Scalable and Robust Dual-Primal Newton–Krylov Deluxe Solvers for Cardiac Electrophysiology with Biophysical Ionic Models
Articolo
Data di Pubblicazione:
2022
Citazione:
Scalable and Robust Dual-Primal Newton–Krylov Deluxe Solvers for Cardiac Electrophysiology with Biophysical Ionic Models / N.M.M. Huynh, L.F. Pavarino, S. Scacchi. - In: VIETNAM JOURNAL OF MATHEMATICS. - ISSN 2305-221X. - 50:4(2022), pp. 1029-1052. [10.1007/s10013-022-00576-1]
Abstract:
The focus of this work is to provide an extensive numerical study of the parallel efficiency and robustness of a staggered dual-primal Newton–Krylov deluxe solver for implicit time discretizations of the Bidomain model. This model describes the propagation of the electrical impulse in the cardiac tissue, by means of a system of parabolic reaction-diffusion partial differential equations. This system is coupled to a system of ordinary differential equations, modeling the ionic currents dynamics. A staggered approach is employed for the solution of a fully implicit time discretization of the problem, where the two systems are solved successively. The arising nonlinear algebraic system is solved with a Newton–Krylov approach, preconditioned by a dual-primal Domain Decomposition algorithm in order to improve convergence. The theoretical analysis and numerical validation of this strategy has been carried out in Huynh et al. (SIAM J. Sci. Comput. 44, B224–B249, 2022) considering only simple ionic models. This paper extends this study to include more complex biophysical ionic models, as well as the presence of ischemic regions, described mathematically by heterogeneous diffusion coefficients with possible discontinuities between subregions. The results of several numerical experiments show robustness and scalability of the proposed parallel solver.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Bidomain system; Deluxe scaling; Domain decomposition; FETI-DP and BDDC preconditioners; Implicit time discretizations
Elenco autori:
N.M.M. Huynh, L.F. Pavarino, S. Scacchi
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