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

作者：Lejay Antoine; Pichot Geraldine^*

来源：Journal of Computational Physics, 2012, 231(21): 7299-7314.

DOI：10.1016/j.jcp.2012.07.011

• Divergence form operators
• Stochastic differential equation
• Skew Brownian motion
• Monte Carlo simulation
• Euler scheme
• Geophysics
• Diffusive media with interfaces

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.

• 出版日期2012-8-30
• 单位INRIA