A modified Jacobi preconditioner for solving ill‐conditioned Biot's consolidation equations using symmetric quasi‐minimal residual method
Identifieur interne : 002D60 ( Istex/Corpus ); précédent : 002D59; suivant : 002D61A modified Jacobi preconditioner for solving ill‐conditioned Biot's consolidation equations using symmetric quasi‐minimal residual method
Auteurs : S. H. Chan ; K. K. Phoon ; F. H. LeeSource :
- International Journal for Numerical and Analytical Methods in Geomechanics [ 0363-9061 ] ; 2001-08-25.
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Abstract
This paper identifies imbalanced columns (or rows) as a significant source of ill‐conditioning in the preconditioned coefficient matrix using the standard Jacobi preconditioner, for finite element solution of Biot's consolidation equations. A simple and heuristic preconditioner is proposed to reduce this source of ill‐conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree‐of‐freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi‐minimal residual method. To alleviate storage requirements, element‐by‐element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. Copyright © 2001 John Wiley & Sons, Ltd.
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DOI: 10.1002/nag.164
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A simple and heuristic preconditioner is proposed to reduce this source of ill‐conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree‐of‐freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi‐minimal residual method. To alleviate storage requirements, element‐by‐element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. 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H.</namePart><namePart type="family">Lee</namePart><affiliation>Department of Civil Engineering, National University of Singapore, Singapore</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>John Wiley & Sons, Ltd.</publisher><place><placeTerm type="text">Chichester, UK</placeTerm></place><dateIssued encoding="w3cdtf">2001-08-25</dateIssued><dateCaptured encoding="w3cdtf">2000-07-01</dateCaptured><copyrightDate encoding="w3cdtf">2001</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><extent unit="figures">14</extent><extent unit="tables">2</extent><extent unit="references">43</extent></physicalDescription><abstract lang="en">This paper identifies imbalanced columns (or rows) as a significant source of ill‐conditioning in the preconditioned coefficient matrix using the standard Jacobi preconditioner, for finite element solution of Biot's consolidation equations. A simple and heuristic preconditioner is proposed to reduce this source of ill‐conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree‐of‐freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi‐minimal residual method. To alleviate storage requirements, element‐by‐element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. Copyright © 2001 John Wiley & Sons, Ltd.</abstract><subject lang="en"><genre>keywords</genre><topic>symmetric indefinite linear system</topic><topic>ill‐conditioned</topic><topic>symmetric quasi‐minimal residual</topic><topic>Jacobi preconditioning</topic><topic>column (row) balancing</topic><topic>Biot's consolidation analysis</topic></subject><relatedItem type="host"><titleInfo><title>International Journal for Numerical and Analytical Methods in Geomechanics</title></titleInfo><titleInfo type="abbreviated"><title>Int. J. Numer. Anal. Meth. 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