High-order spectral/hp element 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/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 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:
- Publication Date:
- Research Org.:
- Univ. of Utah, Salt Lake City, UT (United States)
- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE); British Heart Foundation
- OSTI Identifier:
- 1209733
- Alternate Identifier(s):
- OSTI ID: 1623691
- Grant/Contract Number:
- DOE NETL DE-EE0004449; EE0004449
- Resource Type:
- Published Article
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Name: Journal of Computational Physics Journal Volume: 257 Journal Issue: PA; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Computer Science; Physics; High-order finite elements; Spectral/hp elements; Continuous Galerkin method; Surface PDE; Cardiac electrophysiology; Monodomain equation
Citation Formats
Cantwell, Chris D., Yakovlev, Sergey, Kirby, Robert M., Peters, Nicholas S., and Sherwin, Spencer J. High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology. United States: N. p., 2014.
Web. doi:10.1016/j.jcp.2013.10.019.
Cantwell, Chris D., Yakovlev, Sergey, Kirby, Robert M., Peters, Nicholas S., & Sherwin, Spencer J. High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology. United States. https://doi.org/10.1016/j.jcp.2013.10.019
Cantwell, Chris D., Yakovlev, Sergey, Kirby, Robert M., Peters, Nicholas S., and Sherwin, Spencer J. Wed .
"High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology". United States. https://doi.org/10.1016/j.jcp.2013.10.019.
@article{osti_1209733,
title = {High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology},
author = {Cantwell, Chris D. and Yakovlev, Sergey and Kirby, Robert M. and Peters, Nicholas S. and Sherwin, Spencer J.},
abstractNote = {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 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.},
doi = {10.1016/j.jcp.2013.10.019},
journal = {Journal of Computational Physics},
number = PA,
volume = 257,
place = {United States},
year = {Wed Jan 01 00:00:00 EST 2014},
month = {Wed Jan 01 00:00:00 EST 2014}
}
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https://doi.org/10.1016/j.jcp.2013.10.019
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Cited by: 31 works
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