A fully vectorizable SOR variant

The implementation of a variant of the Successive Overrelaxation (SOR) method for the numerical solution of elliptic partial differential equations is discussed. The convergence of this variant (SORV) is faster than that of SOR for a fixed prescribed error bound, and it is asymptotically as fast as SOR. In addition, SORV is much better suited for vector computers than the classical SOR or SOR with so-called red-black ordering. In the following, we compare SORV with SOR, red-black SOR (SORB1), SORB1 with stride 1 (SORB2) and a one-dimensional long-vector version of SORB2 (SORB3). Implementation is discussed and results are presented for the IBM 3090-200VF and the CRAY-2.