期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 7, 页码 2523-2539出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.12.027
关键词
Shallow water equations; Fully implicit method; Newton-Krylov-Schwarz; Multilevel domain decomposition method; Cubed-sphere mesh; Parallel processing; Strong and weak scalability
资金
- NSF [DMS-0913089]
- DOE [DE-FC-02-06ER25784]
- NSF China [10801125]
- 863 Program of China [2010AA012300]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0913089] Funding Source: National Science Foundation
- Division Of Earth Sciences
- Directorate For Geosciences [0934647] Funding Source: National Science Foundation
High resolution and scalable parallel algorithms for the shallow water equations on the sphere are very important for modeling the global climate. In this paper, we introduce and study some highly scalable multilevel domain decomposition methods for the fully implicit solution of the nonlinear shallow water equations discretized with a second-order well-balanced finite volume method on the cubed-sphere. With the fully implicit approach, the time step size is no longer limited by the stability condition, and with the multilevel preconditioners, good scalabilities are obtained on computers with a large number of processors. The investigation focuses on the use of semismooth inexact Newton method for the case with nonsmooth topography and the use of two- and three-level overlapping Schwarz methods with different order of discretizations for the preconditioning of the Jacobian systems. We test the proposed algorithm for several benchmark cases and show numerically that this approach converges well with smooth and nonsmooth bottom topography, and scales perfectly in terms of the strong scalability and reasonably well in terms of the weak scalability on machines with thousands and tens of thousands of processors. (C) 2010 Elsevier Inc. All rights reserved.
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