Scalable and Robust Dual-Primal Newton-Krylov Deluxe Solvers for Cardiac Electrophysiology with Biophysical Ionic Models

被引:2
|
作者
Huynh, Ngoc Mai Monica [1 ]
Pavarino, Luca F. [1 ]
Scacchi, Simone [2 ]
机构
[1] Univ Pavia, Dipartimento Matemat, Via Ferrata 5, I-27100 Pavia, Italy
[2] Univ Milan, Dipartimento Matemat, Via Saldini 50, I-20133 Milan, Italy
基金
欧盟地平线“2020”;
关键词
Domain decomposition; FETI-DP and BDDC preconditioners; Deluxe scaling; Bidomain system; Implicit time discretizations; BIDOMAIN MODEL; SCHWARZ METHOD; FETI-DP; HEART; MULTISCALE; SYSTEMS; BDDC;
D O I
10.1007/s10013-022-00576-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:1029 / 1052
页数:24
相关论文
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    Ngoc Mai Monica Huynh
    Luca F. Pavarino
    Simone Scacchi
    Vietnam Journal of Mathematics, 2022, 50 : 1029 - 1052
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  • [3] PARALLEL NEWTON-KRYLOV BDDC AND FETI-DP DELUXE SOLVERS FOR IMPLICIT TIME DISCRETIZATIONS OF THE CARDIAC BIDOMAIN EQUATIONS
    Huynh, Ngoc Mai Monica
    Pavarino, Luca F.
    Scacchi, Simone
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2022, 44 (02): : B224 - B249