Iterative algorithms for solution of large sparse systems of linear equations on hypercubes
Cevdet Aykanat, F. Özgüner, Fikret Erçal, Ponnuswamy Sadayappan · IEEE Transactions on Computers · 1988
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.>