lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF > Class Template Reference

Class for local quadrature based computation of element matrix for Lagrangian finite elements and a weighted \(L^2\) inner product. More...

#include <lf/fe/fe.h>

Public Types
using	Scalar
	type of returned element matrix
using	ElemMat = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

Public Member Functions
	MassElementMatrixProvider (std::shared_ptr< const ScalarFESpace< SCALAR > > fe_space, REACTION_COEFF gamma)
	Constructor: cell-independent precomputations.
bool	isActive (const lf::mesh::Entity &) const
	All cells are considered active.
ElemMat	Eval (const lf::mesh::Entity &cell) const
	main routine for the computation of element matrices
	~MassElementMatrixProvider ()=default
	MassElementMatrixProvider (const MassElementMatrixProvider &)=delete
	standard constructors
	MassElementMatrixProvider (MassElementMatrixProvider &&) noexcept=default
MassElementMatrixProvider &	operator= (const MassElementMatrixProvider &)=delete
MassElementMatrixProvider &	operator= (MassElementMatrixProvider &&)=delete

Private Attributes
std::shared_ptr< const ScalarFESpace< SCALAR > >	fe_space_
quad::QuadRuleCache	qr_cache_
functors providing coefficient functions
REACTION_COEFF	gamma_

Detailed Description

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>
class lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >

Class for local quadrature based computation of element matrix for Lagrangian finite elements and a weighted \(L^2\) inner product.

Template Parameters

SCALAR	scalar type of the FiniteElementSpace. Must be a field type such as double or std::complex<double>
REACTION_COEFF	a MeshFunction that defines the reaction coefficient \( \mathbf{\gamma} \). It should be either scalar- or matrix-valued.

Note

This class complies with the type requirements for the template argument ENTITY_MATRIX_PROVIDER of the function lf::assemble::AssembleMatrixLocally().

The element matrix corresponds to the (local) bilinear form

\[ (u,v) \mapsto\int\limits_{K}\gamma(\mathbf{x})u\,\overline{v}\,\mathrm{d}\mathbf{x} \;, \]

with reaction coefficient \(\gamma\), see also Example 2.8.3.29

Template parameter requirement

• SCALAR must be a type like double
• REACTION_COEFF should be compatible with a scalar-valued MeshFunction

Note

If you intend to use this matrix provider with FE Spaces from lf::uscalfe please consider switching to lf::uscalfe::MassEdgeMatrixProvider provided there, as it is specifically optimized for uniform FE Spaces.

Definition at line 256 of file loc_comp_ellbvp.h.

Member Typedef Documentation

ElemMat

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

using lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::ElemMat = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

Definition at line 264 of file loc_comp_ellbvp.h.

Scalar

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

using lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::Scalar

Initial value:

 
      typename decltype(mesh::utils::MeshFunctionReturnType<REACTION_COEFF>() *
                        Eigen::Matrix<SCALAR, Eigen::Dynamic, 1>())::Scalar

type of returned element matrix

Definition at line 261 of file loc_comp_ellbvp.h.

Constructor & Destructor Documentation

MassElementMatrixProvider() [1/3]

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::MassElementMatrixProvider ( const MassElementMatrixProvider< SCALAR, REACTION_COEFF > & )

delete

standard constructors

MassElementMatrixProvider() [2/3]

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::MassElementMatrixProvider ( MassElementMatrixProvider< SCALAR, REACTION_COEFF > && )

defaultnoexcept

MassElementMatrixProvider() [3/3]

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::MassElementMatrixProvider	(	std::shared_ptr< const ScalarFESpace< SCALAR > >	fe_space,
		REACTION_COEFF	gamma )

Constructor: cell-independent precomputations.

Parameters

fe_space	collection of specifications for scalar-valued parametric reference elements
gamma	mesh function providing scalar-valued diffusion coefficient

See also

LocCompLagrFEPreprocessor::LocCompLagrFEPreprocessor()

This constructor uses local quadature rules with double the degree of exactness as the polynomial degree of the finite element space.

Definition at line 342 of file loc_comp_ellbvp.h.

~MassElementMatrixProvider()

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::~MassElementMatrixProvider ( )

default

destructor

Member Function Documentation

Eval()

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::ElemMat lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::Eval

(

const lf::mesh::Entity &

cell

)

const

main routine for the computation of element matrices

Parameters

cell	reference to the (triangular or quadrilateral) cell for which the element matrix should be computed.

Returns

a small dense, containing the element matrix.

Actual computation of the element matrix based on numerical quadrature and mapping techniques. The order of the quadrature rule is tied to the polynomial degree of the underlying finite element spaces: for polynomial degree p a quadrature rule is chosen that is exact for polynomials o degree 2p.

Throws an assertion in case the finite element specification is missing for the type of the cell.

Definition at line 351 of file loc_comp_ellbvp.h.

References lf::geometry::Geometry::DimGlobal(), lf::geometry::Geometry::DimLocal(), lf::mesh::Entity::Geometry(), lf::geometry::Geometry::Global(), lf::geometry::Geometry::IntegrationElement(), lf::fe::MassElementMatrixProviderLogger(), lf::base::RefEl::NodeCoords(), lf::quad::QuadRule::NumPoints(), lf::quad::QuadRule::Points(), lf::mesh::Entity::RefEl(), and lf::quad::QuadRule::Weights().

isActive()

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

bool lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::isActive ( const lf::mesh::Entity & ) const

inline

All cells are considered active.

Definition at line 295 of file loc_comp_ellbvp.h.

operator=() [1/2]

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

MassElementMatrixProvider & lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::operator= ( const MassElementMatrixProvider< SCALAR, REACTION_COEFF > & )

delete

operator=() [2/2]

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

MassElementMatrixProvider & lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::operator= ( MassElementMatrixProvider< SCALAR, REACTION_COEFF > && )

delete

Member Data Documentation

fe_space_

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

std::shared_ptr<const ScalarFESpace<SCALAR> > lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::fe_space_

private

FE Space

Definition at line 325 of file loc_comp_ellbvp.h.

gamma_

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

REACTION_COEFF lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::gamma_

private

Reaction coefficient

Definition at line 321 of file loc_comp_ellbvp.h.

qr_cache_

template<base::Scalar SCALAR, mesh::utils::MeshFunction REACTION_COEFF>

quad::QuadRuleCache lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::qr_cache_

private

Definition at line 327 of file loc_comp_ellbvp.h.

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

• /__w/lehrfempp/lehrfempp/lib/lf/fe/loc_comp_ellbvp.h