#include <linearFormHelper.hh>

Inheritance diagram for hp3D::LinearFormHelper_1< F >:

Public Member Functions
	LinearFormHelper_1 (const concepts::ElementFormulaContainer< F > frm1, const concepts::ElementFormulaContainer< F > frm2, const concepts::ElementFormulaContainer< F > frm3)

	LinearFormHelper_1 (const concepts::ElementFormulaContainer< concepts::Point< F, 3 > > frm)

Protected Member Functions
void	computeIntermediate_ (const Hexahedron &elm) const

Protected Attributes
ArrayElementFormula< concepts::Point< F, 3 > >	intermediateVector_

concepts::ElementFormulaContainer< concepts::Point< F, 3 > >	frm_
	ElementFormula.

Detailed Description

template<class F>
class hp3D::LinearFormHelper_1< F >

Helper class for linearforms l(v), where v is a one form

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

Here, is the element mapping from reference element $\hat{K} = [0,1]^2$ , is the Jacobian matrix.

Precomputes intermediate data for element matrix computation, this is

$\underline{f}(F_K(\xi))^\top \mbox{adj}(J)^\top = \underline{f}(F_K(\xi))^\top J^{-\top}\det J,$

which is stored as a single vector intermediateVector_ for each quadrature point.

The class can be used as well for bilinear forms a(u,v) where u is a 0-form and v is a 1-form. One example is the bilinear form hp2D::Advection

$\int\limits_{K} \underline{k}^\top u \; \nabla{v} \; d\xi = \int\limits_{\hat{K}} \underline{k}^\top \hat{u} \; J^{-\top}\;\nabla{\hat{v}} \;|\det J| \; d\hat{\xi}.$