Bi-parametric operator preconditioning

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 param...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2021-11, Vol.102, p.220-232
Main Authors: Escapil-Inchauspé, Paul, Jerez-Hanckes, Carlos
Format: Article
Language:English
Subjects:
Approximation
Convergence
Galerkin method
Galerkin methods
Hilbert space
Iterative linear solvers
Iterative methods
Numerical approximation
Operator preconditioning
Parameters
Perturbation
Preconditioning
Robust control
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2021.10.012