Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Antoine Lejay 1, 2 Sylvain Maire 2, 3
2 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : Using a kinetic approximation of a linear diffusion operator, we propose an algorithm that allows one to deal with the simulation of a multi-dimensional stochastic process in a media which is locally isotropic except on some surface where the diffusion coefficient presents some discontinuities. Numerical examples are given in dimensions one to three on PDEs or stochastic PDEs with or without source terms.
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Antoine Lejay, Sylvain Maire. Simulating diffusions with piecewise constant coefficients using a kinetic approximation. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2010, 199 (29-32), pp.2014-2023. ⟨inria-00358003v4⟩

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