Vectorizable algorithm for the (multicolour) successive overrelaxation method

✍ Scribed by Jacek Kobus

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 664 KB
• Volume: 78
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(94)90003-5

✦ Synopsis

Simple and well vectorizable algorithms are presented for a solution of a large and sparse system of linear equations by means of the successive overrelaxation method (SOR) and by its multicolour variant (MCSOR). The system of equations results from the general two-dimensional second-order partial differential equation discretized with the second-, fourth-, sixth-and eighth-order central difference cross-like stencils. The corresponding SOR and MCSOR algorithms are tested on the Poisson equation. On a scalar computer the performance of the SOR and MCSOR schemes is identical. On a vector machine, however, the MCSOR algorithms lend themselves well to vectorization and on a Convex 210 computer they run at the rate of 16 mflops (about 5 times as fast as the corresponding SOR schemes). The superiority of the higher-order (MC)SOR methods is demonstrated and their usage advocated: the higher the order of discretization, the shorter the time needed to converge to the solution of desired accuracy. Speedups of the order of 100 can be achieved.