Simulation of SPDE's for Excitable Media using Finite Elements

Muriel Boulakia 1, 2 Alexandre Genadot 3 Michèle Thieullen 3
2 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : In this paper, we address the question of the discretization of Stochastic Partial Differential Equations (SPDE's) for excitable media. Working with SPDE's driven by colored noise, we consider a numerical scheme based on finite differences in time (Euler-Maruyama) and finite elements in space. Motivated by biological considerations, we study numerically the emergence of reentrant patterns in excitable systems such as the Barkley or Mitchell-Schaeffer models.
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Muriel Boulakia, Alexandre Genadot, Michèle Thieullen. Simulation of SPDE's for Excitable Media using Finite Elements. Journal of Scientific Computing, Springer Verlag, 2014, pp.25. ⟨hal-01078727⟩

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