Overlapped Multicolor MILU Preconditioning

MILU preconditioned iterative methods are useful for solving large sparse linear systems, which arise from the finite difference approximations of three-dimensional second-order elliptic partial differential equations. In these schemes, the MILU preconditioning which accelerates the convergence is the most difficult part to vectorize on vector supercomputers. Currently, the reordering techniques like the multicolor ordering strategy are commonly used to obtain sufficiently long vector lengths. However, these reordering techniques deteriorate the convergence compared with the standard MILU preconditioner, and Gustafsson’s acceleration does not work well for them. In this paper, a new preconditioning is proposed and its advantages compared with the multicolor and hyperplane orderings are shown through experiments on NEC vector supercomputer SX-3.