article

Operator Preconditioning

Author:

R. HiptmairAuthors Info & Claims

Computers & Mathematics with Applications, Volume 52, Issue 5

Pages 699 - 706

Published: 01 September 2006 Publication History

Abstract

Operator preconditioning offers a general recipe for constructing preconditioners for discrete linear operators that have arisen from a Galerkin approach. The key idea is to employ matching Galerkin discretizations of operators of complementary mapping properties. If these can be found, the resulting preconditioners will be robust with respect to the choice of the bases for trial and test spaces. I survey the application of operator preconditioning to finite elements and boundary elements.

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Cited By

Pechstein C(2023)A Unified Theory of Non-overlapping Robin–Schwarz Methods: Continuous and Discrete, Including Cross PointsJournal of Scientific Computing10.1007/s10915-023-02248-996:2Online publication date: 6-Jul-2023
https://dl.acm.org/doi/10.1007/s10915-023-02248-9
Gergelits TNielsen BStrakoš Z(2022)Numerical approximation of the spectrum of self-adjoint operators in operator preconditioningNumerical Algorithms10.1007/s11075-022-01263-591:1(301-325)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s11075-022-01263-5
Hiptmair RMao S(2022)Stable multilevel splittings of boundary edge element spacesBIT10.1007/s10543-012-0369-152:3(661-685)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-012-0369-1
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Operator Preconditioning
1. Mathematics of computing
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cover image Computers & Mathematics with Applications

Computers & Mathematics with Applications Volume 52, Issue 5

September, 2006

221 pages

ISSN:0898-1221

Issue’s Table of Contents

Copyright © Elsevier Ltd © 2006.

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Pergamon Press, Inc.

United States

Publication History

Published: 01 September 2006

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Cited By

Pechstein C(2023)A Unified Theory of Non-overlapping Robin–Schwarz Methods: Continuous and Discrete, Including Cross PointsJournal of Scientific Computing10.1007/s10915-023-02248-996:2Online publication date: 6-Jul-2023
https://dl.acm.org/doi/10.1007/s10915-023-02248-9
Gergelits TNielsen BStrakoš Z(2022)Numerical approximation of the spectrum of self-adjoint operators in operator preconditioningNumerical Algorithms10.1007/s11075-022-01263-591:1(301-325)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s11075-022-01263-5
Hiptmair RMao S(2022)Stable multilevel splittings of boundary edge element spacesBIT10.1007/s10543-012-0369-152:3(661-685)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-012-0369-1
Gimperlein HStocek JUrzúa-Torres C(2021)Optimal operator preconditioning for pseudodifferential boundary problemsNumerische Mathematik10.1007/s00211-021-01193-9148:1(1-41)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s00211-021-01193-9
Alouges FAverseng M(2021)New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical resultsNumerische Mathematik10.1007/s00211-021-01189-5148:2(255-292)Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s00211-021-01189-5
Marchand PClaeys XJolivet PNataf FTournier P(2020)Two-level preconditioning for -version boundary element approximation of hypersingular operator with GenEONumerische Mathematik10.1007/s00211-020-01149-5146:3(597-628)Online publication date: 1-Nov-2020
https://dl.acm.org/doi/10.1007/s00211-020-01149-5
Hrnčíř JPultarová IStrakoš Z(2019)Decomposition into subspaces preconditioning: abstract frameworkNumerical Algorithms10.1007/s11075-019-00671-483:1(57-98)Online publication date: 4-Feb-2019
https://dl.acm.org/doi/10.1007/s11075-019-00671-4
Papeź JStrakoš ZVohralík M(2018)Estimating and localizing the algebraic and total numerical errors using flux reconstructionsNumerische Mathematik10.1007/s00211-017-0915-5138:3(681-721)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s00211-017-0915-5
Claeys XHiptmair RSpindler E(2017)Second-kind boundary integral equations for electromagnetic scattering at composite objectsComputers & Mathematics with Applications10.1016/j.camwa.2017.08.01474:11(2650-2670)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1016/j.camwa.2017.08.014
Axelsson OFarouq SNeytcheva M(2017)Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problemsNumerical Algorithms10.1007/s11075-016-0136-574:1(19-37)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1007/s11075-016-0136-5
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