Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart.

J Sundnes; G T Lines; K A Mardal; A Tveito

doi:10.1080/1025584021000025023

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Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart.

J Sundnes·G T Lines·K A Mardal·A Tveito

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Abstract

The electrical activity of the heart may be modeled with a system of partial differential equations (PDEs) known as the bidomain model. Computer simulations based on these equations may become a helpful tool to understand the relationship between changes in the electrical field and various heart diseases. Because of the rapid variations in the electrical field, sufficiently accurate simulations require a fine-scale discretization of the equations. For realistic geometries this leads to a large number of grid points and consequently large linear systems to be solved for each time step. In this paper, we present a fully coupled discretization of the bidomain model, leading to a block structured linear system. We take advantage of the block structure to construct an efficient preconditioner for the linear system, by combining multigrid with an operator splitting technique.

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Action Potentials Anatomy, Cross-Sectional Anisotropy Body Surface Potential Mapping Computer Simulation Computing Methodologies Electric Conductivity Electromagnetic Fields Heart Heart Conduction System Humans Linear Models Models, Cardiovascular Muscle Cells Quality Control Thorax Evaluation Study Journal Article Research Support, Non-U.S. Gov't

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J Sundnes, G T Lines, K A Mardal, A Tveito. 2002. Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart.. https://doi.org/10.1080/1025584021000025023

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