OVERLAPPED MULTICOLOR MILU PRECONDITIONING

MILU preconditioned iterative methods are useful for solving large spa rse linear systems, which arise from the finite difference approximati ons of three-dimensional second-order elliptic partial differential eq uations. In these schemes, the MILU preconditioning which accelerates the convergence is the most difficult part to vectorize on vector supe rcomputers. Currently, the reordering techniques like the multicolor o rdering strategy are commonly used to obtain sufficiently long vector lengths. However, these reordering techniques deteriorate the converge nce compared with the standard MILU preconditioner, and Gustafsson's a cceleration does not work well for them. In this paper, a new precondi tioning is proposed and its advantages compared with the multicolor an d hyperplane orderings are shown through experiments on NEC vector sup ercomputer SX-3.