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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Format: | Article |
Language: | English |
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Publishing House of the Romanian Academy
2008-08-01
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Series: | Journal of Numerical Analysis and Approximation Theory |
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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. |
first_indexed | 2024-04-14T04:30:19Z |
format | Article |
id | doaj.art-18c15aaa3947407e83981d953f8f4574 |
institution | Directory Open Access Journal |
issn | 2457-6794 2501-059X |
language | English |
last_indexed | 2024-04-14T04:30:19Z |
publishDate | 2008-08-01 |
publisher | Publishing House of the Romanian Academy |
record_format | Article |
series | Journal of Numerical Analysis and Approximation Theory |
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 |