GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations (Communications in Computational Physics, 2018)
We discuss the development, verification, and performance of a GPU accelerateddiscontinuous Galerkin method for the solutions of two dimensional nonlinearshallow water equations. The shallow water equations are hyperbolic partial differentialequations and are widely used in the simulation of tsunami wave propagations.Our algorithms are tailored to take advantage of the single instruction multiple data(SIMD) architecture of graphic processing units. The time integration is accelerated bylocal time stepping based on a multi-rate Adams-Bashforth scheme. A total variationalbounded limiter is adopted for nonlinear stability of the numerical scheme. This limiteris coupled with a mass and momentum conserving positivity preserving limiterfor the special treatment of a dry or partially wet element in the triangulation. Accuracy,robustness and performance are demonstrated with the aid of test cases. Furthermore,we developed a unified multi-threading model OCCA. The kernels expressedin OCCA model can be cross-compiled with multi-threading models OpenCL, CUDA,and OpenMP. We compare the performance of the OCCA kernels when cross-compiledwith these models.