Convergence Analysis of GMRES for the SUPG Discretized Convection-Diffusion Model Problem

dc.contributor.authorLiesen, Jörg
dc.contributor.authorStrakos, Zdenek
dc.date.accessioned2021-12-17T10:05:32Z
dc.date.available2021-12-17T10:05:32Z
dc.date.issued2003-09-15
dc.description.abstractWhen GMRES is applied to streamline-diffusion upwind Petrov Galerkin (SUPG) discretized convection-diffusion problems, it typically exhibits an initial period of slow convergence followed by a faster decrease of the residual norms. We concentrate on a well-known model problem with a constant velocity field parallel to one of the axes and with Dirichlet boundary conditions. Instead of the eigendecomposition of the system matrix we use the simultaneous diagonalization of the matrix blocks to offer an explanation of GMRES convergence. We show how the initial period of slow convergence is related to the boundary conditions and address the question why the convergence in the second stage accelerates.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15492
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14265
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherconvection-diffusion problemen
dc.subject.otherSUPG discretizationen
dc.subject.otherGMRESen
dc.subject.otherrate of convergenceen
dc.subject.otherill conditioned eigenvectorsen
dc.subject.othernonnormalityen
dc.subject.othertridiagonal Toeplitz matricesen
dc.titleConvergence Analysis of GMRES for the SUPG Discretized Convection-Diffusion Model Problemen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2003, 26en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065F10 Iterative methods for linear systemsen
tub.subject.msc200065F15 Eigenvalues, eigenvectorsen
tub.subject.msc200065N22 Solution of discretized equationsen
tub.subject.msc200065N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsen

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