The performance model for a parallel SOR algorithm using the red-black scheme

The successive over relaxation (SOR) is a variant of the iterative Gauss-Seidel method for solving a linear system of equations Ax = b. The SOR algorithm is used within the Nucleus for European Modelling of the Ocean (NEMO) model for solving the elliptical equation for the barotropic stream function. The NEMO performance analysis shows that the SOR algorithm introduces a significant communication overhead. Its parallel implementation is based on the red-black method and foresees a communication step at each iteration. An enhanced parallel version of the algorithm has been developed by acting on the size of the overlap region to reduce the frequency of communications. The overlap size must be carefully tuned for reducing the communication overhead without increasing the computing time. This work describes an analytical performance model of the SOR algorithm that can be used for establishing the optimal size of the overlap region.