Volume 18, Issue 1
GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations

Rajesh Gandham, David Medina & Timothy Warburton

Commun. Comput. Phys., 18 (2015), pp. 37-64.

Published online: 2018-04

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  • Abstract

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.

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@Article{CiCP-18-37, author = {}, title = {GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {1}, pages = {37--64}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.070114.271114a}, url = {http://global-sci.org/intro/article_detail/cicp/11017.html} }
TY - JOUR T1 - GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations JO - Communications in Computational Physics VL - 1 SP - 37 EP - 64 PY - 2018 DA - 2018/04 SN - 18 DO - http://dor.org/10.4208/cicp.070114.271114a UR - https://global-sci.org/intro/article_detail/cicp/11017.html KW - AB -

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.

Rajesh Gandham, David Medina & Timothy Warburton. (2020). GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations. Communications in Computational Physics. 18 (1). 37-64. doi:10.4208/cicp.070114.271114a
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