论文标题
强大的平行非线性求解器，用于双域方程的隐式时间离散
Robust parallel nonlinear solvers for implicit time discretizations of the Bidomain equations
论文作者
论文摘要
在这项工作中，我们研究了非线性求解器在将心脏系统的普通和部分微分方程解耦后，非线性求解器的收敛性和性能。首先，我们通过分析在物理合理合理的假设下，通过分析一个辅助变量问题来分析，我们提供了严格证明准牛顿方法的全局融合，例如BFGS和非线性共轭分子方法。其次，我们在执行时间，相对于数据和并行可伸缩性方面比较了几个非线性双域求解器。我们的发现表明，准牛顿的方法是非线性双域系统的最佳选择，因为与标准的牛顿 - 克里洛夫方法相比，它们表现出更快的收敛速率，同时保持稳健性和可伸缩性。此外，一阶方法还表现出竞争力并作为可行的替代方案，尤其是适用于适合GPU计算的无基质实现。
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.
