Toward Efficient Implementation of Preconditioned Conjugate Gradient Methods On Vector Supercomputers

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Abstract
We consider large, sparse linear systems that result from the discretization of partial differential equations on regular and ir regular domains, and we focus on the ap plication of the preconditioned conjugate gradient (PCCG) method to the solution of such systems. More specifically, our goal is the efficient implementation of the PCCG method on vector supercomputers. The contribution to the above goal is made by the introduction of a data struc ture that can be effectively manipulated on vector machines, the utilization of precon ditioning matrices obtained by incomplete factorization with diagonal update sets, and the introduction of new numbering schemes for both regular and irregular grids.