Functionality related to discontinuous Galerkin discretizations of elliptic equations. More...
Namespaces | |
| NumericalFluxes | |
| Numerical fluxes for elliptic systems. | |
| OptionTags | |
| Option tags related to elliptic discontinuous Galerkin schemes. | |
| Tags | |
| DataBox tags related to elliptic discontinuous Galerkin schemes. | |
Functions | |
| template<typename DirichletTags , typename TagsList > | |
| void | homogeneous_dirichlet_boundary_conditions (const gsl::not_null< Variables< TagsList > * > exterior_vars, const Variables< TagsList > &interior_vars) noexcept |
Set the exterior_vars so that they represent homogeneous (zero) Dirichlet boundary conditions. More... | |
| DataVector | penalty (const DataVector &element_size, size_t num_points, double penalty_parameter) noexcept |
| The penalty factor in internal penalty fluxes. More... | |
Functionality related to discontinuous Galerkin discretizations of elliptic equations.
|
noexcept |
Set the exterior_vars so that they represent homogeneous (zero) Dirichlet boundary conditions.
To impose homogeneous Dirichlet boundary conditions we mirror the interior_vars and invert their sign. Variables that are not in the DirichletTags list are mirrored without changing their sign, so no boundary conditions are imposed on them.
|
noexcept |
The penalty factor in internal penalty fluxes.
The penalty factor is computed as
\begin{equation} \sigma = C \frac{N_\text{points}^2}{h} \end{equation}
where \(N_\text{points} = 1 + N_p\) is the number of points (or one plus the polynomial degree) and \(h\) is a measure of the element size. Both quantities are taken perpendicular to the face of the DG element that the penalty is being computed on. \(C\) is the "penalty parameter". For details see section 7.2 in [43].