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GPU-accelerated discontinuous Galerkin methods on hybrid meshes

Jesse Chan, Zheng Wang, Axel Modave, Jean-Francois Remacle, T. Warburton
Department of Computational and Applied Mathematics, Rice University, 6100 Main St, Houston, TX, 77005
arXiv:1507.02557 [math.NA], (10 Jul 2015)

@article{chan2015gpuaccelerated,

   title={GPU-accelerated discontinuous Galerkin methods on hybrid meshes},

   author={Chan, Jesse and Wang, Zheng and Modave, Axel and Remacle, Jean-Francois and Warburton, T.},

   year={2015},

   month={jul},

   archivePrefix={"arXiv"},

   primaryClass={math.NA}

}

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We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.
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