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Main Title: Convergence Analysis of GMRES for the SUPG Discretized Convection-Diffusion Model Problem
Author(s): Liesen, Jörg
Strakos, Zdenek
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15492
http://dx.doi.org/10.14279/depositonce-14265
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: When 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.
Subject(s): convection-diffusion problem
SUPG discretization
GMRES
rate of convergence
ill conditioned eigenvectors
nonnormality
tridiagonal Toeplitz matrices
Issue Date: 15-Sep-2003
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F10 Iterative methods for linear systems
65F15 Eigenvalues, eigenvectors
65N22 Solution of discretized equations
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2003, 26
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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