A GSVD formulation of a domain decomposition method forplanar eigenvalue problems
Identifieur interne : 001902 ( Istex/Corpus ); précédent : 001901; suivant : 001903A GSVD formulation of a domain decomposition method forplanar eigenvalue problems
Auteurs : Timo BetckeSource :
- IMA Journal of Numerical Analysis [ 0272-4979 ] ; 2006-10-27.
Abstract
In this article, we present a modification of the domain decomposition method of Descloux and Tolley for planar eigenvalue problems. Instead of formulating a generalized eigenvalue problem, our method is based on the generalized singular value decomposition. This approach is robust and at the same time highly accurate. Furthermore, we give an improved convergence analysis based on results from complex approximation theory. Several examples show the effectiveness of our method.
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DOI: 10.1093/imanum/drl030
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All rights reserved.</p></availability><date>2006-10-27</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">A GSVD formulation of a domain decomposition method forplanar eigenvalue problems</title><author xml:id="author-1"><persName><forename type="first">Timo</forename><surname>Betcke</surname></persName><email>timo.betcke@maths.man.ac.uk</email><affiliation>School of Mathematics, The University of Manchester, Sackville Street, Manchester, M60 1QD, UK</affiliation></author></analytic><monogr><title level="j">IMA Journal of Numerical Analysis</title><idno type="pISSN">0272-4979</idno><idno type="eISSN">1464-3642</idno><imprint><publisher>Oxford University Press</publisher><date type="published" when="2006-10-27"></date><biblScope unit="volume">27</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="451">451</biblScope><biblScope unit="page" to="478">478</biblScope></imprint></monogr><idno type="istex">E8A9F90D7BBDD5AE71CEAF449C646AC37BDFF9A9</idno><idno type="DOI">10.1093/imanum/drl030</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2006-10-27</date></creation><abstract><p>In this article, we present a modification of the domain decomposition method of Descloux and Tolley for planar eigenvalue problems. Instead of formulating a generalized eigenvalue problem, our method is based on the generalized singular value decomposition. This approach is robust and at the same time highly accurate. Furthermore, we give an improved convergence analysis based on results from complex approximation theory. Several examples show the effectiveness of our method.</p></abstract><textClass><keywords scheme="keyword"><list><item><term>Articles</term></item></list></keywords></textClass><textClass><keywords scheme="keyword"><list><head>keywords</head><item><term>eigenvalues</term></item><item><term>domain decomposition</term></item><item><term>generalized singular values</term></item><item><term>method of particular solutions</term></item><item><term>conformal maps</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2006-10-27">Created</change><change when="2006-10-27">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-12-22">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/E8A9F90D7BBDD5AE71CEAF449C646AC37BDFF9A9/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus oup" wicri:toSee="no header"><istex:docType PUBLIC="-//NLM//DTD Journal Publishing DTD v2.3 20070202//EN" URI="journalpublishing.dtd" name="istex:docType"></istex:docType><istex:document><article article-type="research-article"><front><journal-meta><journal-id journal-id-type="hwp">imanum</journal-id><journal-id journal-id-type="publisher-id">imanum</journal-id><journal-title>IMA Journal of Numerical Analysis</journal-title><issn pub-type="epub">1464-3642</issn><issn pub-type="ppub">0272-4979</issn><publisher><publisher-name>Oxford University Press</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.1093/imanum/drl030</article-id><article-categories><subj-group><subject>Articles</subject></subj-group></article-categories><title-group><article-title>A GSVD formulation of a domain decomposition method forplanar eigenvalue problems</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name><surname>Betcke</surname><given-names>Timo</given-names></name><xref ref-type="corresp" rid="cor1">†</xref></contrib></contrib-group><aff>School of Mathematics, The University of Manchester, Sackville Street, Manchester, M60 1QD, UK</aff><author-notes><corresp id="cor1"><label>†</label>Email: <email>timo.betcke@maths.man.ac.uk</email></corresp></author-notes><pub-date pub-type="epub-ppub"><month>7</month><year>2007</year></pub-date><pub-date pub-type="epub"><day>27</day><month>10</month><year>2006</year></pub-date><volume>27</volume><issue>3</issue><fpage>451</fpage><lpage>478</lpage><history><date date-type="received"><day>12</day><month>4</month><year>2006</year></date><date date-type="rev-recd"><day>1</day><month>10</month><year>2006</year></date></history><permissions><copyright-statement>© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.</copyright-statement><copyright-year>2007</copyright-year></permissions><abstract><p>In this article, we present a modification of the domain decomposition method of Descloux and Tolley for planar eigenvalue problems. Instead of formulating a generalized eigenvalue problem, our method is based on the generalized singular value decomposition. This approach is robust and at the same time highly accurate. Furthermore, we give an improved convergence analysis based on results from complex approximation theory. Several examples show the effectiveness of our method.</p></abstract><kwd-group><kwd>eigenvalues</kwd><kwd>domain decomposition</kwd><kwd>generalized singular values</kwd><kwd>method of particular solutions</kwd><kwd>conformal maps</kwd></kwd-group></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>A GSVD formulation of a domain decomposition method forplanar eigenvalue problems</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A GSVD formulation of a domain decomposition method forplanar eigenvalue problems</title></titleInfo><name type="personal"><namePart type="given">Timo</namePart><namePart type="family">Betcke</namePart><affiliation>School of Mathematics, The University of Manchester, Sackville Street, Manchester, M60 1QD, UK</affiliation><affiliation>E-mail: timo.betcke@maths.man.ac.uk</affiliation></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><subject><topic>Articles</topic></subject><originInfo><publisher>Oxford University Press</publisher><dateIssued encoding="w3cdtf">2006-10-27</dateIssued><dateCreated encoding="w3cdtf">2006-10-27</dateCreated><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract>In this article, we present a modification of the domain decomposition method of Descloux and Tolley for planar eigenvalue problems. Instead of formulating a generalized eigenvalue problem, our method is based on the generalized singular value decomposition. This approach is robust and at the same time highly accurate. Furthermore, we give an improved convergence analysis based on results from complex approximation theory. Several examples show the effectiveness of our method.</abstract><subject><genre>keywords</genre><topic>eigenvalues</topic><topic>domain decomposition</topic><topic>generalized singular values</topic><topic>method of particular solutions</topic><topic>conformal maps</topic></subject><relatedItem type="host"><titleInfo><title>IMA Journal of Numerical Analysis</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0272-4979</identifier><identifier type="eISSN">1464-3642</identifier><identifier type="PublisherID">imanum</identifier><identifier type="PublisherID-hwp">imanum</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>27</number></detail><detail type="issue"><caption>no.</caption><number>3</number></detail><extent unit="pages"><start>451</start><end>478</end></extent></part></relatedItem><identifier type="istex">E8A9F90D7BBDD5AE71CEAF449C646AC37BDFF9A9</identifier><identifier type="DOI">10.1093/imanum/drl030</identifier><accessCondition type="use and reproduction" contentType="copyright">The author 2006. 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