Vectorization of Riemann solvers for the single- and multi-layer Shallow Water Equations

Abstract

We discuss vectorization of normal and transverse Riemann solvers for the single- and multi-layer shallow water equations. Our approach is simple and portable, as it is based on auto-vectorization by the compiler, aided by OpenMP 4.0 directives. Despite the high complexity of the solver routines, the Intel Fortran Compiler proved itself able to successfully vectorize loops containing calls to these solvers, after only a few small changes in their code. We evaluate the performance of the vectorized Riemann solvers within the context of GeoClaw, a software designed for simulation of geophysical flows with finite volume methods. Our performance studies consider two platforms with different sets of SIMD instructions: a dual-socket Haswell system with the AVX2 instruction set (256-bit) and an Intel Xeon Phi (Knights Landing) with AVX-512 instructions (512-bit). The experimental results indicate performance im¬provements of up to 2.1x on the former platform and up to 6.5x on the latter (with double-precision arithmetic). We also show that these speedups can easily compensate for the overhead introduced by the rearrangement of the simulation data structures, which might be necessary to achieve efficient vectorization.