Ma Sang Back

The Transactions of the Korea Information Processing Society (1994 ~ 2000), Vol. 2, No. 4, pp. 535-542, Jul. 1995
10.3745/KIPSTE.1995.2.4.535,   PDF Download:

Abstract

In this paper we present two preconditioners for solving large sparse linear systems arising from elliptic partial differential equations on massively parallel machines, such as the CM-5. Most massively parallel machines do heavily rely on the message-passing for the interprocessor communications, but according to the current manufacturing standards the cost of communications is very high compared to that of floating point arithmetic computations. Due to this we need an algorithm which minimizes the amount of interprocessor communication on the massively parallel machines. We will show that Block SOR(SuccessiveOverRelaxation) method coupled with the multi-coloring technique is one of such preconditioner on the massively parallel machines, by conducting experiments on the CM-5. Also, we implemented the ADI(AlternatingDirectionImplicit) method on the CM-5, which has been conventionally one of the most powerful parallel preconditioner. Our experiment shows that Block SOR method coupled with the multi-coloring technique could yield a speedup with 50% efficiency with the range of number of processors from 16 to 512 for a matrix with dimension 512x512. On the other hand, the ADI method shows a very poor performance.

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