Unstructured spectral elements applied to the bidomain model

Journal article

The electrical activity of the heart is often modelled by a coupled system of partial differential equations and ordinary differential equations called the bidomain equations. Obtaining an accurate numerical solution to this model is extremely computationally expensive. In this paper we present a novel approach that is computationally competitive and combines the use of spectral elements on simplices for the spatial discretisation and a third order linearly implicit time integration scheme. All known approaches to solve this problem have concentrated on the use of low order methods. Our spatial discretisation is a high order continuous Galerkin method which is coupled to an adaptive linearly implicit Rosenbrock time integration scheme. The scheme presented allows the time steps used to be chosen by accuracy considerations rather than stability considerations and allows for highly accurate numerical simulations. © 2007 American Institute of Physics.

Authors: Jeannequin, N; Whiteley, J; Gavaghan, D

• Publication status: Published
• Journal: Numerical Analysis and Applied Mathematics
• Volume: 936
• Pages: 292-295
• Publication date: 2007-01-01
• DOI: 10.1063/1.2790133
• EISSN: 1551-7616
• ISSN: 0094-243X
• Language: English
• Keywords: mathematical biology; bidomain; numerical PDEs; spectral element method; finite element method; physiology; high order