Iterative Algorithms for Solution of Large Sparse Systems of Linear Equations on Hypercubes

Authors:
C. Aykanat;F. Özgüner;F. Ercal;P. Sadayappan
Affiliations:
Ohio State Univ., Columbus, and Bilkent Univ., Ankara, Turkey;Ohio State Univ., Columbus, OH;Ohio State Univ., Columbus, and Bilkent Univ., Ankara, Turkey;Ohio State Univ., Columbus, OH
Venue:
IEEE Transactions on Computers
Year:
1988

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Abstract

Finite-element discretization produces linear equations in the form Ax=b, where A is large, sparse, and banded with proper ordering of the variables x. The solution of such equations on distributed-memory message-passing multiprocessors implementing the hypercube topology is addressed. Iterative algorithms based on the conjugate gradient method are developed for hypercubes designed for coarse-grained parallelism. The communication requirements of different schemes for mapping finite-element meshes onto the processors of a hypercube are analyzed with respect to the effect of communication parameters of the architecture. Experimental results for a 16-node Intel 80386-based iPSC/2 hypercube are presented and discussed.