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 hyperbo...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.展开更多
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.
文摘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.
