Spectral methods on triangles and other domains
Journal of Scientific Computing
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Tetrahedral hp finite elements: algorithms and flow simulations
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces
IEEE Transactions on Visualization and Computer Graphics
The SPHERIGON: A Simple Polygon Patch for Smoothing Quickly Your Polygonal Meshes
CA '98 Proceedings of the Computer Animation
Flows on surfaces of arbitrary topology
ACM SIGGRAPH 2003 Papers
Fourth order partial differential equations on general geometries
Journal of Computational Physics
An Improvement of a Recent Eulerian Method for Solving PDEs on General Geometries
Journal of Scientific Computing
A simple embedding method for solving partial differential equations on surfaces
Journal of Computational Physics
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
Finite element approximation of elliptic partial differential equations on implicit surfaces
Computing and Visualization in Science
A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
International Journal of Computational Fluid Dynamics
Efficient simulation of cardiac electrical propagation using high order finite elements
Journal of Computational Physics
Hi-index | 31.45 |
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.