On parallel algebraic multilevel preconditioner with approximate inversion by basis matrix method

Abstract

. The paper presents a parallel calculation scheme for distributed memory systems for a modification of the AMLI preconditioner that performs incomplete inversions of matrix blocks by a technique that produces approximate inverse of a matrix by an orthogonalization procedure, referred to as the incomplete basis matrix method. Theoretical estimates of algorithm’s performance and the results of its experimental testing are presented. The results of experimental analysis of preconditioner parameters influence on the convergence of the iterative algorithm are given. The characteristics of the proposed algo-rithm are compared with those of known algorithms implemented in the hypre software package. The tests on the matrices obtained from finite element discretization of soil stress-strain state modelling problem showed that the proposed algorithm has better performance for significantly ill-conditioned linear systems when solving them on a small number of computational resources.