Solution of Dirichlet problems by the Exodus method

Applying the Exodus method to Dirichlet problems in rectangular and axisymmetric solution regions is proposed. The stochastic technique is illustrated with specific practical applications to the solution of Laplace's equation. Although the method is probabilistic in its approach, it is not subject to randomness as are the other Monte Carlo techniques because it does not involve the use of a pseudo-random generation subroutine. The method provides a more accurate solution in less amount of time compared with the fixed random walk. It is also found that the accuracy of the Exodus method is comparable to that of the finite difference method.< >