A function class to calculate element matrices for the bilinear form related to a partial derivative of the trial and (!) test functions (scalar). More...

#include <bf_partialderiv.hh>

Inheritance diagram for hp2D::BilinearFormTwoPartDeriv< F >:

Public Member Functions
	BilinearFormTwoPartDeriv (const enum partDerivType i, const enum partDerivType j, const concepts::ElementFormulaContainer< F > frm=concepts::ElementFormulaContainer< F >())
	Constructor. More...

virtual BilinearFormTwoPartDeriv< 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...

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	~BilinearFormTwoPartDeriv ()

Protected Member Functions
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
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...

bool	operator() (const Quad< Real > elmX, const Quad< Real > elmY, concepts::ElementMatrix< F > &em) const
	Assembling for hp2D::Quad. More...

Private Attributes
enum partDerivType i_	j_
	Component of the test or trial function. More...

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

Detailed Description

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

A function class to calculate element matrices for the bilinear form related to a partial derivative of the trial and (!) test functions (scalar).

The shape functions on the physical cell are defined by standard mapping local shape functions defined on the reference square $\hat{K}$ .

$\int\limits_{K} f(\xi)\partial_j u \partial_i v \; d\xi = \int\limits_{\hat{K}} f(F_K\hat{\xi})\nabla{\hat{u}} (J^{-1})_{\cdot,j}(J^{-\top})_{i,\cdot}\nabla{\hat{v}} \;|\det J| \; d\hat{\xi}$

The class can be used to construct other bilinear forms, also for vectorial functions.

See also: vectorial::BilinearForm

Author: Kersten Schmidt, 2010

Definition at line 151 of file bf_partialderiv.hh.

Constructor & Destructor Documentation

◆ BilinearFormTwoPartDeriv()

template<class F = Real>

hp2D::BilinearFormTwoPartDeriv< F >::BilinearFormTwoPartDeriv	(	const enum partDerivType	i,
		const enum partDerivType	j,
		const concepts::ElementFormulaContainer< F >	frm = `concepts::ElementFormulaContainer< F >()`
	)

Constructor.

Parameters

i	Direction of the partial derivative of the test function, X for and Y for .
j	Direction of the partial derivative of the trial function.

◆ ~BilinearFormTwoPartDeriv()

template<class F = Real>

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

inlinevirtual

Definition at line 166 of file bf_partialderiv.hh.

Member Function Documentation

◆ clone() [1/2]

template<class F = Real>

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

inlinevirtual

Virtual constructor.

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

Implements concepts::Cloneable.

Definition at line 168 of file bf_partialderiv.hh.

◆ 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::BilinearFormTwoPartDeriv< F >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::BilinearForm< Real >.

◆ operator()() [1/4]

template<class F = Real>

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

virtual

◆ operator()() [2/4]

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()() [3/4]

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.

◆ operator()() [4/4]

template<class F = Real>

bool hp2D::BilinearFormTwoPartDeriv< F >::operator()	(	const Quad< Real > *	elmX,
		const Quad< Real > *	elmY,
		concepts::ElementMatrix< F > &	em
	)		const

private

Assembling for hp2D::Quad.

Member Data Documentation

◆ 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.

◆ j_

template<class F = Real>

enum partDerivType i_ hp2D::BilinearFormTwoPartDeriv< F >::j_

private

Component of the test or trial function.

Definition at line 177 of file bf_partialderiv.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.

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

hp2D/bf_partialderiv.hh

hp2D::BilinearFormTwoPartDeriv< F > Class Template Referenceabstract

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

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

Constructor & Destructor Documentation

◆ BilinearFormTwoPartDeriv()

◆ ~BilinearFormTwoPartDeriv()

Member Function Documentation

◆ clone() [1/2]

◆ clone() [2/2]

◆ computeadjJ_adjJT_rank1_()

◆ computeIntermediate_()

◆ computeJacobianMatrix_()

◆ data() [1/2]

◆ data() [2/2]

◆ info()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

Member Data Documentation

◆ frm_

◆ frmM_

◆ intermediateMatrix_

◆ intermediateValue_

◆ j_

◆ sharedData_

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