Bi-parametric operator preconditioning

Escapil-Inchauspe, Paul; Jerez-Hanckes, C.

Abstract

We extend the operator preconditioning framework Hiptmair (2006) [10] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their preconditioners, as occurs when performing numerical approximations. By considering different perturbation parameters for the original form and its preconditioner, our bi-parametric abstract setting leads to robust and controlled schemes. For Hilbert spaces, we derive exhaustive linear and super-linear convergence estimates for iterative solvers, such as h-independent convergence bounds, when preconditioning with low-accuracy or, equivalently, with highly compressed approximations.

Más información

Título según WOS: Bi-parametric operator preconditioning
Título según SCOPUS: ID SCOPUS_ID:85117722185 Not found in local SCOPUS DB
Título de la Revista: COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volumen: 102
Editorial: PERGAMON-ELSEVIER SCIENCE LTD
Fecha de publicación: 2021
Página de inicio: 220
Página final: 232
DOI:

10.1016/J.CAMWA.2021.10.012

Notas: ISI, SCOPUS