title: High-order spectral/hpelement discretisation for reaction-diffusion problems on surfaces: Application to cardiac electrophysiology.
abstract: We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/hpelements, 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 anatomically-realistic 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.
authors.affiliation: National Heart and Lung Institute, Imperial College London, London, UK.
authors.forename: Chris D
authors.initials: CD
authors.lastname: Cantwell
authors.affiliation: School of Computing and Scientific Computing and Imaging (SCI) Institute, Univ. of Utah, Salt Lake City, UT, USA.
authors.forename: Sergey
authors.initials: S
authors.lastname: Yakovlev
authors.affiliation: School of Computing and Scientific Computing and Imaging (SCI) Institute, Univ. of Utah, Salt Lake City, UT, USA.
authors.forename: Robert M
authors.initials: RM
authors.lastname: Kirby
authors.affiliation: National Heart and Lung Institute, Imperial College London, London, UK.
authors.forename: Nicholas S
authors.initials: NS
authors.lastname: Peters
authors.affiliation: Department of Aeronautics, Imperial College London, London, UK.
authors.forename: Spencer J
authors.initials: SJ
authors.lastname: Sherwin
keywords: Cardiac electrophysiology; Continuous Galerkin method; High-order finite elements; Monodomain equation; Spectral/hp elements; Surface PDE
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