• On convergence rate of the aug...

Treffer: On convergence rate of the augmented Lagrangian algorithm for nonsymmetric saddle point problems

Title:
On convergence rate of the augmented Lagrangian algorithm for nonsymmetric saddle point problems
Authors:
AWANOU, G. M, LAI, M. J
Source:
6th IMACS International Symposium on Iterative Methods in Scientific ComputingApplied numerical mathematics. 54(2):122-134
Publisher Information:
Amsterdam: Elsevier, 2005.
Publication Year:
2005
Physical Description:
print, 10 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations aux dérivées partielles, problèmes aux valeurs limites, Partial differential equations, boundary value problems, Accélération convergence, Convergence acceleration, Aceleración convergencia, Analyse numérique, Numerical analysis, Análisis numérico, Convergence, Convergencia, Discrétisation, Discretization, Discretización, Décomposition opérateur, Operator splitting, Descomposición operador, Ecoulement cavité, Cavity flow, Flujo cavidad, Equation Navier Stokes, Navier Stokes equation, Ecuación Navier Stokes, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Méthode Lagrange, Lagrangian method, Método Lagrange, Méthode discrétisation, Discretization method, Método discretización, Méthode noyau, Kernel method, Método núcleo, Performance algorithme, Algorithm performance, Resultado algoritmo, Point col, Saddle point, Punto silla, Problème Stokes, Stokes problem, Problema Stokes, Simulation numérique, Numerical simulation, Simulación numérica, Taux convergence, Convergence rate, Relación convergencia, Algorithme lagrangien, Lagrangian algorithm, Augmented Lagrangian algorithm, Saddle point problems
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Institute for Mathematics and its Applications, University of Minnesota, United States
Department of Mathematics, University of Georgia, Athens, GA 30605, United States
ISSN:
0168-9274
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=16907329
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.16907329
Database:
PASCAL Archive

Weitere Informationen

We are interested in solving the system [AL LTO ][cλ]=[FG], by a variant of the augmented Lagrangian algorithm. This type of problem with nonsymmetric A typically arises in certain discretizations of the Navier-Stokes equations. Here A is a (n, n) matrix, c, F ∈ Rn, L is a (m, n) matrix, and λ, G ∈ Rm. We assume that A is invertible on the kernel of L. Convergence rates of the augmented Lagrangian algorithm are known in the symmetric case but the proofs in [R. Glowinski, P. LeTallec, Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics, SIAM, 1989] used spectral arguments and cannot be extended to the nonsymmetric case. The purpose of this paper is to give a rate of convergence of a variant of the algorithm in the nonsymmetric case. We illustrate the performance of this algorithm with numerical simulations of the lid-driven cavity flow problem for the 2D Navier-Stokes equations.