, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

using pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::NodeMatrix

Initial value:

 
        Eigen::Matrix<ScalarType, kDims, Eigen::Dynamic>

Node positions matrix type.

Constructor & Destructor Documentation

Mesh()

template<CElement TElement, int Dims, common::CFloatingPoint TScalar, common::CIndex TIndex>

template<class TDerivedV, class TDerivedC>

pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::Mesh ( Eigen::MatrixBase< TDerivedV > const & V, Eigen::DenseBase< TDerivedC > const & C )

inline

Constructs a finite element mesh given some input geometric mesh.

Warning

The cells of the input mesh should list its vertices in Lagrange order.

Template Parameters

TDerivedV	Type of the vertex positions matrix
TDerivedC	Type of the cell vertex indices matrix

Parameters

V	Dims x |# vertices| matrix of vertex positions
C	|Element::AffineBase::Vertices| x |# cells| matrix of cell vertex indices into V

Member Function Documentation

Construct()

template<CElement TElement, int Dims, common::CFloatingPoint TScalar, common::CIndex TIndex>

template<class TDerivedV, class TDerivedC>

void pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::Construct ( Eigen::MatrixBase< TDerivedV > const & V, Eigen::DenseBase< TDerivedC > const & C )

inline

Constructs a finite element mesh given some input geometric mesh.

Warning

The cells of the input mesh should list its vertices in Lagrange order.

Template Parameters

TDerivedV	Type of the vertex positions matrix
TDerivedC	Type of the cell vertex indices matrix

Parameters

V	Dims x |# vertices| matrix of vertex positions
C	|Element::AffineBase::Vertices| x |# cells| matrix of cell vertex indices into V

Deserialize()

template<CElement TElement, int Dims, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::Deserialize

(

io::Archive const &

archive

)

Deserialize from HDF5 group.

Parameters

archive

Archive to deserialize from

QuadraturePoints()

template<CElement TElement, int Dims, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

template<int QuadratureOrder>

auto pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::QuadraturePoints

(

)

const -> Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic >

Compute quadrature points in domain space on this mesh.

Template Parameters

QuadratureOrder

Quadrature order

Returns

kDims x |# element quad.pts.| matrix of quadrature points

QuadratureWeights()

template<CElement TElement, int Dims, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

template<int QuadratureOrder, int kPoints = TElement::template QuadratureType<QuadratureOrder, ScalarType>::kPoints>

auto pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::QuadratureWeights

(

)

const -> Eigen::Vector< ScalarType, kPoints >

Obtain quadrature weights on the reference element of this mesh.

Template Parameters

QuadratureOrder

Quadrature order

Parameters

kPoints

Number of quadrature points, defaults to Element::template QuadratureType<QuadratureOrder>::kPoints. This template parameter should not be specified, it is there to enhance readability.

Returns

|# element quad.pts.| vector of quadrature weights

Serialize()

template<CElement TElement, int Dims, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::fem::Mesh< TElement, Dims, TScalar, TIndex >::Serialize

(

io::Archive &

archive

)

const

Serialize to HDF5 group.

Parameters

archive

Archive to serialize to

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The documentation for this struct was generated from the following file:

• C:/git/PhysicsBasedAnimationToolkit/source/pbat/fem/Mesh.h