hp2D::LinearFormHelper_1< F > Class Template Reference
Helper class for linearforms l(v), where v is a one form. More...
#include <linearFormHelper.hh>
Public Member Functions | |
| LinearFormHelper_1 (const concepts::ElementFormulaContainer< concepts::Point< F, 2 > > frm) | |
| LinearFormHelper_1 (const concepts::ElementFormulaContainer< F > frm1, const concepts::ElementFormulaContainer< F > frm2) | |
| virtual | ~LinearFormHelper_1 () |
Protected Member Functions | |
| void | computeIntermediate_ (const BaseQuad< concepts::Real > &elm) const |
| Compute the intermediate data for element matrix computation. More... | |
Protected Attributes | |
| concepts::ElementFormulaContainer< concepts::Point< F, 2 > > | frm_ |
| ElementFormula. More... | |
| ArrayElementFormula< concepts::Point< F, 2 > > | intermediateVector_ |
| Intermediate vector (on each quadrature point) More... | |
Detailed Description
template<class F>
class hp2D::LinearFormHelper_1< F >
Helper class for linearforms l(v), where v is a one form.
![\[\displaystyle l(v) = \int\limits_K \underline{f}(x)^\top\underline{v}\,dx = \int\limits_{\hat{K}} \underline{f}(F_K(\xi))^\top J^{-1} \hat{\underline{v}}\,\circ F_K^{-1} \det J\,d\xi = \int\limits_{\hat{K}} \underline{f}(F_K(\xi))^\top \mbox{adj}(J)^\top\hat{\underline{v}}\,\circ F_K^{-1}\,d\xi\]](form_535.png)
Here, 
is the element mapping from reference element ![$\hat{K} = [0,1]^2$](form_534.png)
, 
is the Jacobian matrix.
Precomputes intermediate data for element matrix computation, this is
![\[\underline{f}(F_K(\xi))^\top \mbox{adj}(J)^\top = \underline{f}(F_K(\xi))^\top J^{-\top}\det J,\]](form_536.png)
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
![\[ \int\limits_{K} \underline{k}^\top u \; \nabla{v} \; d\xi = \int\limits_{\hat{K}} \underline{k}^\top \hat{u} \; J^{-\top}\;\nabla{\hat{v}} \;|\det J| \; d\hat{\xi}. \]](form_487.png)
Definition at line 117 of file linearFormHelper.hh.
Constructor & Destructor Documentation
◆ LinearFormHelper_1() [1/2]
| hp2D::LinearFormHelper_1< F >::LinearFormHelper_1 | ( | const concepts::ElementFormulaContainer< F > | frm1, |
| const concepts::ElementFormulaContainer< F > | frm2 | ||
| ) |
◆ LinearFormHelper_1() [2/2]
| hp2D::LinearFormHelper_1< F >::LinearFormHelper_1 | ( | const concepts::ElementFormulaContainer< concepts::Point< F, 2 > > | frm | ) |
◆ ~LinearFormHelper_1()
|
virtual |
Member Function Documentation
◆ computeIntermediate_()
|
protected |
Compute the intermediate data for element matrix computation.
This method is important for the derivated linear forms.
Member Data Documentation
◆ frm_
|
protected |
ElementFormula.
Definition at line 139 of file linearFormHelper.hh.
◆ intermediateVector_
|
mutableprotected |
![\[\underline{f}(F_K(\xi))^\top \mbox{adj}(J)^\top\]](form_539.png)
The documentation for this class was generated from the following file:
- hp2D/linearFormHelper.hh