step-6.h File Reference

Declaration of the dimension-independent SaddlePointProblem class that solves the saddle-point system described on the Introduction page. More...

#include <deal.II/base/quadrature_lib.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/fe/fe_system.h>
#include <deal.II/grid/tria.h>
#include <deal.II/lac/affine_constraints.h>
#include <deal.II/lac/solver_control.h>
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/vector.h>
#include <deal.II/base/point.h>
#include <deal.II/base/convergence_table.h>
#include <deal.II/base/parameter_handler.h>

Include dependency graph for step-6.h:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Classes
class	SaddlePointProblem< dim >
	Solves the two-component saddle-point Laplace system on a disk. More...
class	SaddlePointProblem< dim >::Parameters
	Run-time options read from a ParameterHandler input file. More...

Functions
template<int dim>
double	coefficient (const Point< dim > &p)
	Scalar, spatially variable coefficient \(a(\mathbf{x})\).

Detailed Description

Declaration of the dimension-independent SaddlePointProblem class that solves the saddle-point system described on the Introduction page.

This header declares the templated class SaddlePointProblem together with a nested Parameters class used to read runtime options from a ParameterHandler input file. It also declares a small templated helper function coefficient(...) that is used as the spatially variable coefficient \(a(\mathbf{x})\) in the bilinear form.

See also

source/step-6.cc for the implementation.

rhs_function.h for the right-hand side function class.

Function Documentation

coefficient()

template<int dim>

double coefficient

(

const Point< dim > &

p

)

Scalar, spatially variable coefficient \(a(\mathbf{x})\).

Used inside SaddlePointProblem::assemble_system as the multiplier in front of the \(\nabla u\cdot\nabla v\) term. The current implementation simply returns \(1\) everywhere, mimicking a constant-coefficient Laplace problem; users can edit this function to introduce a discontinuous or spatially varying coefficient such as the classical step-6 jump coefficient.

Template Parameters

dim	Spatial dimension of p.

Parameters

[in]

p

Point at which to evaluate the coefficient.

Returns

The value of \(a(\mathbf{x})\) at p.