Localized Exponential Time DifferencingMethod for Shallow Water Equations: Algorithms and Numerical Study
Localized Exponential Time DifferencingMethod for Shallow Water Equations: Algorithms and Numerical Study
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DOI：
10.4208/cicp.oa-2019-0214
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发表时间：
2021-06
影响因子：
3.7
通讯作者：
X. Meng
中科院分区：
文献类型：
--
作者：
X. Meng
本文研究了指数时间差分（ETD）方法在旋转浅水波方程中的应用。与时间精度相同的显式时间步长相比，ETD算法在许多情况下可以通过允许使用大的时间步长来减少计算时间，同时仍然保持数值稳定性。为了加速ETD模拟，我们提出了一个本地化的方法，综合ETD方法和重叠区域分解。该方法将原问题分解为多个较小的子域问题进行局部求解，加快了矩阵指数向量积的计算速度。考虑了单层或多层浅水方程的几种标准测试情况。结果表明，本地化的ETD方法的高性能计算的巨大潜力，因为每个子域的问题可以自然地并行解决在每个时间步。AMS科目分类：65F60、65L06、65M55、35L60
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. AMS subject classifications: 65F60, 65L06, 65M55, 35L60