Simulation of SPDE's for Excitable Media using Finite Elements

TL;DR

This paper presents a finite element-based numerical scheme for simulating stochastic PDEs in excitable media, focusing on pattern formation like reentrant waves in biological models.

Contribution

It introduces a finite element discretization method for SPDEs driven by colored noise, applied to biological excitable media models.

Findings

Reentrant patterns emerge in simulations of excitable media.

Finite element method effectively captures stochastic effects.

Numerical results align with biological phenomena.

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.