A Robust Iterative Scheme for Symmetric Indefinite Systems

TL;DR

This paper introduces a two-level nested iterative scheme combining MINRES and preconditioned CG methods to efficiently solve symmetric indefinite linear systems with few negative eigenvalues, demonstrating robustness in practical applications.

Contribution

The paper presents a novel nested preconditioned iterative scheme specifically designed for symmetric indefinite systems with few negative eigenvalues, enhancing robustness and efficiency.

Findings

Effective in solving quadratic eigenvalue problems in finite element models.

Demonstrates robustness across various applications involving indefinite systems.

Improves convergence compared to traditional methods.

Abstract

We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed scheme consists of an outer Minimum Residual (MINRES) iteration, preconditioned by an inner Conjugate Gradient (CG) iteration in which CG can be further preconditioned. The robustness of the proposed scheme is illustrated by solving indefinite linear systems that arise in the solution of quadratic eigenvalue problems in the context of model reduction methods for finite element models of disk brakes as well as on other problems that arise in a variety of applications.