parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere

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	parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere
	Chao Yang; Xiao-Chuan Cai
	2011
发表期刊	Journal of Computational Physics
ISSN	0021-9991
卷号	230 期号:7 页码:2523 - 2539
摘要	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.; 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.
收录类别	SCIENCEDIRECT
关键词	Shallow Water Equations Fully Implicit Method Newton&Ndash Krylov&Ndash Schwarz Multilevel Domain Decomposition Method Cubed-sphere Mesh Parallel Processing Strong And Weak Scalability
部门归属	aDepartment of Computer Science University of Colorado at Boulder Boulder CO 80309 USA; bInstitute of Software ChineseAcademy of Sciences Beijing 100190 PR China
学科领域	Computer Science ; Physics
资助者	NSFDMS-0913089; DOEDE-FC-02-06ER25784; NSF China10801125; 863 Program of China2010AA012300
语种	英语
WOS记录号	WOS:000288415200010
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16022
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	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,2011,230(7):2523 - 2539.
APA	Chao Yang,&Xiao-Chuan Cai.(2011).parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere.Journal of Computational Physics,230(7),2523 - 2539.
MLA	Chao Yang,et al."parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere".Journal of Computational Physics 230.7(2011):2523 - 2539.