Fourth-order compact schemes with adaptive time step for monodomain reaction-diffusion equations
Journal of Computational and Applied Mathematics
Algebraic multigrid preconditioners for the bidomain reaction--diffusion system
Applied Numerical Mathematics
A finite volume scheme for cardiac propagation in media with isotropic conductivities
Mathematics and Computers in Simulation
Computational Optimization and Applications
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
Efficient simulation of cardiac electrical propagation using high order finite elements
Journal of Computational Physics
An adaptive mesh algorithm for the numerical solution of electrical models of the heart
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
A parallel accelerated adaptive mesh algorithm for the solution of electrical models of the heart
International Journal of High Performance Systems Architecture
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The paper introduces and studies numerical methods that are fully adaptive in both three-dimensional (3D) space and time to challenging multiscale cardiac reaction-diffusion models. In these methods, temporal adaptivity comes via stepsize control in function space oriented linearly implicit time integration, while spatial adaptivity is realized within multilevel finite element methods controlled by a posteriori local error estimators. In contrast to other recent adaptivity approaches to cardiac modeling that discretize first in space and then in time (so-called method of lines), our method discretizes first in time and then in space (so-called Rothe method)---an approach that has already proven to be highly efficient in a number of challenging multiscale problems in science and technology (KARDOS code library). With this method, the evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated both in the frame of the anisotropic monodomain models and in the more realistic anisotropic bidomain models, coupled with either a variant of the simple FitzHugh--Nagumo model or the more complex phase-I Luo--Rudy ionic model. The numerical results exhibit a rather satisfactory performance of our adaptive method for complex cardiac reaction-diffusion models on 3D domains up to moderate sizes. In particular, the method accurately resolves the evolution of the intra- and extracellular potentials, gating variables, and ion concentrations during the excitation, plateau, and recovery phases.