Parallel iteration space alternate tiling Gauss-Seidel solver

Many important scientific kernels compute solutions using finite difference techniques, and the most time consuming part of them is the iterative method, such as Gauss-Seidel or SOR. To improve performance, iterative method can exploit parallelism, intra-iteration data reuse, and inter-iteration data reuse. This paper describes a new parallel Gauss-Seidel method using iteration space alternate tiling technique, which is developed not only to improve parallelism, intra-iteration, and inter-iteration data locality, but also to decrease communication and synchronization cost in iterative method. Time-skewing can increase cache locality by exploiting locality in the time direction as well as spatial locality. The degree of parallelism can be improved by reordering the execution of cache blocks. Finally numerical results are presented which confirm the effectiveness of Gauss-Seidel parallelized with iteration space alternate tiling technique, specifically compared with owner-computes and red-black coloring based Gauss-Seidel methods, and show that the new method has a good parallel performance on distributed memory machines, as well as scalability.