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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 | |
| Source | Journal of Computational Physics
 |
| ISSN | 0021-9991 |
| Volume | 230Issue:7Pages:2523 - 2539 |
| 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.; 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. |
| Indexed Type | SCIENCEDIRECT |
| 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 |
| Department | aDepartment of Computer Science University of Colorado at Boulder Boulder CO 80309 USA; bInstitute of Software ChineseAcademy of Sciences Beijing 100190 PR China |
| Subject | Computer Science ; Physics |
| Sponsorship | NSFDMS-0913089; DOEDE-FC-02-06ER25784; NSF China10801125; 863 Program of China2010AA012300 |
| Language | 英语 |
| WOS ID | WOS:000288415200010 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16022 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation 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. |
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