Parallel compact multi-dimensional numerical algorithm with application to aeroacoustics

In this study we propose an efficient method to parallelize high-order compact numerical algorithms for the solution of three-dimensional PDEs in a spacetime domain. The proposed parallelization method includes 3-D partitioning and the solution of sets of linear banded systems that split onto processors. Efficient. parallelization of the Thomas algorithm is difficult due to its pipelined nature. We use processors for either non-local data independent computations, solving lines in the next spatial direction, or local datadependent computations by the Runge-Kutta method while processors are idle due to the forward and backward recurrences of the Thomas algorithm. Control of processor communication and computations by a static schedule is adopted in this study. The obtained parallelization speed-up of the novel algorithm is about twice as much as that for the standard pipelined algorithm and close to that for the explicit algorithm.