the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
CUDA-C implementation of the ADER-DG method for linear hyperbolic PDEs
C. E. Castro
J. Behrens
C. Pelties
Abstract. 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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C. E. Castro et al.


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RC C1230: 'Very sketchy description of the implementation and little scientific significance', Anonymous Referee #1, 12 Aug 2013
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AC C1612: 'Authors answer to review RC C1230', Cristobal Castro, 06 Oct 2013
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AC C1612: 'Authors answer to review RC C1230', Cristobal Castro, 06 Oct 2013
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RC C1373: 'Interesting study of the convergence behaviour on GPU of a CUDA unstructured mesh DG high order solver but it loses significance without a clear description of implementation and without a suitable performance study', Anonymous Referee #2, 01 Sep 2013
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AC C1619: 'Authors answer to review RC C1373', Cristobal Castro, 06 Oct 2013
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AC C1619: 'Authors answer to review RC C1373', Cristobal Castro, 06 Oct 2013
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AC C1592: 'General author comments, pseudo-code and cuda kernels', Cristobal Castro, 06 Oct 2013


-
RC C1230: 'Very sketchy description of the implementation and little scientific significance', Anonymous Referee #1, 12 Aug 2013
-
AC C1612: 'Authors answer to review RC C1230', Cristobal Castro, 06 Oct 2013
-
AC C1612: 'Authors answer to review RC C1230', Cristobal Castro, 06 Oct 2013
-
RC C1373: 'Interesting study of the convergence behaviour on GPU of a CUDA unstructured mesh DG high order solver but it loses significance without a clear description of implementation and without a suitable performance study', Anonymous Referee #2, 01 Sep 2013
-
AC C1619: 'Authors answer to review RC C1373', Cristobal Castro, 06 Oct 2013
-
AC C1619: 'Authors answer to review RC C1373', Cristobal Castro, 06 Oct 2013
-
AC C1592: 'General author comments, pseudo-code and cuda kernels', Cristobal Castro, 06 Oct 2013
C. E. Castro et al.
C. E. Castro et al.
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