Received: 27 May 2013 – Accepted for review: 31 May 2013 – Discussion started: 13 Jul 2013
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.
How to cite. Castro, C. E., Behrens, J., and Pelties, C.: CUDA-C implementation of the ADER-DG method for linear hyperbolic PDEs, Geosci. Model Dev. Discuss., 6, 3743–3786, https://doi.org/10.5194/gmdd-6-3743-2013, 2013.