An efficient asynchronous approach for Gauss-Seidel iterative solver for FDM/FEM equations on multi-core processors

In this paper, we proposed a new parallel iterative asynchronous method for Gauss-Seidel and Successive Over-Relaxation (SOR) for finite difference method (FDM) and finite element method (FEM). The approach attempts to minimize the thread synchronization which incurs a lot of thread idle time due to the dependency of computation. Our proposed method maximizes the thread utilization on multi-core processors with some space requirement for storing current states. We implement our proposed method based on the Poisson's equation with FDM. It is found that our proposed algorithm runs 5.88 times faster than the original Gauss-Seidel and achieve speedup up to 1.25 compared with the parallel Sliding Window version.