A preconditioning technique for the efficient solution of problems with local grid refinement
Computer Methods in Applied Mechanics and Engineering
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Domain decomposition methods for problems with partial refinement
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Adaptive mesh refinement for wave propagation in nonlinear solids
SIAM Journal on Scientific Computing
Efficient simulation of complex patterns in reaction-diffusion systems
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
Adaptive mesh refinement and multilevel iteration for flow in porous media
Journal of Computational Physics
A computational study of wave propagation in a model for anisotropic cardiac ventricular tissue
HPCN Europe '95 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
A modular simulation system for the bidomain equations
A modular simulation system for the bidomain equations
Numerical Methods
Fourth-order compact schemes with adaptive time step for monodomain reaction-diffusion equations
Journal of Computational and Applied Mathematics
Pseudospectral method of solution of the Fitzhugh-Nagumo equation
Mathematics and Computers in Simulation
Algebraic multigrid preconditioners for the bidomain reaction--diffusion system
Applied Numerical Mathematics
Compact integration factor methods for complex domains and adaptive mesh refinement
Journal of Computational Physics
Fast Structured AMG Preconditioning for the Bidomain Model in Electrocardiology
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
We apply second-order operator splitting to the Luo-Rudy I model for electrical wave propagation in the heart. The purpose of the operator splitting is to separate the nonlinear but local reaction computations from the linear but globally coupled diffusion computations. This approach allows us to use local nonlinear iterations for the stiff nonlinear reactions and to solve global linear systems for the implicit treatment of diffusion. For computational efficiency, we use dynamically adaptive mesh refinement (AMR), involving hierarchies of unions of grid patches on distinct levels of refinement. The linear system for the discretization of the diffusion on the composite AMR grid is formulated via standard conforming finite elements on unions grid patches within a level of refinement and aligned mortar elements along interfaces between levels of refinement. The linear systems are solved iteratively by preconditioned conjugate gradients. Our preconditioner uses multiplicative domain decomposition between levels of refinement; the smoother involves algebraic additive domain decomposition between patches within a level of refinement, and Gauss-Seidel iteration within grid patches. Numerical results are presented in 1D and 2D, including spiral waves.