A semi-alternating direction method for a 2-D fractional FitzHugh-Nagumo monodomain model on an approximate irregular domain

JOURNAL OF COMPUTATIONAL PHYSICS

卷:293

Article

Liu, F.¹  Zhuang, P.²  Turner, I.¹  Anh, V.¹  Burrage, K.^1,3 

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[3] Univ Oxford, Dept Comp Sci, Oxford OX1 3QD, England

关键词: Alternating direction method;    Two-sided space fractional diffusion equation;    Fractional FitzHugh-Nagumo monodomain model;    Alternating direction method;    Stability and convergence;    Irregular domain;   

DOI  :  10.1016/j.jcp.2014.06.001

来源: Elsevier

【 摘 要 】

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Second, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Third, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional FitzHugh-Nagumo model on both an approximate circular and an approximate irregular domain. (C) 2014 Elsevier Inc. All rights reserved.

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