Robust parallel nonlinear solvers for implicit time discretizations of the Bidomain equations

In this work, we study the convergence and performance of nonlinear solvers for the Bidomain equations after decoupling the ordinary and partial differential equations of the cardiac system. Firstly, we provide a rigorous proof of the global convergence of Quasi-Newton methods, such as BFGS, and non...

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Bibliographic Details
Published inarXiv.org
Main Authors Barnafi, Nicolás A, Ngoc Mai Monica Huynh, Pavarino, Luca F, Scacchi, Simone
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.12.2023
Subjects
Convergence
Decoupling
Mathematical analysis
Partial differential equations
Quasi Newton methods
Robustness (mathematics)
Solvers
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Summary:In this work, we study the convergence and performance of nonlinear solvers for the Bidomain equations after decoupling the ordinary and partial differential equations of the cardiac system. Firstly, we provide a rigorous proof of the global convergence of Quasi-Newton methods, such as BFGS, and nonlinear Conjugate-Gradient methods, such as Fletcher--Reeves, for the Bidomain system, by analyzing an auxiliary variational problem under physically reasonable hypotheses. Secondly, we compare several nonlinear Bidomain solvers in terms of execution time, robustness with respect to the data and parallel scalability. Our findings indicate that Quasi-Newton methods are the best choice for nonlinear Bidomain systems, since they exhibit faster convergence rates compared to standard Newton-Krylov methods, while maintaining robustness and scalability. Furthermore, first-order methods also demonstrate competitiveness and serve as a viable alternative, particularly for matrix-free implementations that are well-suited for GPU computing.
ISSN:2331-8422