POD‐Galerkin approximations in PDE‐constrained optimization
Identifieur interne : 001437 ( Istex/Corpus ); précédent : 001436; suivant : 001438POD‐Galerkin approximations in PDE‐constrained optimization
Auteurs : Ekkehard W. Sachs ; Stefan VolkweinSource :
- GAMM‐Mitteilungen [ 0936-7195 ] ; 2010-10.
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Abstract
Proper orthogonal decomposition (POD) is one of the most popular model reduction techniques for nonlinear partial differential equations. It is based on a Galerkin‐type approximation, where the POD basis functions contain information from a solution of the dynamical system at pre‐specified time instances, so‐called snapshots. POD models have been applied very successfully in the area of optimization with PDEs or feedback control laws. Nevertheless, various issues are still unclear and are currently under research, e.g. timely updates of the snapshot information and error analyses for the POD approximations (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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DOI: 10.1002/gamm.201010015
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Sachs</name><affiliation><mods:affiliation>FB 4 –Department of Mathematics, University of Trier, 54286 Trier, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: sachs@uni‐trier.de</mods:affiliation></affiliation></author><author><name sortKey="Volkwein, Stefan" sort="Volkwein, Stefan" uniqKey="Volkwein S" first="Stefan" last="Volkwein">Stefan Volkwein</name><affiliation><mods:affiliation>Department of Mathematics and Statistics, University of Constance, 78457 Konstanz, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: Stefan.Volkwein@uni‐konstanz.de</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">GAMM‐Mitteilungen</title><title level="j" type="abbrev">GAMM‐Mitteilungen</title><idno type="ISSN">0936-7195</idno><idno type="eISSN">1522-2608</idno><imprint><publisher>WILEY‐VCH Verlag</publisher><pubPlace>Berlin</pubPlace><date type="published" when="2010-10">2010-10</date><biblScope unit="volume">33</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="194">194</biblScope><biblScope unit="page" to="208">208</biblScope></imprint><idno type="ISSN">0936-7195</idno></series><idno type="istex">2FA9274B98B52374707962E181C0099CF65A9813</idno><idno type="DOI">10.1002/gamm.201010015</idno><idno type="ArticleID">GAMM201010015</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0936-7195</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Proper orthogonal decomposition</term><term>reduced‐order modelling</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Proper orthogonal decomposition (POD) is one of the most popular model reduction techniques for nonlinear partial differential equations. It is based on a Galerkin‐type approximation, where the POD basis functions contain information from a solution of the dynamical system at pre‐specified time instances, so‐called snapshots. POD models have been applied very successfully in the area of optimization with PDEs or feedback control laws. Nevertheless, various issues are still unclear and are currently under research, e.g. timely updates of the snapshot information and error analyses for the POD approximations (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>Ekkehard W. Sachs</name><affiliations><json:string>FB 4 –Department of Mathematics, University of Trier, 54286 Trier, Germany</json:string><json:string>E-mail: sachs@uni‐trier.de</json:string></affiliations></json:item><json:item><name>Stefan Volkwein</name><affiliations><json:string>Department of Mathematics and Statistics, University of Constance, 78457 Konstanz, Germany</json:string><json:string>E-mail: Stefan.Volkwein@uni‐konstanz.de</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Proper orthogonal decomposition</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>reduced‐order modelling</value></json:item></subject><articleId><json:string>GAMM201010015</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>article</json:string></originalGenre><abstract>Proper orthogonal decomposition (POD) is one of the most popular model reduction techniques for nonlinear partial differential equations. 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KGaA, Weinheim)</abstract><note type="funding">German Science Foundation DFG (SPP 1253) - No. Sa289‐20‐1; </note><note type="funding">Austrian Science Fund FWF - No. P19588‐N18; </note><note type="funding">research center forumstat (Trier)</note><subject lang="en"><genre>keywords</genre><topic>Proper orthogonal decomposition</topic><topic>reduced‐order modelling</topic></subject><relatedItem type="host"><titleInfo><title>GAMM‐Mitteilungen</title></titleInfo><titleInfo type="abbreviated"><title>GAMM‐Mitteilungen</title></titleInfo><genre type="journal">journal</genre><subject><genre>article-category</genre><topic>Original Paper</topic></subject><identifier type="ISSN">0936-7195</identifier><identifier type="eISSN">1522-2608</identifier><identifier type="DOI">10.1002/(ISSN)1522-2608</identifier><identifier type="PublisherID">GAMM</identifier><part><date>2010</date><detail type="volume"><caption>vol.</caption><number>33</number></detail><detail type="issue"><caption>no.</caption><number>2</number></detail><extent unit="pages"><start>194</start><end>208</end><total>15</total></extent></part></relatedItem><identifier type="istex">2FA9274B98B52374707962E181C0099CF65A9813</identifier><identifier type="DOI">10.1002/gamm.201010015</identifier><identifier type="ArticleID">GAMM201010015</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 2010 WILEY‐VCH Verlag GmbH & Co. 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