Bi-parametric operator preconditioning
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 |