Newton-Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model

Huynh Ngoc Mai Monica

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Newton-Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model

机译：Newton-Krylov-BDDC豪华求解器，用于双域模型的非对称全隐式时间离散化

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A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac bidomain model, describing the propagation of the electric impulse in the cardiac tissue. The non-linear system arises from a fully implicit time discretization and a monolithic solution approach. The preconditioned non-symmetric operator is constructed from the linearized system arising within the Newton-Krylov approach for the solution of the non-linear problem; we theoretically analyze and prove a convergence rate bound for the Generalised Minimal Residual iterations' residual. The theory is confirmed by extensive parallel numerical tests, widening the class of robust and efficient solvers for implicit time discretizations of the bidomain model.

机译：在心脏双域模型的求解中，证明了一种基于约束的平衡域分解算法的新理论收敛速率估计，描述了电脉冲在心脏组织中的传播。非线性系统源于完全隐式时间离散化和单片求解方法。根据Newton-Krylov方法中产生的线性化系统构造预处理非对称算子，用于求解非线性问题;我们从理论上分析并证明了广义最小残差迭代残差的收敛率。该理论通过广泛的并行数值测试得到证实，拓宽了双域模型隐式时间离散化的鲁棒高效求解器类别。

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来源
《Numerische Mathematik》 |2022年第4期|841-879|共39页
作者
Huynh Ngoc Mai Monica;
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作者单位

Univ Pavia;

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原文格式 PDF
正文语种英语
中图分类数值分析;
关键词
65N55; 65M55; 65F10; 92C30; BALANCING DOMAIN DECOMPOSITION; ELECTRICAL-ACTIVITY; SCHWARZ METHOD; FETI-DP; PRECONDITIONER; ELECTROPHYSIOLOGY; CONSTRAINTS; MONODOMAIN; ALGORITHM; PATIENT;

机译：65N55;65米55;65F10;92C30;平衡域分解;电活动;施瓦茨方法;FETI-DP;预处理器;电生理学;约束;单域;算法;病人;

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Newton-Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model

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