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Towards a complete FEM-based simulation toolkit on GPUs: Geometric Multigrid solvers

Markus Geveler, Dirk Ribbrock, Dominik Goddeke, Peter Zajac, Stefan Turek
Institute of Applied Mathematics, TU Dortmund University, Germany
23rd International Conference on Parallel Computational Fluid Dynamics (ParCFD 2011), 2011

@inproceedings{Geveler:2011:TAC,

   author={Markus Geveler and Dirk Ribbrock and Dominik G{"o}ddeke and Peter Zajac and Stefan Turek},

   title={Towards a complete FEM-based simulation toolkit on GPUs: Geometric Multigrid solvers},

   booktitle={23rd International Conference on Parallel Computational Fluid Dynamics (ParCFD’11)},

   year={2011},

   month={may}

}

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We describe a GPU- and multicore-oriented implementation technique for a key component of finite element based simulation toolkits for partial differential equations on unstructured grids: Geometric Multigrid solvers. We use efficient sparse matrix-vector multiplications throughout the solver pipeline: within the coarse-grid solver, smoothers and even grid transfers. Our implementation can handle several low- and high-order finite element spaces in 2D and 3D, and for representative benchmark problems, we achieve close to an order of magnitude speedup on a single GPU over a multithreaded CPU code. In addition we present preliminary results for experiments with strong smoothers for unstructured problems on the GPU, aiming at augmenting numerical and computational efficiency simultaneously.
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