A function class to calculate element matrices for the Laplacian. More...

#include <bf_laplace.hh>

Inheritance diagram for hp2D::Laplace< F >:

Public Types
typedef concepts::Combtype< Real, typename concepts::Realtype< Real >::type >::type	value_type

Public Member Functions
virtual Laplace< F > *	clone () const
	Virtual constructor. More...

virtual BilinearForm *	clone () const=0
	Virtual constructor. More...

concepts::RCP< concepts::SharedJacobianAdj< 2 > >	data () const
	Gets the pointer to the shared data. More...

void	data (const concepts::RCP< concepts::SharedJacobianAdj< 2 > > d)
	Set the pointer to the shared data. More...

	Laplace (const concepts::ElementFormulaContainer< F > frm=concepts::ElementFormulaContainer< F >(), bool all=false)
	Constructor. More...

virtual void	operator() (const concepts::Element< Real > &elmX, const concepts::Element< Real > &elmY, concepts::ElementMatrix< F > &em) const

virtual void	operator() (const Element< typename Realtype< Real >::type > &elmX, const Element< typename Realtype< Real >::type > &elmY, ElementMatrix< Real > &em) const=0
	Evaluates the bilinear form for all shape functions on `elmX` and `elmY` and stores the result in the matrix `em`. More...

virtual void	operator() (const Element< typename Realtype< Real >::type > &elmX, const Element< typename Realtype< Real >::type > &elmY, ElementMatrix< Real > &em, const ElementPair< typename Realtype< Real >::type > &ep) const
	Evaluates the bilinear form for all shape functions on `elmX` and `elmY` and stores the result in the matrix `em`. More...

virtual	~Laplace ()

Protected Member Functions
bool	assemble_ (const Quad< Real > elmX, const Quad< Real > elmY, concepts::ElementMatrix< value_type > &em) const

void	computeIntermediate_ (const BaseQuad< Real > &elm, const int i=-1, const int j=-1) const
	Compute the intermediate data for element matrix computation. More...

virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...

Protected Attributes
concepts::ElementFormulaContainer< Real >	frm_
	Element formula. More...

concepts::ElementFormulaContainer< concepts::Mapping< typename concepts::Realtype< Real >::type, 2 > >	frmM_
	Matrix element formula. More...

concepts::Array< concepts::Mapping< typename concepts::Realtype< Real >::type, 2 > >	intermediateMatrix_
	Intermediate matrix. More...

concepts::Array< Real >	intermediateValue_
	Intermediate value. More...

Private Member Functions
bool	assembleLaguerre_ (const InfiniteLaguerreQuad elmX, const InfiniteLaguerreQuad elmY, concepts::ElementMatrix< F > &em) const

void	computeadjJ_adjJT_rank1_ (concepts::Array< concepts::Mapping< Real, 2 > > &intermediateMatrix, const int i, const int j) const
	Computes the either adj(J)*adj(J)^T or in the case of partial derivatives (i > NONE, j > NONE) the rank-1 product of j-th column of adj(J) with i-th row of adj(J)^T. More...

void	computeJacobianMatrix_ (const BaseQuad< Real > &elm, concepts::Array< concepts::Mapping< Real, 2 > > &J, concepts::Array< Real > &detJ_inv) const
	Compute the Jacobian matrix and the inverse of its determinant on each quadrature point. More...

Private Attributes
bool	all_
	Parameter for the sum factorisation. More...

concepts::ElementMatrix< Real >	mass1D_

concepts::RCP< concepts::SharedJacobianAdj< 2 > >	sharedData_
	Shared data for vectorial bilinear forms. More...

concepts::ElementMatrix< Real >	stiff1D_
	Local 1D stiffness and mass matrices for Karniadakis basis. More...

Detailed Description

template<class F = Real>
class hp2D::Laplace< F >

A function class to calculate element matrices for the Laplacian.

Test:: test::TestMatrices2D

Author: Kersten Schmidt, 2003

Examples: BGT_0.cc, exactDtN.cc, howToGetStarted.cc, hpFEM2d-simple.cc, hpFEM2d.cc, inhomDirichletBCs.cc, inhomDirichletBCsLagrange.cc, inhomNeumannBCs.cc, parallelizationTutorial.cc, and RobinBCs.cc.

Definition at line 90 of file bf_laplace.hh.

Member Typedef Documentation

◆ value_type

typedef concepts::Combtype<Real ,typename concepts::Realtype<Real >::type >::type hp2D::LaplaceBase< Real , typename concepts::Realtype<Real >::type >::value_type

inherited

Definition at line 64 of file bf_laplace.hh.

Constructor & Destructor Documentation

◆ Laplace()

template<class F = Real>

hp2D::Laplace< F >::Laplace	(	const concepts::ElementFormulaContainer< F >	frm = `concepts::ElementFormulaContainer< F >()`,
		bool	all = `false`
	)

Constructor.

The formula frm is evaluated in each quadrature point.

◆ ~Laplace()

template<class F = Real>

virtual hp2D::Laplace< F >::~Laplace ( )

virtual

Member Function Documentation

◆ assemble_()

bool hp2D::LaplaceBase< Real , typename concepts::Realtype<Real >::type >::assemble_	(	const Quad< Real > *	elmX,
		const Quad< Real > *	elmY,
		concepts::ElementMatrix< value_type > &	em
	)		const

protectedinherited

◆ assembleLaguerre_()

template<class F = Real>

bool hp2D::Laplace< F >::assembleLaguerre_	(	const InfiniteLaguerreQuad *	elmX,
		const InfiniteLaguerreQuad *	elmY,
		concepts::ElementMatrix< F > &	em
	)		const

private

◆ clone() [1/2]

template<class F = Real>

virtual Laplace<F>* hp2D::Laplace< F >::clone ( ) const

virtual

Virtual constructor.

Returns a pointer to a copy of itself. The caller is responsible to destroy this copy.

Implements concepts::Cloneable.

◆ clone() [2/2]

virtual BilinearForm* concepts::BilinearForm< Real , typename Realtype<Real >::type >::clone ( ) const

pure virtualinherited

Virtual constructor.

Returns a pointer to a copy of itself. The caller is responsible to destroy this copy.

◆ computeadjJ_adjJT_rank1_()

void hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::computeadjJ_adjJT_rank1_	(	concepts::Array< concepts::Mapping< Real, 2 > > &	intermediateMatrix,
		const int	i,
		const int	j
	)		const

privateinherited

Computes the either adj(J)*adj(J)^T or in the case of partial derivatives (i > NONE, j > NONE) the rank-1 product of j-th column of adj(J) with i-th row of adj(J)^T.

◆ computeIntermediate_()

void hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::computeIntermediate_	(	const BaseQuad< Real > &	elm,
		const int	i = `-1`,
		const int	j = `-1`
	)		const

protectedinherited

Compute the intermediate data for element matrix computation.

Parameters

i	if i=0 or 1, then take only i-th column of Jacobian matrix (for test function)
j	if j=0 or 1, then take only j-th column of Jacobian matrix (for trial function)

The Jacobian matrices have to been taken both full (i,j = -1) or both partial (i,j = 0 or 1).

Matrix formulas and complex valued scalar formulas are only implemented for full Jacobians.

◆ computeJacobianMatrix_()

void hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::computeJacobianMatrix_	(	const BaseQuad< Real > &	elm,
		concepts::Array< concepts::Mapping< Real, 2 > > &	J,
		concepts::Array< Real > &	detJ_inv
	)		const

privateinherited

Compute the Jacobian matrix and the inverse of its determinant on each quadrature point.

◆ data() [1/2]

concepts::RCP<concepts::SharedJacobianAdj<2> > hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::data

inherited

Gets the pointer to the shared data.

◆ data() [2/2]

void hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::data ( const concepts::RCP< concepts::SharedJacobianAdj< 2 > > d )

inherited

Set the pointer to the shared data.

◆ info()

template<class F = Real>

virtual std::ostream& hp2D::Laplace< F >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::BilinearForm< Real >.

◆ operator()() [1/3]

template<class F = Real>

virtual void hp2D::Laplace< F >::operator()	(	const concepts::Element< Real > &	elmX,
		const concepts::Element< Real > &	elmY,
		concepts::ElementMatrix< F > &	em
	)		const

virtual

◆ operator()() [2/3]

virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::operator()	(	const Element< G > &	elmX,
		const Element< G > &	elmY,
		ElementMatrix< F > &	em
	)		const

pure virtualinherited

Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em.

Postcondition: The returned matrix em has the correct size.

Parameters

elmX	Left element (test functions)
elmY	Right element (trial functions)
em	Return element matrix

◆ operator()() [3/3]

virtual void concepts::BilinearForm< Real , typename Realtype<Real >::type >::operator()	(	const Element< G > &	elmX,
		const Element< G > &	elmY,
		ElementMatrix< F > &	em,
		const ElementPair< G > &	ep
	)		const

inlinevirtualinherited

Evaluates the bilinear form for all shape functions on elmX and elmY and stores the result in the matrix em.

If this method is not reimplemented in a derived class, the default behaviour is to call the application operator without ep.

Postcondition: The returned matrix em has the correct size.

Parameters

elmX	Left element
elmY	Right element
em	Return element matrix
ep	Element pair holding more information on the pair `elmX` and `elmY`

Definition at line 57 of file bilinearForm.hh.

Member Data Documentation

◆ all_

template<class F = Real>

bool hp2D::Laplace< F >::all_

private

Parameter for the sum factorisation.

Definition at line 109 of file bf_laplace.hh.

◆ frm_

concepts::ElementFormulaContainer<Real > hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::frm_

protectedinherited

Element formula.

Definition at line 193 of file bilinearFormHelper.hh.

◆ frmM_

concepts::ElementFormulaContainer<concepts::Mapping<typename concepts::Realtype< Real >::type ,2> > hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::frmM_

protectedinherited

Matrix element formula.

Definition at line 195 of file bilinearFormHelper.hh.

◆ intermediateMatrix_

concepts::Array<concepts::Mapping<typename concepts::Realtype< Real >::type ,2> > hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::intermediateMatrix_

mutableprotectedinherited

Intermediate matrix.

In case of a scalar formula:

$\mbox{adj}(J) \mbox{adj}(J)^\top$

In case of a matrix formula :

$\mbox{adj}(J) M \mbox{adj}(J)^\top$

In case of partial Jacobian:

$\mbox{adj}(J)_{\cdot,j} (\mbox{adj}(J)_{\cdot,i})^\top$

Definition at line 191 of file bilinearFormHelper.hh.

◆ intermediateValue_

concepts::Array<Real > hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::intermediateValue_

mutableprotectedinherited

Intermediate value.

In case of a scalar formula:

$\frac{f(F_K(\xi))}{\det J}$

In case of a matrix formula:

$\frac{1}{\det J}$

Definition at line 179 of file bilinearFormHelper.hh.

◆ mass1D_

template<class F = Real>

concepts::ElementMatrix<Real> hp2D::Laplace< F >::mass1D_

private

Definition at line 112 of file bf_laplace.hh.

◆ sharedData_

concepts::RCP<concepts::SharedJacobianAdj<2> > hp2D::BilinearFormHelper_1_1< Real , typename concepts::Realtype< Real >::type >::sharedData_

privateinherited

Shared data for vectorial bilinear forms.

Definition at line 212 of file bilinearFormHelper.hh.

◆ stiff1D_

template<class F = Real>

concepts::ElementMatrix<Real> hp2D::Laplace< F >::stiff1D_

private

Local 1D stiffness and mass matrices for Karniadakis basis.

Definition at line 112 of file bf_laplace.hh.

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

hp2D/bf_laplace.hh

hp2D::Laplace< F > Class Template Referenceabstract

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

template<class F = Real> class hp2D::Laplace< F >

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ Laplace()

◆ ~Laplace()

Member Function Documentation

◆ assemble_()

◆ assembleLaguerre_()

◆ clone() [1/2]

◆ clone() [2/2]

◆ computeadjJ_adjJT_rank1_()

◆ computeIntermediate_()

◆ computeJacobianMatrix_()

◆ data() [1/2]

◆ data() [2/2]

◆ info()

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

Member Data Documentation

◆ all_

◆ frm_

◆ frmM_

◆ intermediateMatrix_

◆ intermediateValue_

◆ mass1D_

◆ sharedData_

◆ stiff1D_

template<class F = Real>
class hp2D::Laplace< F >