Toward Efficient Implementations of PCCG (Preconditioned Conjugate Gradient) Methods on Vector Supercomputers

摘要

The authors considers large, sparse linear systems which result from the discretization of partial differential equations on regular and irregular domains, and he focuses on the application of the preconditioned conjugate gradient (PCCG) method to the solution of such systems. More specifically, the goal of this paper is the efficient implementation of the PCCG method on vector supercomputers. The contribution to the above goal is made by 1) the introduction of a data structure which way be effectively manipulated on vector machines, 2) the utilization of preconditioning matrices which are obtained by incomplete factorization with diagonal update sets, and 3) the introduction of new numbering schemes for both regular and irregular grids. (Author)