Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study
作者机构：Department of MathematicsUniversity of South CarolinaColumbiaSC 29208USA Department of Mathematics and StatisticsAuburn UniversityAuburnAL 36849USA SUSTech International Center for MathematicsSouthern University of Science and TechnologyShenzhenGuangdong 518055China Center for Mathematical studiesAdvanced Institute of Natural SciencesBeijing Normal University at ZhuhaiZhuhaiGuangdong 519087China
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2021年第29卷第1期
页 面：80-110页
核心收录：
学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学]
基 金：supported by U.S.Department of Energy through the grants DE-SC0016540,DE-SC0020270 U.S.National Science Foundation through the grant DMS-1912626,Office of the Vice President for Research at the University of South Carolina through an ASPIRE grant Natural Science Foundation of China through the grant 11871454
主 题：Exponential time differencing domain decomposition rotating shallow water equa-tions finite volume discretization
摘 要：In this paper,we investigate the performance of the exponential time differencing(ETD)method applied to the rotating shallow water *** with explicit time stepping of the same order accuracy in time,the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical *** accelerate the ETD simulations,we propose a localized approach that synthesizes the ETD method and overlapping domain *** dividing the original problem into many subdomain problems of smaller sizes and solving them locally,the proposed approach could speed up the calculation of matrix exponential vector *** standard test cases for shallow water equations of one or multiple layers are *** results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.
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