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Stochastic finite differences for elliptic diffusion equations in stratified domains

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  • Maire, Sylvain
  • Nguyen, Giang

Abstract

We describe Monte Carlo algorithms to solve elliptic partial differential equations with piecewise constant diffusion coefficients and general boundary conditions including Robin and transmission conditions as well as a damping term. The treatment of the boundary conditions is done via stochastic finite differences techniques which possess a higher order than the usual methods. The simulation of Brownian paths inside the domain relies on variations around the walk on spheres method with or without killing. We check numerically the efficiency of our algorithms on various examples of diffusion equations illustrating each of the new techniques introduced here.

Suggested Citation

  • Maire, Sylvain & Nguyen, Giang, 2016. "Stochastic finite differences for elliptic diffusion equations in stratified domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 146-165.
    • Handle: RePEc:eee:matcom:v:121:y:2016:i:c:p:146-165
    DOI: 10.1016/j.matcom.2015.09.008
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    References listed on IDEAS

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    1. Hwang, Chi-Ok & Mascagni, Michael & Given, James A., 2003. "A Feynman–Kac path-integral implementation for Poisson’s equation using an h-conditioned Green’s function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 347-355.
    2. Madalina Deaconu & Antoine Lejay, 2006. "A Random Walk on Rectangles Algorithm," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 135-151, March.
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