A Parallel Scheduling of Multi-Step Diakoptics for Three Dimensional Finite Differece Method

Kazuhiro MOTEGI  Shigeyoshi WATANABE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.10   pp.1822-1829
Publication Date: 1993/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Numerical Analysis and Self-Validation
parallel scheduling,  parallel direct solution method,  finite difference method,  

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Many simulators in several fields use the finite difference method and they must solve the large sparse linear equations related. Particularly, if we use the direct solution method because of the convergency problem, it is necessary to adopt a method that can reduce the CPU time greatly. The Multi-Step Diakoptics (MSD) method is proposed as a parallel computation method with a direct solution which is based on Diakoptics, that is, a tearing-based parallel computation method for the sparse linear equations. We have applied the MSD algorithm for one, two and three dimensional finite difference methods. We require a parallel schedule that automatically partitions the desired object's region for study, assigns the processor elements to the partitioned regions according to the MSD method, and controls communications among the processor elements. This paper describes a parallel scheduling that was extended from a one dimensional case to a three dimensional case for the MSD method, and the evaluation of the algorithm using a massively parallel computer with distribuled memory(AP1000).