A parallel multi-subdomain strategy for solving Boussinesq water wave equations

Abstract

This paper describes a general parallel multi-subdomain strategy for solving the weakly dispersive and nonlinear Boussinesq water wave equations. The parallelization strategy is derived from the additive Schwarz method based on overlapping subdomains. Besides allowing the subdomains to independently solve their local problems, the strategy is also flexible in the sense that different discretization schemes, or even different mathematical models, are allowed in different subdomains. The parallelization strategy is particularly attractive from an implementational point of view, because it promotes the reuse of existing serial software and opens for the possibility of using different software in different subdomains. We study the strategy’s performance with respect to accuracy, convergence properties of the Schwarz iterations, and scalability through numerical experiments concerning waves in a basin, solitary waves, and waves generated by a moving vessel. We find that the proposed technique is promising for large-scale parallel wave simulations. In particular, we demonstrate that satisfactory accuracy and convergence speed of the Schwarz iterations are obtainable independent of the number of subdomains, provided there is sufficient overlap. Moreover, existing serial wave solvers are readily reusable when implementing the parallelization strategy.