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 >:
concepts::BilinearForm< Real > hp2D::BilinearFormHelper_1_1< Real > concepts::Cloneable concepts::OutputOperator

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 $K$ 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
iDirection of the partial derivative of the test function, X for $partial_x$ and Y for $partial_y$.
jDirection 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
iif i=0 or 1, then take only i-th column of Jacobian matrix (for test function)
jif 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
elmXLeft element (test functions)
elmYRight element (trial functions)
emReturn 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
elmXLeft element
elmYRight element
emReturn element matrix
epElement 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 $M$:

\[\mbox{adj}(J) M \mbox{adj}(J)^\top\]

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:
Page URL: http://wiki.math.ethz.ch/bin/view/Concepts/WebHome
21 August 2020
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