Sylvain Maire (LSIS Univ. Sud Toulon Var)

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Date(s) - 20/03/2015
14 h 00 min - 15 h 00 min

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Title: Improved Monte Carlo simulations of diffusions in stratified media\n\nAbstract: We deal with the simulation of diffusions in a media where the diffusion is constant or piecewise constant with different kinds of boundary conditions. The simulation before reaching the boundary of the domain or the interface between subdomains is ensured thanks to the Walk on Spheres method. The main simulation problems is to compute weak approximations which appears when a boundary is reached.\nWe introduce finite differences techniques to deal with this problem for Neumann\, Robin and transmission conditions. These techniques lead to a local bias of order three when hitting a boundary and in general to a global bias of order two. We focus on equations related to inverse problems in electrical impedance tomography for which we introduce in addition a variance reduction method. This method uses the computation of the solution on a simple reference domain as a control variate and correlated trajectories.

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