Vectorization of an augmented Riemann solver for the shallow water equations

Abstract

We discuss the vectorization of two different Riemann solvers for the shallow water equations. For a wave propagation method that is formulated in terms of f-waves only, the respective implementation is still simple enough such that compiler auto-vectorization is successful. For a substantially more complex augmented Riemann solver, we present a vectorized implementation based on intrinsics functions. The two solvers are tested in SWE, an education-oriented code to solve the shallow water equations, which we use as a “mini application” for performance evaluation in this work. We provide performance studies on two different platforms featuring different vector widths (Intel Sandy Bridge and Intel Xeon Phi). We show that for both the f-Wave solver and the augmented Riemann solver the computation of Riemann problems stays compute-bound, even using the vectorized implementation. However, the speedups are limited by the complicated algorithmic structure of the solver.