GPU accelerated spectral finite elements on all-hex meshes

J.-F. Remacle, R. Gandham, T. Warburton
Department of Computational and Applied Mathematics, Rice University
arXiv:1506.05996 [cs.CE], (19 Jun 2015)


   title={GPU accelerated spectral finite elements on all-hex meshes},

   author={Remacle, J.-F. and Gandham, R. and Warburton, T.},






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This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An additive Schwartz two-scale preconditioner is employed that allows h-independence convergence. An extensible multi-threading programming API is used as a common kernel language that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Performance tests demonstrate that problems with over 50 million degrees of freedom can be solved in a few seconds on an off-the-shelf GPU.
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