SaddlePointProblem< dim > Class Template Reference

Solves the two-component saddle-point Laplace system on a disk. More...

#include <step-6.h>

Classes
class	Parameters
	Run-time options read from a ParameterHandler input file. More...

Public Member Functions
	SaddlePointProblem (const Parameters &parameters)
	Build a SaddlePointProblem problem from a fully populated Parameters object.
void	run ()
	Top-level driver that performs the adaptive-refinement loop.

Detailed Description

template<int dim>
class SaddlePointProblem< dim >

Solves the two-component saddle-point Laplace system on a disk.

The SaddlePointProblem class implements the full solve-cycle for the saddle-point problem described on the Introduction page. It owns the Triangulation, the FESystem (two copies of a scalar \(Q_k\) element), the DoFHandler, the constraint object that stores both hanging-node and Dirichlet constraints, the sparsity pattern, and the global system matrix and vectors.

The class is implemented as a template in the spatial dimension dim so that the same code can in principle be reused for 2D and 3D triangulations (in practice the program is only instantiated for dim = 2 because the manufactured solution and the right-hand sides are written for the 2D problem).

Typical usage from main():

ParameterHandler            prm;
SaddlePointProblem<2>::Parameters        parameters;
parameters.declare_parameters(prm);
prm.parse_input(filename);
parameters.get_parameters(prm);
 
SaddlePointProblem<2> problem(parameters);
problem.run();

Template Parameters

dim	Spatial dimension of the Laplace problem (currently 2).

Constructor & Destructor Documentation

SaddlePointProblem()

template<int dim>

SaddlePointProblem< dim >::SaddlePointProblem

(

const Parameters &

parameters

)

Build a SaddlePointProblem problem from a fully populated Parameters object.

The constructor stores a reference to parameters, creates a vector-valued FESystem with two copies of a scalar \(Q_k\) element (where \(k\) comes from parameters.fe_degree), and associates the DoFHandler with the (still empty) triangulation. The triangulation itself is generated in run().

Parameters

[in]

parameters

Run-time configuration read from param.prm.

Member Function Documentation

run()

template<int dim>

void SaddlePointProblem< dim >::run

(

)

Top-level driver that performs the adaptive-refinement loop.

Drive the full solve-cycle loop for parameters.n_refinement_cycles cycles.

For each refinement cycle the function calls, in order, setup_system(), assemble_system(), solve(), output_results(), output_exact_results(), compute_error() and write_convergence_table(). On the first cycle the function generates the initial hyper-ball mesh of radius \(\pi\); on subsequent cycles it calls refine_grid() to globally refine the mesh.

This function calls all the other functions of the SaddlePointProblem class. The main loop of the function deals with mesh generation: on cycle 0 it creates a circular domain (a hyper-ball of radius \(\pi\)) and performs one global refinement; on subsequent cycles it refines the existing grid.

For each cycle it then calls, in order, setup_system(), assemble_system(), solve(), output_results(), output_exact_results(), compute_error() and write_convergence_table(). It also prints informational messages about the number of active cells and degrees of freedom.

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The documentation for this class was generated from the following files:

• include/step-6.h
• source/step-6.cc