An analysis of some element-by-element techniques
Computer Methods in Applied Mechanics and Engineering
Mathematical physiology
The Chebyshev iteration revisited
Parallel Computing - Parallel matrix algorithms and applications
Enabling Numerical and Software Technologies for Studying the Electrical Activity in Human Heart
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Multilevel Additive Schwarz Preconditioners for the Bidomain Reaction-Diffusion System
SIAM Journal on Scientific Computing
Algebraic multigrid preconditioners for the bidomain reaction--diffusion system
Applied Numerical Mathematics
New challenges in dynamic load balancing
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Extreme scalability challenges in micro-finite element simulations of human bone
Concurrency and Computation: Practice & Experience - International Supercomputing Conference
Simulating drug-induced effects on the heart: from ion channel to body surface electrocardiogram
FIMH'11 Proceedings of the 6th international conference on Functional imaging and modeling of the heart
Unstructured mesh partition improvement for implicit finite element at extreme scale
The Journal of Supercomputing
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The simulation of cardiac electrophysiology is a mature field in computational physiology. Recent advances in medical imaging, high-performance computing and numerical methods mean that computational models of electrical propagation in human heart tissue are ripe for use in patient-specific simulation for diagnosis, for prognosis and for selection of treatment methods. However, in order to move in this direction, it is necessary to make efficient use of modern petascale computing resources.This paper focuses on an existing open source simulation framework (Chaste) and documents work done to improve the parallel scaling on a small range of electrophysiology benchmark problems.These benchmarks involve the numerical solution of the monodomain or bidomain equations via the finite-element method. At the beginning of this study the electrophysiology libraries within Chaste were already enabled to run in parallel and were able to solve for electrical propagation using the monodomain or bidomain equations, but parallel efficiency dropped rapidly when run on more than about 64 processors.Throughout the course of the study, improvements were made to problem definition input; geometric mesh partitioning; finite-element assembly of large, sparse linear systems; problem-specific matrix preconditioning; numerical solution of the linear system; and output of the approximate solution. The consequence of these improvements is that, at the end of the study, Chaste is able to solve a monodomain benchmark problem in close to real time. While some of the improvements made to the parallel Chaste code are specific to cardiac electrophysiology, many of the techniques documented in this paper are generic to the parallel finite-element method in other scientific application areas.