Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study
- Univ. of South Carolina, Columbia, SC (United States); Southern Univ. of Science and Technology, Guangdong (China); Beijing Normal Univ. at Zhuhai, Guangdong (China)
- Auburn Univ., AL (United States)
- Univ. of South Carolina, Columbia, SC (United States)
Here, we explore 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.
- Research Organization:
- Univ. of South Carolina, Columbia, SC (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Biological and Environmental Research (BER). Earth and Environmental Systems Science Division; National Science Foundation (NSF); ASPIRE; National Science Foundation of China; USDOE Office of Science (SC), Biological and Environmental Research (BER)
- Grant/Contract Number:
- SC0020270; SC0016540; DMS-1912626; 11871454
- OSTI ID:
- 1785012
- Alternate ID(s):
- OSTI ID: 1616019
- Journal Information:
- Communications in Computational Physics, Vol. 29, Issue 1; ISSN 1815-2406
- Publisher:
- Global Science PressCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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