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Discontinuous Galerkin Methods on Graphics Processing Units for Nonlinear Hyperbolic Conservation Laws

Martin Fuhry, Lilia Krivodonova
Department of Applied Mathematics, University of Waterloo
University of Waterloo, 2013

@article{fuhry2013discontinuous,

   title={Discontinuous Galerkin Methods on Graphics Processing Units for Nonlinear Hyperbolic Conservation Laws},

   author={Fuhry, Martin and Krivodonova, Lilia},

   year={2013}

}

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We present an implementation of the discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA’s Compute Unified Device Architecture (CUDA). Both flexible and highly accurate, DG methods accommodate parallel architectures well, as their discontinuous nature produces entirely element-local approximations. High performance scientific computing suits GPUs well, as these powerful, massively parallel, cost-effective devices have recently included support for double-precision floating point numbers. Computed examples for Euler equations over unstructured triangle meshes demonstrate the effectiveness of our implementation. Benchmarking our method against a serial implementation reveals a speedup factor of over 50 times using double-precision with an NVIDIA GTX 580.
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