A Parallel Solver for Reaction–diffusion Systems in Computational Electrocardiology

Franzone, Piero Colli; Pavarino, Luca F.

doi:10.1142/s0218202504003489

Cited by 156 publications

(154 citation statements)

References 47 publications

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“…An early contribution in this context was made by Colli Franzone & Pavarino (2004), who developed a parallel bidomain solver based on the PETSC library (http://www. mcs.anl.gov/petsc; Balay et al 2007).…”

Section: Parallel Solversmentioning

confidence: 99%

Numerical solution of the bidomain equations

Linge

Sundnes

Hanslien

et al. 2009

Phil. Trans. R. Soc. A.

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Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra-and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.

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Section: Parallel Solversmentioning

confidence: 99%

Numerical solution of the bidomain equations

Linge

Sundnes

Hanslien

et al. 2009

Phil. Trans. R. Soc. A.

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“…Early examples are Vigmond et al (2003) and Colli-Franzone and Pavarino (2004). A similar PETSc-based approach is used in dos Santos et al (2004) combined with parallel geometric multi-grid preconditioning.…”

Section: Introductionmentioning

confidence: 99%

Chaste

Bernabéu

Southern

Wilson

et al. 2013

The International Journal of High Performance Computing Applica

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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.

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“…For more details the reader is referred to Sundnes et al (2005), Lines, Buist, Grottum, Pullan, Sundnes & Tveito (2003); , and Weber Dos Santos et al (2003)). To reduce the computational time at each time step, parallel computing techniques are used (see Colli Franzone & Pavarino (2004), Karpoukhin et al (1995) and Weber dos Santos et al (2004)). Several timestepping strategies have also been used, fully implicit ( Bourgault et al (2003), and Murillo & Cai (2004)), and semi-implicit , Ethier & Bourgault (2008)) Recently, mesh adaptation methods have been introduced to reduce the size of the spatial mesh as well as the computational time.…”

Section: Introductionmentioning

confidence: 99%

Recent Numerical Methods in Electrocardiology

Belhamadia¹

2010

New Developments in Biomedical Engineering

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A Parallel Solver for Reaction–diffusion Systems in Computational Electrocardiology

Cited by 156 publications

References 47 publications

Numerical solution of the bidomain equations

Numerical solution of the bidomain equations

Chaste

Recent Numerical Methods in Electrocardiology

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