Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study (Communications in Computational Physics, 2020)
In this paper, we investigate the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparingwith explicit time stepping of the same order accuracy in time, the ETD algorithmscould reduce the computational time in many cases by allowing the use of large timestep 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 subdomainproblems of smaller sizes and solving them locally, the proposed approach could speedup the calculation of matrix exponential vector products. Several standard test casesfor shallow water equations of one or multiple layers are considered. The results showgreat potential of the localized ETD method for high-performance computing becauseeach subdomain problem can be naturally solved in parallel at every time step.