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 subj...

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Bibliographic Details
Published in:IEEE transactions on microwave theory and techniques 1992-01, Vol.40 (1), p.89-95
Main Authors: Sadiku, M.N.O., Hunt, D.T.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Boundary conditions
Difference equations
Exact sciences and technology
Finite difference methods
Laplace equations
Monte Carlo methods
Probability
Radiocommunications
Radiowave propagation
Stochastic processes
Telecommunications
Telecommunications and information theory
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Summary: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.< >
ISSN:0018-9480
1557-9670
DOI:10.1109/22.108327