|
Namespaces | |
| namespace | LocalIntegrators::Divergence |
Local integrators related to the divergence operator and its trace. | |
| namespace | LocalIntegrators::Elasticity |
Local integrators related to elasticity problems. | |
| namespace | LocalIntegrators::L2 |
Local integrators related to L2-inner products. | |
| namespace | LocalIntegrators::Laplace |
Local integrators related to the Laplacian and its DG formulations. | |
| namespace | LocalIntegrators |
Library of integrals over cells and faces. | |
| namespace | LocalIntegrators::Maxwell |
Local integrators related to curl operators and their traces. | |
| namespace | LocalIntegrators::Patches |
Integrators writing patches with values in quadrature points. | |
| namespace | MeshWorker |
Modules | |
| The MeshWorker interface | |
Functions | |
| template<int dim> | |
| void | LocalIntegrators::L2::mass_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.) |
| template<int dim> | |
| void | LocalIntegrators::L2::L2 (Vector< double > &result, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< double > > > &input, const double factor=1.) |
| template<int dim> | |
| void | LocalIntegrators::L2::jump_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const double factor1=1., const double factor2=1.) |
| template<int dim> | |
| void | LocalIntegrators::Laplace::cell_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.) |
| template<int dim> | |
| void | LocalIntegrators::Laplace::nitsche_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, double penalty, double factor=1.) |
| template<int dim> | |
| void | LocalIntegrators::Laplace::nitsche_residual (Vector< double > &result, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< double > > > &input, const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > &Dinput, const VectorSlice< const std::vector< std::vector< double > > > &data, double penalty, double factor=1.) |
| template<int dim> | |
| void | LocalIntegrators::Laplace::ip_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, double penalty, double factor1=1., double factor2=-1.) |
A collection of namespaces and functions which simplify the coding of forms and bilinear forms on finite element spaces. Functions for two different purposes are gathered here: the abstract integration on finite element meshes in MeshWorker and actual implementations of the integration of cell and face terms for concrete problems in LocalIntegrators.
When we integrate a function or a functional on a finite element space, the structure of the integration loop is always the same. We have between 3 and 5 nested loops, from outside to inside:
These loops naturally fall into two classes, namely the computation of cell and face contributions (loops 3 to 5), and the outer loops over the mesh objects, often referred to as assembling.
Support for the outer loop in deal.II can be found in the namespace MeshWorker (see the documentation there). In order to support the cell and face contributions (referred to as local contributions from now on), deal.II offers FEValuesBase and its derived classes. While the outer loop is generic (with exception of the data types), the computation of local contributions is problem dependent. Therefore, no generic algorithm is possible here. Nevertheless, we can define a generic interface for functions for this purpose and provide a library of local integrators for use in applications. These are collected in the namespace LocalIntegrators
| void LocalIntegrators::L2::mass_matrix | ( | FullMatrix< double > & | M, |
| const FEValuesBase< dim > & | fe, | ||
| const double | factor = 1. |
||
| ) |
The mass matrix for scalar or vector values finite elements.
Likewise, this term can be used on faces, where it computes the integrals
Definition at line 53 of file l2.h.
References FEValuesBase< dim, spacedim >::dofs_per_cell, FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FEValuesBase< dim, spacedim >::n_quadrature_points, and FEValuesBase< dim, spacedim >::shape_value_component().
| void LocalIntegrators::L2::L2 | ( | Vector< double > & | result, |
| const FEValuesBase< dim > & | fe, | ||
| const VectorSlice< const std::vector< std::vector< double > > > & | input, | ||
| const double | factor = 1. |
||
| ) |
L2-inner product for a slice of a vector valued right hand side.
Definition at line 112 of file l2.h.
References AssertDimension, FEValuesBase< dim, spacedim >::dofs_per_cell, FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FEValuesBase< dim, spacedim >::n_quadrature_points, FEValuesBase< dim, spacedim >::shape_value_component(), and Vector< Number >::size().
| void LocalIntegrators::L2::jump_matrix | ( | FullMatrix< double > & | M11, |
| FullMatrix< double > & | M12, | ||
| FullMatrix< double > & | M21, | ||
| FullMatrix< double > & | M22, | ||
| const FEValuesBase< dim > & | fe1, | ||
| const FEValuesBase< dim > & | fe2, | ||
| const double | factor1 = 1., |
||
| const double | factor2 = 1. |
||
| ) |
The jump matrix between two cells for scalar or vector values finite elements. Note that the factor
can be used to implement weighted jumps.
Using appropriate weights, this term can be used to penalize violation of conformity in H1.
Definition at line 149 of file l2.h.
References Assert, AssertDimension, FEValuesBase< dim, spacedim >::dofs_per_cell, StandardExceptions::ExcNotImplemented(), FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FullMatrix< number >::m(), FullMatrix< number >::n(), FEValuesBase< dim, spacedim >::n_quadrature_points, and FEValuesBase< dim, spacedim >::shape_value_component().
| void LocalIntegrators::Laplace::cell_matrix | ( | FullMatrix< double > & | M, |
| const FEValuesBase< dim > & | fe, | ||
| const double | factor = 1. |
||
| ) |
Laplacian in weak form, namely on the cell Z the matrix
The FiniteElement in fe may be scalar or vector valued. In the latter case, the Laplacian is applied to each component separately.
Definition at line 52 of file laplace.h.
References FEValuesBase< dim, spacedim >::dofs_per_cell, FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FEValuesBase< dim, spacedim >::n_quadrature_points, and FEValuesBase< dim, spacedim >::shape_grad_component().
| void LocalIntegrators::Laplace::nitsche_matrix | ( | FullMatrix< double > & | M, |
| const FEValuesBase< dim > & | fe, | ||
| double | penalty, | ||
| double | factor = 1. |
||
| ) |
Weak boundary condition of Nitsche type for the Laplacian, namely on the face F the matrix
Here,
is the penalty parameter suitably computed with compute_penalty().
Definition at line 86 of file laplace.h.
References Assert, FEValuesBase< dim, spacedim >::dofs_per_cell, StandardExceptions::ExcDimensionMismatch(), FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FullMatrix< number >::m(), FullMatrix< number >::n(), FEValuesBase< dim, spacedim >::n_quadrature_points, FEValuesBase< dim, spacedim >::normal_vector(), FEValuesBase< dim, spacedim >::shape_grad_component(), and FEValuesBase< dim, spacedim >::shape_value_component().
| void LocalIntegrators::Laplace::nitsche_residual | ( | Vector< double > & | result, |
| const FEValuesBase< dim > & | fe, | ||
| const VectorSlice< const std::vector< std::vector< double > > > & | input, | ||
| const VectorSlice< const std::vector< std::vector< Tensor< 1, dim > > > > & | Dinput, | ||
| const VectorSlice< const std::vector< std::vector< double > > > & | data, | ||
| double | penalty, | ||
| double | factor = 1. |
||
| ) |
Weak boundary condition for the Laplace operator by Nitsche, vector valued version, namely on the face F the vector
Here, u is the finite element function whose values and gradient are given in the arguments input and Dinput, respectively. g is the inhomogeneous boundary value in the argument data.
is the usual penalty parameter.
Definition at line 131 of file laplace.h.
References AssertVectorVectorDimension, FEValuesBase< dim, spacedim >::dofs_per_cell, FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FEValuesBase< dim, spacedim >::n_quadrature_points, FEValuesBase< dim, spacedim >::normal_vector(), FEValuesBase< dim, spacedim >::shape_grad_component(), and FEValuesBase< dim, spacedim >::shape_value_component().
| void LocalIntegrators::Laplace::ip_matrix | ( | FullMatrix< double > & | M11, |
| FullMatrix< double > & | M12, | ||
| FullMatrix< double > & | M21, | ||
| FullMatrix< double > & | M22, | ||
| const FEValuesBase< dim > & | fe1, | ||
| const FEValuesBase< dim > & | fe2, | ||
| double | penalty, | ||
| double | factor1 = 1., |
||
| double | factor2 = -1. |
||
| ) |
Flux for the interior penalty method for the Laplacian, namely on the face F the matrices associated with the bilinear form
The penalty parameter should always be the mean value of the penalties needed for stability on each side. In the case of constant coefficients, it can be computed using compute_penalty().
If factor2 is missing or negative, the factor is assumed the same on both sides. If factors differ, note that the penalty parameter has to be computed accordingly.
Definition at line 231 of file laplace.h.
References AssertDimension, FEValuesBase< dim, spacedim >::dofs_per_cell, FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FullMatrix< number >::m(), FullMatrix< number >::n(), FEValuesBase< dim, spacedim >::n_quadrature_points, FEValuesBase< dim, spacedim >::normal_vector(), FEValuesBase< dim, spacedim >::shape_grad_component(), and FEValuesBase< dim, spacedim >::shape_value_component().
documentation generated on Tue May 22 2012 12:06:59 by
doxygen
1.7.3