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DirichletProblemExample Class Reference

#include <DirichletProblem.h>

Inheritance diagram for DirichletProblemExample:

DirichletProblem List of all members.

Detailed Description

Dirichlet problem on the unit ball with boundary function . This function is harmonic everywhere so the solution is the same function on the interior of the ball.

Definition at line 114 of file DirichletProblem.h.

Public Member Functions

 DirichletProblemExample (int dim, int T, Real dt=0.01)
Real boundaryFunction (const RealVector &u)

Static Public Member Functions

void runExample (int d, int T)

Constructor & Destructor Documentation

DirichletProblemExample::DirichletProblemExample int    dim,
int    T,
Real    dt = 0.01

The number of time steps necessary to reliably hit the boundary depnds on the size dt of the time steps and the dimension. For the default dt=0.01, T=500 suffices in dimension d=2, while T=10 suffices in dimension d=30.

Member Function Documentation

Real DirichletProblemExample::boundaryFunction const RealVector   u [virtual]

The boundary function h.

Implements DirichletProblem.

void DirichletProblemExample::runExample int    d,
int    T

Computes f(x) for the boundary function on the unit ball in . This function is harmonic ( ) and so the solution on the interior has the same form. We compute the solution f(x) for and then compare the known analytic value with what we get. Size of time steps 0.01. Number of paths: 30000.

d dimension.
T time steps alloted to hit boundary.

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