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

Class to evaluate element vectors of DPG methods. More...

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

Public Types
using	elem_vec_t = typename ProductElementVectorProvider< SCALAR >::elem_vec_t
	internal type for element vectors More...
using	ElemVec = typename ProductElementVectorProvider< SCALAR >::ElemVec
	Return type of the Eval() method. More...
using	ElemMat = typename ProductElementMatrixProvider< SCALAR >::ElemMat
	return type of the Eval() method of the ProductElementMatrixProvider class More...

Public Member Functions
	DpgElementVectorProvider (const DpgElementVectorProvider &)=delete
	standard constructors More...
	DpgElementVectorProvider (DpgElementVectorProvider &&) noexcept=default
DpgElementVectorProvider &	operator= (const DpgElementVectorProvider &)=delete
DpgElementVectorProvider &	operator= (DpgElementVectorProvider &&)=delete
	DpgElementVectorProvider (std::shared_ptr< ProductElementVectorProvider< SCALAR > > extendedLoadVectorProvider, 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...
ElemVec	Eval (const lf::mesh::Entity &cell)
	main routine for the computation of DPG element vectors More...
virtual	~DpgElementVectorProvider ()=default

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

Detailed Description

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

Class to evaluate element vectors of DPG methods.

Template Parameters

SCALAR

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

Note

This interface class complies with the requirements for the template parameter ELEM_VEC_COMP of the function lf::assemble::AssembleVectorLocally().

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

In an abstract setting to evaluate the DPG element vector 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 \( (\cdot , \cdot )_V : V \times V \rightarrow \mathbb{R} \)
• A linear form \( \ell: V \rightarrow \mathbb{R} \)

The practical DPG method can be implemented by computing a DPG element vector. 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 vector 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 extended element load vector \( l_{i} = \ell(b^i_v) \)
• Evaluate the DPG element vector \( \phi^K = B^T G^{-1} l \)

Definition at line 56 of file dpg_element_vector_provider.h.

Member Typedef Documentation

elem_vec_t

template<typename SCALAR >

using projects::dpg::DpgElementVectorProvider< SCALAR >::elem_vec_t = typename ProductElementVectorProvider<SCALAR>::elem_vec_t

internal type for element vectors

Definition at line 59 of file dpg_element_vector_provider.h.

ElemMat

template<typename SCALAR >

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

return type of the Eval() method of the ProductElementMatrixProvider class

Definition at line 64 of file dpg_element_vector_provider.h.

ElemVec

template<typename SCALAR >

using projects::dpg::DpgElementVectorProvider< SCALAR >::ElemVec = typename ProductElementVectorProvider<SCALAR>::ElemVec

Return type of the Eval() method.

Definition at line 61 of file dpg_element_vector_provider.h.

Constructor & Destructor Documentation

DpgElementVectorProvider() [1/3]

template<typename SCALAR >

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

delete

standard constructors

DpgElementVectorProvider() [2/3]

template<typename SCALAR >

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

defaultnoexcept

DpgElementVectorProvider() [3/3]

template<typename SCALAR >

projects::dpg::DpgElementVectorProvider< SCALAR >::DpgElementVectorProvider ( std::shared_ptr< ProductElementVectorProvider< SCALAR > >  extendedLoadVectorProvider, std::shared_ptr< ProductElementMatrixProvider< SCALAR > >  extendedStiffnessMatrixProvider, std::shared_ptr< ProductElementMatrixProvider< SCALAR > >  gramianProvider  )

inline

main constructor

Parameters

extendedLoadVectorProvider	evaluates the extended element load vector \( l \)
extendedStiffnessMatrixProvider	evaluates the extended element stiffness matrix \(B \)
gramianProvider	evaluates the local Gramian \( G \)

Definition at line 81 of file dpg_element_vector_provider.h.

~DpgElementVectorProvider()

template<typename SCALAR >

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

virtualdefault

Member Function Documentation

Eval()

template<typename SCALAR >

DpgElementVectorProvider< SCALAR >::ElemVec projects::dpg::DpgElementVectorProvider< SCALAR >::Eval

(

const lf::mesh::Entity &

cell

)

main routine for the computation of DPG element vectors

Parameters

cell	refernce to the cell for which the DPG element vector should be computed

Returns

a small vector, containing the DPG element vector.

Definition at line 132 of file dpg_element_vector_provider.h.

isActive()

template<typename SCALAR >

virtual bool projects::dpg::DpgElementVectorProvider< 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 98 of file dpg_element_vector_provider.h.

operator=() [1/2]

template<typename SCALAR >

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

delete

operator=() [2/2]

template<typename SCALAR >

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

delete

Member Data Documentation

extendedLoadVectorProvider_

template<typename SCALAR >

std::shared_ptr<ProductElementVectorProvider<SCALAR> > projects::dpg::DpgElementVectorProvider< SCALAR >::extendedLoadVectorProvider_

private

A ProductElementVectorProvider, that evaluates the extended load vector l

Definition at line 114 of file dpg_element_vector_provider.h.

extendedStiffnessMatrixProvider_

template<typename SCALAR >

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

private

A ProductElementMatrixProvider, that evaluates the extended element stiffness matrix B

Definition at line 118 of file dpg_element_vector_provider.h.

gramianProvider_

template<typename SCALAR >

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

private

A ProductElementMatrixProvider, that evaluates the local Gramian G

Definition at line 120 of file dpg_element_vector_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_vector_provider.h