#include <bilinearFormHelper.hh>

Inheritance diagram for hp2D::BilinearFormHelper_1_1< F, G >:

Public Member Functions
	BilinearFormHelper_1_1 (const concepts::ElementFormulaContainer< F > frm)
	Constructor for scalar function.

	BilinearFormHelper_1_1 (const concepts::ElementFormulaContainer< concepts::Mapping< G, 2 > > frmM)
	Constructor for matrix valued function.

virtual	~BilinearFormHelper_1_1 ()
	Destructor.

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

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

Protected Member Functions
void	computeIntermediate_ (const BaseQuad< Real > &elm, const int i=-1, const int j=-1) const

Protected Attributes
concepts::Array< F >	intermediateValue_

concepts::Array< concepts::Mapping< G, 2 > >	intermediateMatrix_

concepts::ElementFormulaContainer< F >	frm_
	Element formula.

concepts::ElementFormulaContainer< concepts::Mapping< G, 2 > >	frmM_
	Matrix element formula.

Detailed Description

template<class F, class G = typename concepts::Realtype<F>::type>
class hp2D::BilinearFormHelper_1_1< F, G >

Helper class for bilinearforms a(u,v), where u and v are 1-forms, which computes intermediate data for element matrix computation.

It works with scalar functions and matrix valued functions.

For scalar function we have

$\displaystyle a(u,v) = \int\limits_K f(x)\underline{u}^T\underline{v}\,dx = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}J^{-1}J^{-\top}\hat{\underline{v}}\,\circ F_K^{-1}f(F_K(\xi))\det J\,d\xi = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}\mbox{adj}(J)\mbox{adj}(J)^\top\hat{\underline{v}}\,\circ F_K^{-1}\frac{f(F_K(\xi))}{\det J}\,d\xi$

For matrix valued function we have

$\displaystyle a(u,v) = \int\limits_K \underline{u}^TA(x)\underline{v}\,dx = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}J^{-1}A(F_K(\xi))J^{-\top}\hat{\underline{v}}\,\circ F_K^{-1}\det J\,d\xi = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}\mbox{adj}(J)A(F_K(\xi))\mbox{adj}(J)^\top\hat{\underline{v}}\,\circ F_K^{-1}\frac{1}{\det J}\,d\xi$

For scalar functions also the intermediate data for a bilinear form with partial derivatives can be stored, where the intermediate matrix is the rank-1 product of j-th column of with i-th row of .

Here, J is the Jacobian matrix.

The adjunct of the Jacobian matrix and the inverse of the determinant of the Jacobian matrix can be shared between different instances of the class. This is useful for bilinear forms on vectorial spaces.

Author: Kersten Schmidt, 2007

Definition at line 140 of file bilinearFormHelper.hh.

Member Function Documentation

◆ computeIntermediate_()

template<class F , class G = typename concepts::Realtype<F>::type>

void hp2D::BilinearFormHelper_1_1< F, G >::computeIntermediate_	(	const BaseQuad< Real > &	elm,
		const int	i = `-1`,
		const int	j = `-1`
	)		const

protected

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.