GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Iterative solution methods
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Efficient algebraic solution of reaction-diffusion systems for the cardiac excitation process
Journal of Computational and Applied Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
The Mortar Finite Element Method for the Cardiac “Bidomain” Model of Extracellular Potential
Journal of Scientific Computing
Operator splitting and adaptive mesh refinement for the Luo-Rudy I model
Journal of Computational Physics
Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology
SIAM Journal on Scientific Computing
Substructuring Preconditioners for Mortar Discretization of a Degenerate Evolution Problem
Journal of Scientific Computing
Multilevel Additive Schwarz Preconditioners for the Bidomain Reaction-Diffusion System
SIAM Journal on Scientific Computing
A model-based block-triangular preconditioner for the Bidomain system in electrocardiology
Journal of Computational Physics
Algebraic multigrid preconditioners for the bidomain reaction--diffusion system
Applied Numerical Mathematics
A Scalable Newton-Krylov-Schwarz Method for the Bidomain Reaction-Diffusion System
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
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The electrical activity of the heart may be modeled by a nonlinear system of partial differential equations known as the bidomain model. Due to the rapid variations in the electrical field, accurate simulations require a fine-scale discretization of the equations and consequently the solution of large severely ill-conditioned linear systems at each time step. Solving these systems is a major bottleneck of the whole simulation. We propose a highly effective preconditioning strategy for a general and popular three-dimensional formulation of the problem. A theoretical analysis of the preconditioned matrix ensuring mesh independence of the spectrum is also described. Numerical comparisons with state-of-the-art approaches confirm the effectiveness of our preconditioning technique. Finally, we show that an equivalent but less exercised formulation provides the best performance, in terms of CPU time.