A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
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DOI：
10.1137/080727348
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
Chao Yang;Jianwen Cao;Xiaobin Cai
中科院分区：
文献类型：
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作者：
Chao Yang;Jianwen Cao;Xiaobin Cai
求解浅水方程（SWE）的气候模拟的流行方法是显式和半隐式方法，都有一定的时间步长的限制。在本文中，我们提出并研究了一种全隐式方法，它不限制时间步长，但需要在每个时间步长的大型稀疏非线性方程组的解决方案。本文的重点是一个并行的，完全耦合的，牛顿Krylov RAS算法的雅可比矩阵显式计算的弱非匹配立方球网格。在这里，RAS是一个受限制的加性施瓦茨方法。我们数值表明，这样一个预处理，非线性隐式方法的时间步长不再受到CFL条件的约束，我们报告超线性加速的算法上千处理器的机器上的问题，光滑和非光滑的解决方案。
Popular approaches for solving shallow water equations (SWEs) for climate modeling are explicit and semiimplicit methods, and both have certain constraints on the time step size. In this paper, we propose and study a fully implicit method which imposes no limit on the time step size but requires the solution of a large sparse nonlinear system of equations at every time step. The focus of the paper is a parallel, fully coupled, Newton-Krylov-RAS algorithm with a Jacobian matrix explicitly calculated on a weakly nonmatching cubed-sphere mesh. Here, RAS is a restricted additive Schwarz method. We show numerically that with such a preconditioned, nonlinearly implicit method the time step size is no longer constrained by the CFL condition, and we report superlinear speedup of the algorithm on machines with thousands of processors for problems with smooth and nonsmooth solutions.