GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations  

作　　者：Rajesh Gandham David Medina Timothy Warburton 

机构地区：[1]Department of Computational and Applied Mathematics,Rice University,6100 Main Street,MS-134,Houston,TX-77005,USA

出　　处：《Communications in Computational Physics》2015年第6期37-64,共28页计算物理通讯（英文）

基　　金：The authors gratefully acknowledge travel grants from Pan-American Advanced Studies Institute,grant from DOE and ANL(ANL Subcontract No.1F-32301 on DOE grant No.DE-AC02-06CH11357);grant from ONR(Award No.N00014-13-1-0873);fellowships from Ken Kennedy Institute of technology at Rice University and support from Shell(Shell Agreement No.PT22584),NVIDIA,and AMD.The authors also acknowledge Dr.Jesse Chan for fruitful discussions during the preparation of this manuscript.

摘　　要：We discuss the development,verification,and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations.The shallow water equations are hyperbolic partial differential equations 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 by local time stepping based on a multi-rate Adams-Bashforth scheme.A total variational bounded limiter is adopted for nonlinear stability of the numerical scheme.This limiter is coupled with a mass and momentum conserving positivity preserving limiter for 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 expressed in OCCA model can be cross-compiled with multi-threading models OpenCL,CUDA,and OpenMP.We compare the performance of the OCCA kernels when cross-compiled with these models.

关 键 词：Shallow water equations discontinuous Galerkin positivity preserving slope limiting GPUS ACCELERATORS MULTI-THREADING 

分 类 号：O17[理学—数学]