class for local quadrature based computations of sub element matrices corresponding to element matrices associated to a flux variable in the trial space More...
#include <projects/dpg/loc_comp_dpg.h>
Public Types | |
| using | elem_mat_t = typename SubElementMatrixProvider< SCALAR >::elem_mat_t |
| inherited types for element matrices More... | |
| using | ElemMat = typename SubElementMatrixProvider< SCALAR >::ElemMat |
 Public Types inherited from projects::dpg::SubElementMatrixProvider< SCALAR > | |
| using | size_type = lf::uscalfe::size_type |
| using | elem_mat_t = Eigen::Matrix< SCALAR, Eigen::Dynamic, Eigen::Dynamic > |
| internal type for element matrices More... | |
| using | ElemMat = elem_mat_t |
Public Member Functions | |
| FluxElementMatrixProvider (const FluxElementMatrixProvider &)=delete | |
| FluxElementMatrixProvider (FluxElementMatrixProvider &&) noexcept=default | |
| FluxElementMatrixProvider & | operator= (const FluxElementMatrixProvider &)=delete |
| FluxElementMatrixProvider & | operator= (FluxElementMatrixProvider &&)=delete |
| FluxElementMatrixProvider (std::shared_ptr< ProductUniformFESpace< SCALAR > > fe_space_trial, std::shared_ptr< ProductUniformFESpace< SCALAR > > fe_space_test, size_type trial_component, size_type test_component, DIFF_COEFF alpha) | |
| Constructor: performs cell-independent precomputations. More... | |
| ElemMat | Eval (const lf::mesh::Entity &cell) override |
| main routine for the computation of element matrices More... | |
| size_type | TrialComponent () const override |
| returns the index of the trial space component \( u_{i_k} \) which is the trial space for the bilinear form \( b_k \) More... | |
| size_type | TestComponent () const override |
| returns the index of the test space component \( v_{j_k} \) which is the test space for the bilinear form \( b_k \) More... | |
| ~FluxElementMatrixProvider () override=default | |
| Public Member Functions inherited from projects::dpg::SubElementMatrixProvider< SCALAR > | |
| SubElementMatrixProvider ()=default | |
| virtual | ~SubElementMatrixProvider ()=default |
| SubElementMatrixProvider (const SubElementMatrixProvider &)=delete | |
| standard constructors More... | |
| SubElementMatrixProvider (SubElementMatrixProvider &&) noexcept=default | |
| SubElementMatrixProvider & | operator= (const SubElementMatrixProvider &)=delete |
| SubElementMatrixProvider & | operator= (SubElementMatrixProvider &&)=delete |
| virtual bool | isActive (const lf::mesh::Entity &) |
| All cells are considered active in the default implementation. More... | |
| virtual ElemMat | Eval (const lf::mesh::Entity &cell)=0 |
| main routine for the computation of (sub) element matrices More... | |
| virtual size_type | TrialComponent () const =0 |
| returns the index of the trial space component \( u_{i_k} \) which is the trial space for the bilinear form \( b_k \) More... | |
| virtual size_type | TestComponent () const =0 |
| returns the index of the test space component \( v_{j_k} \) which is the test space for the bilinear form \( b_k \) More... | |
Private Attributes | |
| DIFF_COEFF | alpha_ |
| functor providing the coefficient invoved in the bilinear form More... | |
| std::array< lf::uscalfe::PrecomputedScalarReferenceFiniteElement< SCALAR >, 5 > | fe_precomp_trial_ |
| array containing the precomputed information for the trial space flux component: fe_precomp_trial[i] contains the precomputed reference finite element of flux which is used in the computations of element matrices on cells of ref_el i. Note that the actual precomputed reference finite element is associated with ref_el lf::base::RefEl::kSegment(). More... | |
| std::array< std::vector< lf::uscalfe::PrecomputedScalarReferenceFiniteElement< SCALAR > >, 5 > | fe_precomp_test_ |
| array containing the precomputed information for the trial space: fe_precomp_trial[i][j] contains the precomputed reference finite element of \( v \) for ref_el i, evaluated on the quadrature points transformed to edge j of the boundary of the reference element More... | |
| size_type | trial_component_ |
| index of the trial component \( \hat{q}_n \) More... | |
| size_type | test_component_ |
| index of test component v More... | |
| PrescribedSignProvider | sign_provider_ |
| helper class, to evaluate the sgn_K function More... | |
Detailed Description
class projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >
class for local quadrature based computations of sub element matrices corresponding to element matrices associated to a flux variable in the trial space
- Template Parameters
-
SCALAR type for the entries of the element matrices. Must be a field type such as doubleorstd::complex<double>DIFF_COEFF a MeshFunction that defines the coefficient \( \alpha \). It should scalar valued.
- Note
- This class complies with the type requirements for the template argument ENTITY_MATRIX_PROVIDER of the function lf::assemble::AssembleMatrixLocally().
The element matrix corresponds to the (local) bilinear form
\[ (\hat{q}_n,v) \mapsto\int\limits_{\partial K} \hat{q}_n \mathrm{sgn}_K(\mathbf{x}) \alpha(\mathbf{x}) v \mathrm{d}\mathbf{x} \;, \]
\( \hat{q_n} \) is a flux component of the trial space and \( v\) is a component of the test space. *We assume that the flux is represented by discontinuous (interior) local shape functions on segments.
Template parameter requirement
- SCALAR must be a type like
double - DIFF_COEFF must provide a scalar-valued evaluation operator
operator (const Entity &,ref_coord_t).
Definition at line 789 of file loc_comp_dpg.h.
Member Typedef Documentation
◆ elem_mat_t
| using projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::elem_mat_t = typename SubElementMatrixProvider<SCALAR>::elem_mat_t |
inherited types for element matrices
Definition at line 794 of file loc_comp_dpg.h.
◆ ElemMat
| using projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::ElemMat = typename SubElementMatrixProvider<SCALAR>::ElemMat |
Definition at line 795 of file loc_comp_dpg.h.
Constructor & Destructor Documentation
◆ FluxElementMatrixProvider() [1/3]
|
delete |
◆ FluxElementMatrixProvider() [2/3]
|
defaultnoexcept |
◆ FluxElementMatrixProvider() [3/3]
| projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::FluxElementMatrixProvider | ( | std::shared_ptr< ProductUniformFESpace< SCALAR > > | fe_space_trial, |
| std::shared_ptr< ProductUniformFESpace< SCALAR > > | fe_space_test, | ||
| size_type | trial_component, | ||
| size_type | test_component, | ||
| DIFF_COEFF | alpha | ||
| ) |
Constructor: performs cell-independent precomputations.
- Parameters
-
fe_space_trial collection of specifications for the trial fe space fe_space_test collection of specification for the test fe space trial_component Index of the trial space component \(\hat{q}_n\). This component should represent a flux and be described via local discontinuous (interior) shape functions on the reference line segment. test_component Index of the test space component \(v\) alpha mesh function for the scalar valued coefficient involved in the bilinear form.
This constructur uses local quadrature rules. On each edge of the boundary a quadrature rule with degree of exactness chosen as the sum of the polynomial degree of the two components \( \hat{q}_n \) and \( v \) is used.
Definition at line 888 of file loc_comp_dpg.h.
References projects::dpg::BoundaryQuadRule(), projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::fe_precomp_test_, projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::fe_precomp_trial_, lf::base::RefEl::kQuad(), lf::base::RefEl::kSegment(), lf::base::RefEl::kTria(), lf::quad::make_QuadRule(), projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::test_component_, and projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::trial_component_.
◆ ~FluxElementMatrixProvider()
|
overridedefault |
Member Function Documentation
◆ Eval()
|
overridevirtual |
main routine for the computation of element matrices
- Parameters
-
cell reference to a (triangular or quadrilateral) cell for which the element matirx should be computed.
- Returns
- small dense matrix containing the element matrix
Actual computation is based on numerical quadrature and mapping techniques.
Throws an assertion, in case any specification is missing for the type of cell.
Implements projects::dpg::SubElementMatrixProvider< SCALAR >.
Definition at line 947 of file loc_comp_dpg.h.
References lf::geometry::Geometry::DimLocal(), lf::mesh::Entity::Geometry(), lf::base::RefEl::Id(), lf::base::RefEl::NumSubEntities(), lf::mesh::Entity::RefEl(), lf::mesh::Entity::SubEntities(), and lf::geometry::Geometry::SubGeometry().
◆ operator=() [1/2]
|
delete |
◆ operator=() [2/2]
|
delete |
◆ TestComponent()
|
inlineoverridevirtual |
returns the index of the test space component \( v_{j_k} \) which is the test space for the bilinear form \( b_k \)
Implements projects::dpg::SubElementMatrixProvider< SCALAR >.
Definition at line 842 of file loc_comp_dpg.h.
References projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::test_component_.
◆ TrialComponent()
|
inlineoverridevirtual |
returns the index of the trial space component \( u_{i_k} \) which is the trial space for the bilinear form \( b_k \)
Implements projects::dpg::SubElementMatrixProvider< SCALAR >.
Definition at line 838 of file loc_comp_dpg.h.
References projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::trial_component_.
Member Data Documentation
◆ alpha_
|
private |
functor providing the coefficient invoved in the bilinear form
Definition at line 850 of file loc_comp_dpg.h.
◆ fe_precomp_test_
|
private |
array containing the precomputed information for the trial space: fe_precomp_trial[i][j] contains the precomputed reference finite element of \( v \) for ref_el i, evaluated on the quadrature points transformed to edge j of the boundary of the reference element
Definition at line 868 of file loc_comp_dpg.h.
Referenced by projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::FluxElementMatrixProvider().
◆ fe_precomp_trial_
|
private |
array containing the precomputed information for the trial space flux component: fe_precomp_trial[i] contains the precomputed reference finite element of flux which is used in the computations of element matrices on cells of ref_el i. Note that the actual precomputed reference finite element is associated with ref_el lf::base::RefEl::kSegment().
Definition at line 859 of file loc_comp_dpg.h.
Referenced by projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::FluxElementMatrixProvider().
◆ sign_provider_
|
private |
helper class, to evaluate the sgn_K function
Definition at line 875 of file loc_comp_dpg.h.
◆ test_component_
|
private |
index of test component v
Definition at line 873 of file loc_comp_dpg.h.
Referenced by projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::FluxElementMatrixProvider(), and projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::TestComponent().
◆ trial_component_
|
private |
index of the trial component \( \hat{q}_n \)
Definition at line 871 of file loc_comp_dpg.h.
Referenced by projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::FluxElementMatrixProvider(), and projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::TrialComponent().
The documentation for this class was generated from the following file:
- /home/nico/bildung/SemVI/thesis/lehrfempp/projects/dpg/loc_comp_dpg.h
