A high performance level-block approximate LU factorization preconditioner algorithm

Abstract

Many application problems that lead to solving linear systems make use of preconditioned Krylov subspace solvers to compute their solution. Among the most popular preconditioning approaches are incomplete factorization methods either as single-level approaches or within a multilevel framework. We will present a block incomplete factorization that is based on skillfully blocking the system initially and throughout the factorization. Our objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. We will demonstrate how our level-block approximate algorithm outperforms a single level-block scalar method often by orders of magnitude on modern architectures, thus paving the way for its prospective use inside various multilevel incomplete factorization approaches or other applications where the core part relies on an efficient incomplete factorization algorithms.