Bi-parametric operator preconditioning. (15th November 2021)

• Record Type: Journal Article
• Authors: Escapil-Inchauspé, Paul; Jerez-Hanckes, Carlos
• Is Part Of: Computers & mathematics with applications. Volume 102(2021)
• Page Start: 220
• Page End: 232
• Publication Date: 2021-11-15
• Subjects: Operator preconditioning -- Galerkin methods -- Numerical approximation -- Iterative linear solvers; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.10.012
• Languages: English
• ISSNs: 0898-1221

Abstract

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.