Stochastic finite differences for elliptic diffusion equations in stratified domains

Creators: Maire, Sylvain; Nguyen, Giang

Others:: TO Simulate and CAlibrate stochastic models (TOSCA) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL) ; Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS); Laboratoire des Sciences de l'Information et des Systèmes (LSIS) ; Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Arts et Métiers Paristech ENSAM Aix-en-Provence-Centre National de la Recherche Scientifique (CNRS)

Description

We describe Monte Carlo algorithms to solve elliptic partial differen- tial 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 an 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.

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Stochastic finite differences for elliptic diffusion equations in stratified domains

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Abstract

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