کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
522096 | 867811 | 2011 | 17 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere](/preview/png/522096.png)
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.
Journal: Journal of Computational Physics - Volume 230, Issue 7, 1 April 2011, Pages 2523–2539