Accelerating the red/black SOR method using GPUs with CUDA

Abstract

This work presents our strategy, applied optimizations and results in our effort to exploit the computational capabilities of GPUs under the CUDA environment in solving the Laplacian PDE. The parallelizable red/black SOR method was used. Additionally, a program for the CPU, featuring OpenMP, was developed as a performance reference. Significant performance improvements were achieved by using optimization methods which proved to have substantial speedup in performance. Eventually, a direct comparison of performance of both versions was realised. A 51x speedup was measured for the CUDA version over the CPU version, exceeding 134GB/sec bandwidth. Memory access patterns prove to be a critical factor in efficient program execution on GPUs and it is, therefore, appropriate to follow data reorganization in order to achieve the highest feasible memory throughput. © 2012 Springer-Verlag.