Volume 29, Issue 1
Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Xucheng Meng, Thi-Thao-Phuong Hoang, Zhu WangLili Ju

Commun. Comput. Phys., 29 (2021), pp. 80-110.

Published online: 2020-11

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  • Abstract

In this paper, we investigate the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing 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 stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By 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 products. Several standard test cases for shallow water equations of one or multiple layers are considered. The 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.

  • Keywords

Exponential time differencing, domain decomposition, rotating shallow water equations, finite volume discretization.

  • AMS Subject Headings

65F60, 65L06, 65M55, 35L60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-80, author = {Meng , Xucheng and Hoang , Thi-Thao-Phuong and Wang , Zhu and Ju , Lili}, title = {Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {1}, pages = {80--110}, abstract = {

In this paper, we investigate the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing 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 stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By 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 products. Several standard test cases for shallow water equations of one or multiple layers are considered. The 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0214}, url = {http://global-sci.org/intro/article_detail/cicp/18423.html} }
TY - JOUR T1 - Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study AU - Meng , Xucheng AU - Hoang , Thi-Thao-Phuong AU - Wang , Zhu AU - Ju , Lili JO - Communications in Computational Physics VL - 1 SP - 80 EP - 110 PY - 2020 DA - 2020/11 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2019-0214 UR - https://global-sci.org/intro/article_detail/cicp/18423.html KW - Exponential time differencing, domain decomposition, rotating shallow water equations, finite volume discretization. AB -

In this paper, we investigate the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing 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 stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By 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 products. Several standard test cases for shallow water equations of one or multiple layers are considered. The 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.

Xucheng Meng, Thi-Thao-Phuong Hoang, Zhu Wang & Lili Ju. (2020). Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study. Communications in Computational Physics. 29 (1). 80-110. doi:10.4208/cicp.OA-2019-0214
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