A model-based block-triangular preconditioner for the Bidomain system in electrocardiology
Journal of Computational Physics
Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction
SIAM Journal on Scientific Computing
Preconditioning the bidomain model with almost linear complexity
Journal of Computational Physics
Fast Structured AMG Preconditioning for the Bidomain Model in Electrocardiology
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Poster: hybrid parallelization of a realistic heart model
Proceedings of the 2011 companion on High Performance Computing Networking, Storage and Analysis Companion
International Journal of High Performance Computing Applications
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Multilevel additive Schwarz methods are analyzed and studied numerically for the anisotropic cardiac Bidomain model in three dimensions. This is the most complete model to date of the bioelectrical activity of the heart tissue, consisting of a degenerate parabolic system of nonlinear reaction-diffusion equations coupled with a stiff system of several ordinary differential equations describing the ionic currents through the cellular membrane. Due to the presence of very different scales in both space and time, the numerical discretization of this system by finite elements in space and semi-implicit methods in time produces very ill-conditioned linear systems that must be solved at each time step. The proposed multilevel algorithm employs a hierarchy of nested meshes with overlapping Schwarz preconditioners on each level and is fully additive, hence parallel, within and among levels. Convergence estimates are proved for the resulting multilevel algorithm, showing that its convergence rate is independent of the number of subdomains (scalability), of the mesh sizes of each level and of the number of levels (optimality). Several parallel tests on a Linux cluster confirm the scalability and optimality of the method, as well as its parallel efficiency on both Cartesian and deformed domains in three dimensions.