High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology

Chris D. Cantwell, Sergey Yakovlev, Robert M. Kirby, Nicholas S. Peters, Spencer J. Sherwin
2014 Journal of Computational Physics  
We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/hp elements, which provide exponential convergence of the solution with increasing polynomial order, while retaining geometric flexibility in the representation of the domain. Our work is motivated by applications in cardiac electrophysiology where sharp gradients in the solution benefit from the high-order discretisation, while the computational cost of
more » ... tic models can be significantly reduced through the surface representation and use of high-order methods. We describe and validate our discretisation and provide a demonstration of its application to modelling electrochemical propagation across a human left atrium.
doi:10.1016/j.jcp.2013.10.019 pmid:24748685 pmcid:PMC3991332 fatcat:zint4dq3andu3ogz4tk2becguu