A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems

Abstract

In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems.The novelty of the proposed method is to combine factorization techniques of both implicit and explicit type, recursive combinatorial algorithms, multilevel mechanisms and overlapping strategies to maximize sparsity in the inverse factors and consequently reduce the factorization costs. Numerical experiments demonstrate the good potential of the proposed solver to precondition effectively general linear systems, also against other state-ofthe-art iterative solvers of both implicit and explicit form.

Multilevel approaches for FSAI preconditioning

“…There are many different preconditioning techniques available in the literature. Among the algebraic algorithms, the most popular categories are perhaps the incomplete factorizations, multigrid and multilevel methods, domain decomposition techniques, and sparse approximate inverses . Regarding its application, three possibilities may arise, namely the left, right, and split preconditioning, which may be preferred one to the other according to the selected Krylov scheme.…”