test_problems.h File Reference

Provides test problems for examining the convergence of embedded (Dirichlet) boundary conditions. More...

#include <madness/mra/mra.h>
#include <madness/mra/lbdeux.h>
#include <madness/mra/sdf_shape_3D.h>
#include <string>

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Classes
class	ConstantSphere
	The constant on a sphere problem. More...
class	CosineSphere
	The cos(theta) on a sphere problem. More...
class	DirichletCondIntOp
	The operator needed for solving for with GMRES. More...
struct	DirichletLBCost< NDIM >
class	EmbeddedDirichlet
	Abstract base class for embedded Dirichlet problems. More...
class	InhomoConstantSphere
	The constant on a sphere problem, with inhomogeneity. More...
class	Y20Sphere
	The Y_2^0 on a sphere problem. More...

Enumerations
enum	FunctorOutput { SURFACE , DIRICHLET_RHS , EXACT , DOMAIN_MASK }
enum	Mask { LLRV , Gaussian }

Detailed Description

Provides test problems for examining the convergence of embedded (Dirichlet) boundary conditions.

The auxiliary PDE being solved is

where

• is the solution function
• is the thickness of the boundary layer
• is the penalty prefactor, seems to work well.
• is the surface function
• is the Dirichlet condition to be enforced on the surface
• is the domain mask (1 inside, 0 outside, blurry on the border)
• is the inhomogeneity.

The available test problems are

1. A sphere of radius with , homogeneous (ConstantSphere)
2. A sphere of radius with , homogeneous (CosineSphere)
3. A sphere of radius with , homogeneous (Y20Sphere)
4. A sphere of radius with , inhomogeneous (InhomoConstantSphere)

This file sets up the various details of the problems... the main program is found in embedded_dirichlet.cc.

Enumeration Type Documentation

FunctorOutput

enum FunctorOutput

Enumerator
SURFACE
DIRICHLET_RHS
EXACT
DOMAIN_MASK

Mask

enum Mask

Enumerator
LLRV
Gaussian