High-order spectral/\(hp\) element discretisation for reaction-diffusion problems on surfaces: application to cardiac electrophysiology
From MaRDI portal
Publication:348514
DOI10.1016/j.jcp.2013.10.019zbMath1349.92007OpenAlexW2130292558WikidataQ34416134 ScholiaQ34416134MaRDI QIDQ348514
Publication date: 5 December 2016
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2013.10.019
continuous Galerkin methodhigh-order finite elementsspectral/\(hp\) elementsCardiac electrophysiologymonodomain equationsurface PDE
Physiology (general) (92C30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Computational methods for problems pertaining to biology (92-08)
Related Items
Nektar++: an open-source spectral/\(hp\) element framework, Numerical analysis of Darcy problem on surfaces, High-order method with moving frames to compute the covariant derivatives of vectors on general 2D curved surfaces, Relative acceleration of orthonormal basis vectors for the geometric conduction blocks of the cardiac electric signal propagation on anisotropic curved surfaces, A matrix-free high-order solver for the numerical solution of cardiac electrophysiology, \textit{Nektar}++: enhancing the capability and application of high-fidelity spectral/\(hp\) element methods, Dynamical behavior of reaction-diffusion neural networks and their synchronization arising in modeling epileptic seizure: a numerical simulation study, Isogeometric analysis for surface PDEs with extended Loop subdivision, Enabling local time stepping in the parallel implicit solution of reaction-diffusion equations via space-time finite elements on shallow tree meshes, Isogeometric analysis of the electrophysiology in the human heart: numerical simulation of the bidomain equations on the atria, Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy, Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium, The multi-level \(hp\)-method for three-dimensional problems: dynamically changing high-order mesh refinement with arbitrary hanging nodes, Optimising the performance of the spectral/\(hp\) element method with collective linear algebra operations, Development of Unstructured Curved Meshes with G 1 Surface Continuity for High-Order Finite Element Simulations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Efficient simulation of cardiac electrical propagation using high order finite elements
- Level set equations on surfaces via the closest point method
- The spectral element method for the shallow water equations on the sphere
- An improvement of a recent Eulerian method for solving PDEs on general geometries
- Eulerian finite element method for parabolic PDEs on implicit surfaces
- From \(h\) to \(p\) efficiently: implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations
- Finite element approximation of elliptic partial differential equations on implicit surfaces
- Spectral methods on triangles and other domains
- Tetrahedral \(hp\) finite elements: Algorithms and flow simulations
- A simple embedding method for solving partial differential equations on surfaces
- Fourth order partial differential equations on general geometries
- A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems
- A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes
- The Implicit Closest Point Method for the Numerical Solution of Partial Differential Equations on Surfaces
- An h-narrow band finite-element method for elliptic equations on implicit surfaces
- Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
- Spectral/hp Element Methods for Computational Fluid Dynamics
- Adaptive numerical treatment of elliptic systems on manifolds
