| 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. |
