SsebuggwawoD.(2002). A Hybrid Relaxed Incomplete Factorization and Approximate Subspace Preconditioning Method for Solving SPD Problems in Diffusion.

Master Class (Scientific Computing)  Report, Wiskunde Onderzoekschool (WONDER), formerly Mathematical Research Institute (MRI), Radboud University Nijmegen, The Netherlands.

Abstract: In this research we study an iterative solution procedure for solving sparse linear systems which arise from finite-element discretization of a (strongly anisotropic) diffusion equation. To solve such a severely ill-conditioned system, we develop a preconditioning strategy that is based on the relaxed incomplete factorization (RILU(w)) and the approximate subspace projection (ASP) method. This hybrid preconditioning method collects the anisotropic part of the spectrum by moving the small eigenvalues to the cluster of bigger eigenvalues. Moving these small eigenvalues is necessary since their presence slows down the convergence of the iterative method. It is noted that combining a relaxed incomplete factorization preconditioner (RILU(w)) and the ASP preconditioner, the hybrid preconditioner reduces the bigger eigenvalues too. This significantly improves the conditioning of the iterative method and allows us to solve the diffusion problem with an arithmetic cost that is independent of the anisotropy of the problem.