Preconditioning by an extended matrix technique for convection-diffusion-reaction equations

In this paper we consider a preconditioning technique for the ill-conditioned systems arising from discretisations of nonsymmetric elliptic boundary value problems. The rectangular preconditioning matrix is constructed via the transfer operators between successive discretization levels of the initia...

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Main Authors: Aurelian Nicola, Constantin Popa
Format: Article
Language:English
Published: Publishing House of the Romanian Academy 2008-08-01
Series:Journal of Numerical Analysis and Approximation Theory
Subjects:
Online Access:https://www.ictp.acad.ro/jnaat/journal/article/view/890
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author Aurelian Nicola
Constantin Popa
author_facet Aurelian Nicola
Constantin Popa
author_sort Aurelian Nicola
collection DOAJ
description In this paper we consider a preconditioning technique for the ill-conditioned systems arising from discretisations of nonsymmetric elliptic boundary value problems. The rectangular preconditioning matrix is constructed via the transfer operators between successive discretization levels of the initial problem. In this way we get an extended, square, singular, consistent, but mesh independent well-conditioned linear system. Numerical experiments are presented for a 2D convection-diffusion-reaction problem.
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spelling doaj.art-18c15aaa3947407e83981d953f8f45742022-12-22T02:12:03ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2008-08-01372Preconditioning by an extended matrix technique for convection-diffusion-reaction equationsAurelian Nicola0Constantin Popa1Ovidius University, ConstanţaOvidius University, ConstanţaIn this paper we consider a preconditioning technique for the ill-conditioned systems arising from discretisations of nonsymmetric elliptic boundary value problems. The rectangular preconditioning matrix is constructed via the transfer operators between successive discretization levels of the initial problem. In this way we get an extended, square, singular, consistent, but mesh independent well-conditioned linear system. Numerical experiments are presented for a 2D convection-diffusion-reaction problem.https://www.ictp.acad.ro/jnaat/journal/article/view/890multilevel discretizationspectrally equivalent matricesmesh independent preconditioningpositive semidefinite systemsCGLS algorithm
spellingShingle Aurelian Nicola
Constantin Popa
Preconditioning by an extended matrix technique for convection-diffusion-reaction equations
Journal of Numerical Analysis and Approximation Theory
multilevel discretization
spectrally equivalent matrices
mesh independent preconditioning
positive semidefinite systems
CGLS algorithm
title Preconditioning by an extended matrix technique for convection-diffusion-reaction equations
title_full Preconditioning by an extended matrix technique for convection-diffusion-reaction equations
title_fullStr Preconditioning by an extended matrix technique for convection-diffusion-reaction equations
title_full_unstemmed Preconditioning by an extended matrix technique for convection-diffusion-reaction equations
title_short Preconditioning by an extended matrix technique for convection-diffusion-reaction equations
title_sort preconditioning by an extended matrix technique for convection diffusion reaction equations
topic multilevel discretization
spectrally equivalent matrices
mesh independent preconditioning
positive semidefinite systems
CGLS algorithm
url https://www.ictp.acad.ro/jnaat/journal/article/view/890
work_keys_str_mv AT aureliannicola preconditioningbyanextendedmatrixtechniqueforconvectiondiffusionreactionequations
AT constantinpopa preconditioningbyanextendedmatrixtechniqueforconvectiondiffusionreactionequations