Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners

0579035 - ÚGN 2024 RIV US eng J - Journal Article
Axelsson, Owe - Karátson, J. - Magoulès, F.
Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners.
SIAM Journal on Numerical Analysis. Roč. 61, č. 2 (2023), s. 1057-1079. ISSN 0036-1429. E-ISSN 1095-7170
Institutional support: RVO:68145535
Keywords : Krylov iteration * preconditioning * noncoercive operators * mesh independence * shifted Laplace
OECD category: Applied mathematics
Impact factor: 2.9, year: 2022
Method of publishing: Limited access
https://epubs.siam.org/doi/10.1137/21M1466955

Preconditioning for Krylov methods often relies on operator theory when mesh independent estimates are looked for. The goal of this paper is to contribute to the long development of the analysis of superlinear convergence of Krylov iterations when the preconditioned operator is a compact perturbation of the identity. Mesh independent superlinear convergence of GMRES and CGN iterations is derived for Galerkin solutions for complex non-Hermitian and noncoercive operators. The results are applied to noncoercive boundary value problems, including shifted Laplacian preconditioners for Helmholtz problem
Permanent Link: https://hdl.handle.net/11104/0347919