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Subject: Computer Science ; Physics
Title:
parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere
Author: Chao Yang ; Xiao-Chuan Cai
Keyword: Shallow water equations ; Fully implicit method ; Newton&ndash ; Krylov&ndash ; Schwarz ; Multilevel domain decomposition method ; Cubed-sphere mesh ; Parallel processing ; Strong and weak scalability
Source: Journal of Computational Physics
Issued Date: 2011
Volume: 230, Issue:7, Pages:2523 - 2539
Indexed Type: SCIENCEDIRECT
Department: aDepartment of Computer Science University of Colorado at Boulder Boulder CO 80309 USA; bInstitute of Software ChineseAcademy of Sciences Beijing 100190 PR China
Sponsorship: NSFDMS-0913089; DOEDE-FC-02-06ER25784; NSF China10801125; 863 Program of China2010AA012300
Abstract: 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.
English Abstract: 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.
Language: 英语
WOS ID: WOS:000288415200010
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16022
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Chao Yang,Xiao-Chuan Cai. parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere[J]. Journal of Computational Physics,2011-01-01,230(7):2523 - 2539.
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