Application of Vector Processors To Solve Finite Difference Equations

Abstract

Abstract As computer technology approaches limitations imposed by the speed of light, increased emphasis is placed on vector processors. These have the ability to increase greatly the speed of arithmetic even without improvements in such basic computer characteristics as memory cycle time. This paper deals with solving systems of finite difference equations on the STAR 100 and the CYBER 203, two Control Data Corp. computers with built-in vector processors. Systems of three-dimensional finite difference equations having from 2,000 to 8,000 unknowns were solved by means of Gaussian elimination and line successive overrelaxation (LSOR). On these machines, the D4 Gaussian elimination technique reduced computer time by factors as large as 4.6 relative to standard Gaussian elimination. Vectorization of the D4 code on the STAR 100 reduced computer times relative to scalar results by factors as large as 26, despite nonoptimal coding. LSOR was vectorized successfully with computer time reduction factors of 35 to 43 on the STAR 100. On the CYBER 203, run times were reduced by factors of 45 to 54, relative to the scalar performance of the STAR 100. On an 8,000-block problem, average processing speed for a complete LSOR solution was approximately 25 million floating operations per second (megaflops).