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dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorGalvis, Juan
dc.contributor.authorLazarov, Raytcho
dc.contributor.authorWillems, Joerg
dc.date.accessioned2016-02-28T05:52:49Z
dc.date.available2016-02-28T05:52:49Z
dc.date.issued2012
dc.identifier.citationEfendiev Y, Galvis J, Lazarov R, Willems J (2012) Robust Solvers for Symmetric Positive Definite Operators and Weighted Poincaré Inequalities. Lecture Notes in Computer Science: 43–51. Available: http://dx.doi.org/10.1007/978-3-642-29843-1_4.
dc.identifier.issn0302-9743
dc.identifier.issn1611-3349
dc.identifier.doi10.1007/978-3-642-29843-1_4
dc.identifier.urihttp://hdl.handle.net/10754/599528
dc.description.abstractAn abstract setting for robustly preconditioning symmetric positive definite (SPD) operators is presented. The term "robust" refers to the property of the condition numbers of the preconditioned systems being independent of mesh parameters and problem parameters. Important instances of such problem parameters are in particular (highly varying) coefficients. The method belongs to the class of additive Schwarz preconditioners. The paper gives an overview of the results obtained in a recent paper by the authors. It, furthermore, focuses on the importance of weighted Poincaré inequalities, whose notion is extended to general SPD operators, for the analysis of stable decompositions. To demonstrate the applicability of the abstract preconditioner the scalar elliptic equation and the stream function formulation of Brinkman's equations in two spatial dimensions are considered. Several numerical examples are presented. © 2012 Springer-Verlag.
dc.description.sponsorshipThe research of Y. Efendiev was partially supported bythe DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180). The re-search of Y. Efendiev, J. Galvis, and R. Lazarov was supported in parts by awardKUS-C1-016-04, made by King Abdullah University of Science and Technology(KAUST). The research of R. Lazarov and J. Willems was supported in partsby NSF Grant DMS-1016525.
dc.publisherSpringer Nature
dc.subjectBrinkman's problem
dc.subjectdomain decomposition
dc.subjectgeneralized weighted Poincaré inequalities
dc.subjecthigh contrast
dc.subjectrobust additive Schwarz preconditioner
dc.subjectspectral coarse spaces
dc.titleRobust Solvers for Symmetric Positive Definite Operators and Weighted Poincaré Inequalities
dc.typeBook Chapter
dc.identifier.journalLecture Notes in Computer Science
dc.contributor.institutionTexas A and M University, College Station, United States
dc.contributor.institutionJohann Radon Institute for Computational and Applied Mathematics, Linz, Austria
kaust.grant.numberKUS-C1-016-04


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