Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Lejay, Antoine^2,3,4,5  Pichot, Geraldine¹ 

[1] INRIA, F-35042 Rennes, France

[2] Univ Lorraine, IECN, UMR 7502, F-54500 Vandoeuvre Les Nancy, France

[3] CNRS, IECN, UMR 7502, F-54500 Vandoeuvre Les Nancy, France

[4] Inria, F-54600 Villers Les Nancy, France

[5] IECN, F-54506 Vandoeuvre Les Nancy, France

关键词: Divergence form operators;    Stochastic differential equation;    Skew Brownian motion;    Monte Carlo simulation;    Euler scheme;    Geophysics;    Diffusive media with interfaces;   

DOI  :  10.1016/j.jcp.2012.07.011

来源: Elsevier

【 摘 要 】

In this article, we propose new Monte Carlo techniques for moving a diffusive particle in a discontinuous media. In this framework, we characterize the stochastic process that governs the positions of the particle. The key tool is the reduction of the process to a Skew Brownian motion (SBM). In a zone where the coefficients are locally constant on each side of the discontinuity, the new position of the particle after a constant time step is sampled from the exact distribution of the SBM process at the considered time. To do so, we propose two different but equivalent algorithms: a two-steps simulation with a stop at the discontinuity and a one-step direct simulation of the SBM dynamic. Some benchmark tests illustrate their effectiveness. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free