On the efficiency of a SOR-like method suited to vector processors
Consider the Poisson equation on the unit square, with the five point discretization. In the rowwise left to right and upwards ordering of the nodes, the successive overrelaxation (SOR) method uses the western and southern updates from the current iteration and the northern and eastern ones from the preceding iteration. The SOR-like method uses the new southern updates and the old ones for the remaining directions. This method has the advantage of being easily vectorizable with constant vector length, in opposition to the hyperplane version of SOR. On the other hand, the convergence rate of SOR is better by an order of magnitude. The authors also discuss the nine point discretization. They finally present a careful set of experiments carried on several powerful supercomputers. These experiments show that vectorized SOR, based on the hyperplane version, is always faster than vectorized SOR-like.
scientific article; zbMATH DE number 4205866