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A second-order Cartesian method for the simulation of electropermeabilization cell models

Michael Leguèbe 1, 2 Clair Poignard 1, 2 Lisl Weynans 1, 2, *
* Corresponding author
1 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : In this paper we present a new finite-difference method to simulate electropermeabilization models, like the model of Neu and Krassowska or the recent model of Kavian et al.. These models are based on the evolution of the electric potential in conducting media. The main feature lies in the transmission of the voltage potential which is proportional to the electric flux (the normal derivative of the potential). An adapted scheme is necessary to accurately simulate the voltage potential in the whole cell, notably at the membrane separating the cell from the outer medium. Our finite difference scheme is inspired by the method of Cisternino and Weynans for elliptic problems with immersed interfaces.This is a Cartesian grid method based on the accurate discretization of the fluxes at the interface, through the use of additional interface unknowns. The aim of the paper is to present the method and to study its stability and convergence properties. We prove the first-order convergence of the method for the dynamic non-linear model in one dimension, and the second order convergence in the stationary linear one-dimensional case. This results are corroborated by numerical experiments in two dimensions.
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Michael Leguèbe, Clair Poignard, Lisl Weynans. A second-order Cartesian method for the simulation of electropermeabilization cell models. [Research Report] RR-8302, INRIA Bordeaux; INRIA. 2013, pp.35. ⟨hal-00821758⟩

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