hp2D::BilinearFormHelper_1_1< F, G > Class Template Reference
Helper class for bilinearforms a(u,v), where u and v are 1-forms, which computes intermediate data for element matrix computation. More...
#include <bilinearFormHelper.hh>
Public Member Functions | |
| BilinearFormHelper_1_1 (const concepts::ElementFormulaContainer< concepts::Mapping< G, 2 > > frmM) | |
| Constructor for matrix valued function. More... | |
| BilinearFormHelper_1_1 (const concepts::ElementFormulaContainer< F > frm) | |
| Constructor for scalar function. 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 | ~BilinearFormHelper_1_1 () |
| Destructor. More... | |
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... | |
Protected Attributes | |
| concepts::ElementFormulaContainer< F > | frm_ |
| Element formula. More... | |
| concepts::ElementFormulaContainer< concepts::Mapping< G, 2 > > | frmM_ |
| Matrix element formula. More... | |
| concepts::Array< concepts::Mapping< G, 2 > > | intermediateMatrix_ |
| Intermediate matrix. More... | |
| concepts::Array< F > | 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... | |
Private Attributes | |
| concepts::RCP< concepts::SharedJacobianAdj< 2 > > | sharedData_ |
| Shared data for vectorial bilinear forms. More... | |
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
![\[\displaystyle a(u,v) = \int\limits_K f(x)\underline{u}^T\underline{v}\,dx = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}J^{-1}J^{-\top}\hat{\underline{v}}\,\circ F_K^{-1}f(F_K(\xi))\det J\,d\xi = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}\mbox{adj}(J)\mbox{adj}(J)^\top\hat{\underline{v}}\,\circ F_K^{-1}\frac{f(F_K(\xi))}{\det J}\,d\xi\]](form_503.png)
For matrix valued function 
we have
![\[\displaystyle a(u,v) = \int\limits_K \underline{u}^TA(x)\underline{v}\,dx = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}J^{-1}A(F_K(\xi))J^{-\top}\hat{\underline{v}}\,\circ F_K^{-1}\det J\,d\xi = \int\limits_{\hat{K}} \hat{\underline{u}}\,\circ F_K^{-1}\mbox{adj}(J)A(F_K(\xi))\mbox{adj}(J)^\top\hat{\underline{v}}\,\circ F_K^{-1}\frac{1}{\det J}\,d\xi\]](form_505.png)
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.
Definition at line 140 of file bilinearFormHelper.hh.
Constructor & Destructor Documentation
◆ BilinearFormHelper_1_1() [1/2]
| hp2D::BilinearFormHelper_1_1< F, G >::BilinearFormHelper_1_1 | ( | const concepts::ElementFormulaContainer< F > | frm | ) |
Constructor for scalar function.
◆ BilinearFormHelper_1_1() [2/2]
| hp2D::BilinearFormHelper_1_1< F, G >::BilinearFormHelper_1_1 | ( | const concepts::ElementFormulaContainer< concepts::Mapping< G, 2 > > | frmM | ) |
Constructor for matrix valued function.
◆ ~BilinearFormHelper_1_1()
|
virtual |
Destructor.
Member Function Documentation
◆ computeadjJ_adjJT_rank1_()
|
private |
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_()
|
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.
◆ computeJacobianMatrix_()
|
private |
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< F, G >::data | ( | ) | const |
Gets the pointer to the shared data.
◆ data() [2/2]
| void hp2D::BilinearFormHelper_1_1< F, G >::data | ( | const concepts::RCP< concepts::SharedJacobianAdj< 2 > > | d | ) |
Set the pointer to the shared data.
Member Data Documentation
◆ frm_
|
protected |
Element formula.
Definition at line 193 of file bilinearFormHelper.hh.
◆ frmM_
|
protected |
Matrix element formula.
Definition at line 195 of file bilinearFormHelper.hh.
◆ intermediateMatrix_
|
mutableprotected |
Intermediate matrix.
In case of a scalar formula:
![\[\mbox{adj}(J) \mbox{adj}(J)^\top\]](form_515.png)
In case of a matrix formula 
:
![\[\mbox{adj}(J) M \mbox{adj}(J)^\top\]](form_516.png)
In case of partial Jacobian:
![\[\mbox{adj}(J)_{\cdot,j} (\mbox{adj}(J)_{\cdot,i})^\top\]](form_517.png)
Definition at line 191 of file bilinearFormHelper.hh.
◆ intermediateValue_
|
mutableprotected |
Intermediate value.
In case of a scalar formula:
![\[\frac{f(F_K(\xi))}{\det J}\]](form_513.png)
In case of a matrix formula:
![\[\frac{1}{\det J}\]](form_514.png)
Definition at line 179 of file bilinearFormHelper.hh.
◆ sharedData_
|
private |
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: