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

TL;DR

This paper presents a new algebraic recursive multilevel incomplete factorization preconditioner that combines various techniques to efficiently solve general linear systems, reducing costs and improving preconditioning effectiveness.

Contribution

It introduces a novel hybrid preconditioner combining implicit and explicit factorization techniques with multilevel and overlapping strategies.

Findings

Effective preconditioning of general linear systems

Reduces factorization costs compared to existing methods

Demonstrates superior performance in numerical experiments

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-of-the-art iterative solvers of both implicit and explicit form.