ON PARALLELISM AND CONVERGENCE OF INCOMPLETE LU FACTORIZATIONS

This paper discusses the effects of ordering on the speed of convergence to solutions for ILU preconditioned CGS methods. Two parallel ordering strategies are introduced and defined. They are referred to as parallel block (PB(m)) and parallel diagonal (PD(m)) orderings, where m is a parameter related to the degree of parallelism. These two types of ordering are so defined that, depending on the value of m, PB(m) ordering will include row and four-color orderings, while PD(m) ordering will include diagonal and red-black orderings. These orderings are suitable to the execution of ILU preconditioned methods on mesh- or torus-connected parallel processors. Analytical and empirical studies are carried out, using 2D convection-diffusion model equations, to determine how the degree of parallelism affects the speed of convergence for these preconditioned methods.