Asymptotic diffusion limit of the symbolic Monte-Carlo method for the transport equation

We use asymptotic analysis to study the diffusion limit of the Symbolic Implicit Monte-Carlo (SIMC) method for the transport equation. For standard SIMC with piecewise constant basis functions, we demonstrate mathematically that the solution converges to the solution of a wrong diffusion equation. N...

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Bibliographic Details
Published in:Journal of computational physics 2004-03, Vol.195 (1), p.293-319
Main Authors: Clouët, J.-F., Samba, G.
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Monte-Carlo method
Physics
Radiative transfer
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Summary:We use asymptotic analysis to study the diffusion limit of the Symbolic Implicit Monte-Carlo (SIMC) method for the transport equation. For standard SIMC with piecewise constant basis functions, we demonstrate mathematically that the solution converges to the solution of a wrong diffusion equation. Nevertheless a simple extension to piecewise linear basis functions enables to obtain the correct solution. We present numerical examples which illustrate the analysis.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2003.10.008