Ordering Strategies for Modified Block Incomplete Factorizations

In this study the aim is to first investigate how the rate of convergence of unperturbed modified block incomplete factorization methods depends on the discrete partial differential equation (PDE) to solve, and next, on this basis, to provide simple practical rules for easily selecting orderings that result in rapid convergence. It emerges from the analysis here that for discrete PDEs, ordering schemes that optimize the rate of convergence strongly depend on the variation of both the PDE coefficients and the mesh sizes. The arguments made, which bring to light the appreciable potentialities of modified methods, also display insight into why block versions are more robust than pointwise ones.