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CUDA-C implementation of the ADER-DG method for linear hyperbolic PDEs

C. E. Castro, J. Behrens, C. Pelties
Instituto de Alta Investigacion, Universidad de Tarapaca, Casilla 7D Arica, Chile
Geoscientific Model Development Discuss., 6, 3743-3786, 2013

@article{gmdd-6-3743-2013,

   author={Castro, C. E. and Behrens, J. and Pelties, C.},

   title={CUDA-C implementation of the ADER-DG method for linear hyperbolic PDEs},

   journal={Geoscientific Model Development Discussions},

   volume={6},

   year={2013},

   number={3},

   pages={3743–3786},

   url={http://www.geosci-model-dev-discuss.net/6/3743/2013/},

   doi={10.5194/gmdd-6-3743-2013}

}

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We implement the ADER-DG numerical method using the CUDA-C language to run the code in a Graphic Processing Unit (GPU). We focus on solving linear hyperbolic partial differential equations where the method can be expressed as a combination of precomputed matrix multiplications becoming a good candidate to be used on the GPU hardware. Moreover, the method is arbitrarily high-order involving intensive work on local data, a property that is also beneficial for the target hardware. We compare our GPU implementation against CPU versions of the same method observing similar convergence properties up to a threshold where the error remains fixed. This behaviour is in agreement with the CPU version but the threshold is larger that in the CPU case. We also observe a big difference when considering single and double precision where in the first case the threshold error is significantly larger. Finally, we did observe a speed up factor in computational time but this is relative to the specific test or benchmark problem.
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