Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart.
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.
Sundnes
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Simula Research Laboratory, Lysaker, Norway.
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D000200:Action Potentials / Q000502:physiology*; D019412:Anatomy, Cross-Sectional; D016880:Anisotropy; D018780:Body Surface Potential Mapping / Q000379:methods*; D003198:Computer Simulation; D003205:Computing Methodologies; D004553:Electric Conductivity; D004574:Electromagnetic Fields; D006321:Heart / Q000502:physiology*; D006329:Heart Conduction System / Q000502:physiology; D006801:Humans; D016014:Linear Models; D008955:Models, Cardiovascular; D032342:Muscle Cells / Q000502:physiology*; D011786:Quality Control; D013909:Thorax / Q000502:physiology