Volume 63, pp. 129-149, 2025.

Two-grid deflated Krylov methods for linear equations

Ronald B. Morgan, Travis Whyte, Walter Wilcox, and Zhao Yang

Abstract

An approach is proposed for solving large linear systems that combines Krylov methods with the use of two different grid levels. Eigenvectors are computed on the coarse grid and then used to deflate the eigenvalues on the fine grid with an efficient projection. GMRES-type methods are first used on both the coarse and fine grids. Then another approach is given that uses a novel restarted BiCGStab (or IDR) method on the fine grid. While BiCGStab is generally considered to be a non-restarted method, restarting works well in this context. Tests show that this new approach can be very efficient for difficult linear equations problems.

Full Text (PDF) [1.6 MB], BibTeX , DOI: 10.1553/etna_vol63s129

Key words

linear equations, deflation, GMRES, BiCGStab, eigenvalues, two-grid

AMS subject classifications

65F10, 15A06