Stochastic finite differences for elliptic diffusion equations in stratified domains

Sylvain Maire and Giang Nguyen

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 121, issue C, 146-165

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.

Keywords: Monte Carlo method; Elliptic diffusion equations; Stratified media; Stochastic finite differences; Walk on spheres (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:121:y:2016:i:c:p:146-165

DOI: 10.1016/j.matcom.2015.09.008

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