Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Antoine Lejay (1, 2) , Sylvain Maire (2, 3)

1 IECN - Institut Élie Cartan de Nancy
2 TOSCA - Simuler et calibrer des modèles stochastiques
3 MNC - Modélisation Numérique et Couplages

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.

Mots clés: Discontinuous media; divergence-form operator; stochastic process; kinetic approximation; Monte Carlo methods

Domaines: Probabilités [math.PR]

Antoine Lejay, Sylvain Maire. Simulating diffusions with piecewise constant coefficients using a kinetic approximation. Computer Methods in Applied Mechanics and Engineering, 2010, 199 (29-32), pp.2014-2023. ⟨10.1016/j.cma.2010.03.002⟩. ⟨inria-00358003v4⟩