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

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

New computational methods in tsunami science

“…It turns out that some numerical methods can benefit greatly from porting them to GPGPUs, while others are limited by their memory access and computation patterns. One approach using a high-order ADER (arbitrary high-order derivative) discontinuous Galerkin method for accurate tsunami wave simulation is described in [73]. This code benefits moderately from the GPGPU architecture with a maximum speed-up of approx.…”