Twinned buffering: A simple and highly effective scheme for parallelization of Successive Over-Relaxation on GPUs and other accelerators

In this paper we present a new scheme for parallelization of the Successive Over-Relaxation method for solving the Poisson equation over a 3-D volume. Our new scheme is both simple and effective, outperforming the conventional Red-Black scheme by a factor of 16 on an NVIDIA GeForce GTX 590 GPU, a factor of 11 on an NVIDIA GeForce TITAN Black GPU and a factor of 5 on an Intel Xeon Phi. The speed-up compared to the fully optimised reference implementation running on an Intel Xeon CPU is 16 times on the GTX 590, 22 times on the TITAN and 5 times on the Xeon Phi. We explain the rationale and the implementation in OpenCL and present the performance evaluation results.