pbat::fem::LoadVector< TMesh, QuadratureOrder > Struct Template Reference

A matrix-free representation of a finite element load vector \( \mathbf{f}_i = \int_\Omega \mathbf{f}(X) \phi_i(X) \) under Galerkin projection. More...

#include <LoadVector.h>

Public Types
using	SelfType = LoadVector<TMesh, QuadratureOrder>
	Self type.
using	MeshType = TMesh
	Mesh type.
using	ElementType = typename TMesh::ElementType
	Element type.
using	QuadratureRuleType
	Quadrature rule type.

Public Member Functions
template<class TDerived>
	LoadVector (MeshType const &mesh, Eigen::Ref< MatrixX const > const &detJe, Eigen::DenseBase< TDerived > const &fe, int dims=1)
	Construct a new LoadVector object.
SelfType &	operator= (SelfType const &)=delete
VectorX	ToVector () const
	Transforms this element-wise load vector representation into a global load vector.
template<class TDerived>
void	SetLoad (Eigen::DenseBase< TDerived > const &fe)
	Set the external loading.
void	CheckValidState () const
	Check if the state of this load vector is valid.

Public Attributes
MeshType const &	mesh
	The finite element mesh.
MatrixX	fe
	|dims|x|# elements| piecewise element constant load
MatrixX	N
Eigen::Ref< MatrixX const >	detJe
int	dims
	Dimensionality of external loading. Should have dims >= 1.

Static Public Attributes
static int constexpr	kOrder = ElementType::kOrder
	Polynomial order of the load vector.
static int constexpr	kQuadratureOrder = QuadratureOrder
	Quadrature order.

Detailed Description

template<CMesh TMesh, int QuadratureOrder>
struct pbat::fem::LoadVector< TMesh, QuadratureOrder >

A matrix-free representation of a finite element load vector \( \mathbf{f}_i = \int_\Omega \mathbf{f}(X) \phi_i(X) \) under Galerkin projection.

Note

Assumes \( \mathbf{f}(X) \) is piecewise constant over the elements.

Todo

Link to my higher-level FEM crash course doc.

Template Parameters

TMesh	Type satisfying concept CMesh
QuadratureOrder	Quadrature order for integrating the load vector

Member Typedef Documentation

QuadratureRuleType

template<CMesh TMesh, int QuadratureOrder>

using pbat::fem::LoadVector< TMesh, QuadratureOrder >::QuadratureRuleType

Initial value:

 
        typename ElementType::template QuadratureType<QuadratureOrder>

Quadrature rule type.

Constructor & Destructor Documentation

LoadVector()

template<CMesh TMesh, int QuadratureOrder>

template<class TDerived>

pbat::fem::LoadVector< TMesh, QuadratureOrder >::LoadVector ( MeshType const & mesh, Eigen::Ref< MatrixX const > const & detJe, Eigen::DenseBase< TDerived > const & fe, int dims = 1 )

inline

Construct a new LoadVector object.

Template Parameters

TDerived

Eigen dense expression type

Parameters

mesh	Finite element mesh
detJe	|# quad.pts.|x|# elements| affine element jacobian determinants at quadrature points
fe	|dims|x|# elements| piecewise element constant load, or |dims|x1 constant load
dims	Dimensionality of image of FEM function space

Precondition

dims >= 1 and fe.cols() == 1 || fe.cols() == mesh.E.cols() and fe.rows() == dims

Member Function Documentation

SetLoad()

template<CMesh TMesh, int QuadratureOrder>

template<class TDerived>

void pbat::fem::LoadVector< TMesh, QuadratureOrder >::SetLoad ( Eigen::DenseBase< TDerived > const & fe )

inline

Set the external loading.

Template Parameters

TDerived

Eigen dense expression type

Parameters

fe	|dims|x|# elements| piecewise element constant load, or |dims|x1 constant load

ToVector()

template<CMesh TMesh, int QuadratureOrder>

VectorX pbat::fem::LoadVector< TMesh, QuadratureOrder >::ToVector ( ) const

inline

Transforms this element-wise load vector representation into a global load vector.

Returns

Global load vector

Member Data Documentation

detJe

template<CMesh TMesh, int QuadratureOrder>

Eigen::Ref<MatrixX const> pbat::fem::LoadVector< TMesh, QuadratureOrder >::detJe

|# element quadrature points|x|# elements| matrix of jacobian determinants at element quadrature points

N

template<CMesh TMesh, int QuadratureOrder>

MatrixX pbat::fem::LoadVector< TMesh, QuadratureOrder >::N

|ElementType::kNodes|x|# elements| integrated element shape functions. See (IntegratedShapeFunctions()).

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

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