projects::dpg::DpgElementMatrixProvider< SCALAR > Class Template Reference

Class to evaluate element matrices for DPG methods. More...

#include </home/nico/bildung/SemVI/thesis/lehrfempp/projects/dpg/dpg_element_matrix_provider.h>

Public Types
using	elem_mat_t = typename ProductElementMatrixProvider< SCALAR >::elem_mat_t
	internal type for element matrices More...
using	ElemMat = typename ProductElementMatrixProvider< SCALAR >::ElemMat

Public Member Functions
	DpgElementMatrixProvider (const DpgElementMatrixProvider &)=delete
	standard constructors More...
	DpgElementMatrixProvider (DpgElementMatrixProvider &&) noexcept=default
DpgElementMatrixProvider &	operator= (const DpgElementMatrixProvider &)=delete
DpgElementMatrixProvider &	operator= (DpgElementMatrixProvider &&)=delete
	DpgElementMatrixProvider (std::shared_ptr< ProductElementMatrixProvider< SCALAR > > extendedStiffnessMatrixProvider, std::shared_ptr< ProductElementMatrixProvider< SCALAR > > gramianProvider)
	main constructor More...
virtual bool	isActive (const lf::mesh::Entity &)
	All cells are considered active in the default implementation. More...
ElemMat	Eval (const lf::mesh::Entity &cell)
	main routine for the computation of DPG element matrices More...
virtual	~DpgElementMatrixProvider ()=default

Private Attributes
std::shared_ptr< ProductElementMatrixProvider< SCALAR > >	extendedStiffnessMatrixProvider_
std::shared_ptr< ProductElementMatrixProvider< SCALAR > >	gramianProvider_

Detailed Description

template<typename SCALAR>
class projects::dpg::DpgElementMatrixProvider< SCALAR >

Class to evaluate element matrices for DPG methods.

Template Parameters

SCALAR

type for the entries of the element matrix. Usually 'double'.

Note

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

This class evaluates the DPG element matrix associated to a practical DPG method

In an abstract setting to evaluate the DPG element matrix the following ingredients are needed

• A diescrete Test space \( U_h \subset U \) with
• An enriched discrete test space \( V^r \subset V \)
• A bilinear form \( b : U \times V \rightarrow \mathbb{R} \)
• A localizable inner product \( (\cdot , \cdot )_V : V \times V \rightarrow \mathbb{R} \)

The practical DPG method can be implemented by computing a DPG element matrix . If \( \{ b^1_u \dots b^{Q_U}_u \} \) denote the local shape functions of \( U_h \) and \( \{ b^2_v \dots b^{Q_V}_v \} \) denote the local shape functiosn of \( V^R \) on an elment \( K \), the computation of the DPG element matrix boils down to

• Evaluate the extended element stiffness Matrix \( B_{i,j} = b(b^j_u,b^i_v) \)
• Evaluate the local Gramian matrix \( G_{i,j} = (b^i_v,b^j_v)_V \)
• Evaluate the DPG elment matrix \( A^K = B^T G^{-1} B \)

Definition at line 52 of file dpg_element_matrix_provider.h.

Member Typedef Documentation

elem_mat_t

template<typename SCALAR >

using projects::dpg::DpgElementMatrixProvider< SCALAR >::elem_mat_t = typename ProductElementMatrixProvider<SCALAR>::elem_mat_t

internal type for element matrices

Definition at line 55 of file dpg_element_matrix_provider.h.

ElemMat

template<typename SCALAR >

using projects::dpg::DpgElementMatrixProvider< SCALAR >::ElemMat = typename ProductElementMatrixProvider<SCALAR>::ElemMat

Return type of the Eval() method

Definition at line 57 of file dpg_element_matrix_provider.h.

Constructor & Destructor Documentation

DpgElementMatrixProvider() [1/3]

template<typename SCALAR >

projects::dpg::DpgElementMatrixProvider< SCALAR >::DpgElementMatrixProvider ( const DpgElementMatrixProvider< SCALAR > &  )

delete

standard constructors

DpgElementMatrixProvider() [2/3]

template<typename SCALAR >

projects::dpg::DpgElementMatrixProvider< SCALAR >::DpgElementMatrixProvider ( DpgElementMatrixProvider< SCALAR > &&  )

defaultnoexcept

DpgElementMatrixProvider() [3/3]

template<typename SCALAR >

projects::dpg::DpgElementMatrixProvider< SCALAR >::DpgElementMatrixProvider ( std::shared_ptr< ProductElementMatrixProvider< SCALAR > >  extendedStiffnessMatrixProvider, std::shared_ptr< ProductElementMatrixProvider< SCALAR > >  gramianProvider  )

inline

main constructor

Parameters

extendedStiffnessMatrixProvider	evaluates the extended element stiffness matrix \( B \)
gramianProvider	evaluates the local Gramian matrix \( G \)

Definition at line 72 of file dpg_element_matrix_provider.h.

~DpgElementMatrixProvider()

template<typename SCALAR >

virtual projects::dpg::DpgElementMatrixProvider< SCALAR >::~DpgElementMatrixProvider ( )

virtualdefault

Member Function Documentation

Eval()

template<typename SCALAR >

DpgElementMatrixProvider< SCALAR >::ElemMat projects::dpg::DpgElementMatrixProvider< SCALAR >::Eval

(

const lf::mesh::Entity &

cell

)

main routine for the computation of DPG element matrices

Parameters

cell	reference to the cell for which the DPG element matrix should be computed

Returns

a small dense, containing the DPG element matrix.

Definition at line 116 of file dpg_element_matrix_provider.h.

isActive()

template<typename SCALAR >

virtual bool projects::dpg::DpgElementMatrixProvider< SCALAR >::isActive ( const lf::mesh::Entity &  )

inlinevirtual

All cells are considered active in the default implementation.

This method is meant to be overloaded if assembly should be restricted to a subset of cells.

Definition at line 86 of file dpg_element_matrix_provider.h.

operator=() [1/2]

template<typename SCALAR >

DpgElementMatrixProvider & projects::dpg::DpgElementMatrixProvider< SCALAR >::operator= ( const DpgElementMatrixProvider< SCALAR > &  )

delete

operator=() [2/2]

template<typename SCALAR >

DpgElementMatrixProvider & projects::dpg::DpgElementMatrixProvider< SCALAR >::operator= ( DpgElementMatrixProvider< SCALAR > &&  )

delete

Member Data Documentation

extendedStiffnessMatrixProvider_

template<typename SCALAR >

std::shared_ptr<ProductElementMatrixProvider<SCALAR> > projects::dpg::DpgElementMatrixProvider< SCALAR >::extendedStiffnessMatrixProvider_

private

A ProductElementMatrixProvider that evaluates the extended element stiffness matrix \(B\)

Definition at line 102 of file dpg_element_matrix_provider.h.

gramianProvider_

template<typename SCALAR >

std::shared_ptr<ProductElementMatrixProvider<SCALAR> > projects::dpg::DpgElementMatrixProvider< SCALAR >::gramianProvider_

private

A ProductElementMatrixProvider that evaluates the local Gramian \( G \)

Definition at line 105 of file dpg_element_matrix_provider.h.

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

• /home/nico/bildung/SemVI/thesis/lehrfempp/projects/dpg/dpg_element_matrix_provider.h