A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model
Identifieur interne : 001535 ( Istex/Corpus ); précédent : 001534; suivant : 001536A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model
Auteurs : X. Chen ; I. M. Navon ; F. FangSource :
- International Journal for Numerical Methods in Fluids [ 0271-2091 ] ; 2011-02-20.
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Abstract
We consider a limited‐area finite‐element discretization of the shallow‐water equations model. Our purpose in this paper is to solve an inverse problem for the above model controlling its initial conditions in presence of observations being assimilated in a time interval (window of assimilation). We then attempt to obtain a reduced‐order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4‐D VAR. Different approaches of POD implementation of the reduced inverse problem are compared, including a dual‐weighed method for snapshot selection coupled with a trust‐region POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dual‐weighing choice of snapshots is combined with POD adaptivity of the trust‐region type. Results of ad‐hoc adaptivity of the POD 4‐D VAR turn out to yield less accurate results than trust‐region POD when compared with high‐fidelity model. Directions of future research are finally outlined. Copyright © 2009 John Wiley & Sons, Ltd.
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DOI: 10.1002/fld.2198
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model</title><author><name sortKey="Chen, X" sort="Chen, X" uniqKey="Chen X" first="X." last="Chen">X. Chen</name><affiliation><mods:affiliation>Department of Mathematics, Florida State University, Tallahassee, FL, 32306, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Navon, I M" sort="Navon, I M" uniqKey="Navon I" first="I. M." last="Navon">I. M. Navon</name><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.</mods:affiliation></affiliation><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.===</mods:affiliation></affiliation></author><author><name sortKey="Fang, F" sort="Fang, F" uniqKey="Fang F" first="F." last="Fang">F. Fang</name><affiliation><mods:affiliation>Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, London, SW7 2AZ, U.K.</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:91F2F75600EBD0F72EEAE10E0E1BD988895990BB</idno><date when="2011" year="2011">2011</date><idno type="doi">10.1002/fld.2198</idno><idno type="url">https://api.istex.fr/document/91F2F75600EBD0F72EEAE10E0E1BD988895990BB/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001535</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001535</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model</title><author><name sortKey="Chen, X" sort="Chen, X" uniqKey="Chen X" first="X." last="Chen">X. Chen</name><affiliation><mods:affiliation>Department of Mathematics, Florida State University, Tallahassee, FL, 32306, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Navon, I M" sort="Navon, I M" uniqKey="Navon I" first="I. M." last="Navon">I. M. Navon</name><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.</mods:affiliation></affiliation><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.===</mods:affiliation></affiliation></author><author><name sortKey="Fang, F" sort="Fang, F" uniqKey="Fang F" first="F." last="Fang">F. Fang</name><affiliation><mods:affiliation>Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, London, SW7 2AZ, U.K.</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">International Journal for Numerical Methods in Fluids</title><title level="j" type="abbrev">Int. J. Numer. Meth. Fluids</title><idno type="ISSN">0271-2091</idno><idno type="eISSN">1097-0363</idno><imprint><publisher>John Wiley & Sons, Ltd.</publisher><pubPlace>Chichester, UK</pubPlace><date type="published" when="2011-02-20">2011-02-20</date><biblScope unit="volume">65</biblScope><biblScope unit="issue">5</biblScope><biblScope unit="page" from="520">520</biblScope><biblScope unit="page" to="541">541</biblScope></imprint><idno type="ISSN">0271-2091</idno></series><idno type="istex">91F2F75600EBD0F72EEAE10E0E1BD988895990BB</idno><idno type="DOI">10.1002/fld.2198</idno><idno type="ArticleID">FLD2198</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0271-2091</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>4‐D VAR</term><term>dual weighting</term><term>inverse problem</term><term>proper orthogonal decomposition</term><term>shallow water equations</term><term>trust‐region method</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We consider a limited‐area finite‐element discretization of the shallow‐water equations model. Our purpose in this paper is to solve an inverse problem for the above model controlling its initial conditions in presence of observations being assimilated in a time interval (window of assimilation). We then attempt to obtain a reduced‐order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4‐D VAR. Different approaches of POD implementation of the reduced inverse problem are compared, including a dual‐weighed method for snapshot selection coupled with a trust‐region POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dual‐weighing choice of snapshots is combined with POD adaptivity of the trust‐region type. Results of ad‐hoc adaptivity of the POD 4‐D VAR turn out to yield less accurate results than trust‐region POD when compared with high‐fidelity model. Directions of future research are finally outlined. Copyright © 2009 John Wiley & Sons, Ltd.</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>X. Chen</name><affiliations><json:string>Department of Mathematics, Florida State University, Tallahassee, FL, 32306, U.S.A.</json:string></affiliations></json:item><json:item><name>I. M. Navon</name><affiliations><json:string>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.</json:string><json:string>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.===</json:string></affiliations></json:item><json:item><name>F. Fang</name><affiliations><json:string>Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, London, SW7 2AZ, U.K.</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>4‐D VAR</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>shallow water equations</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>dual weighting</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>trust‐region method</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>inverse problem</value></json:item></subject><articleId><json:string>FLD2198</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>article</json:string></originalGenre><abstract>We consider a limited‐area finite‐element discretization of the shallow‐water equations model. Our purpose in this paper is to solve an inverse problem for the above model controlling its initial conditions in presence of observations being assimilated in a time interval (window of assimilation). We then attempt to obtain a reduced‐order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4‐D VAR. Different approaches of POD implementation of the reduced inverse problem are compared, including a dual‐weighed method for snapshot selection coupled with a trust‐region POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dual‐weighing choice of snapshots is combined with POD adaptivity of the trust‐region type. Results of ad‐hoc adaptivity of the POD 4‐D VAR turn out to yield less accurate results than trust‐region POD when compared with high‐fidelity model. Directions of future research are finally outlined. Copyright © 2009 John Wiley & Sons, Ltd.</abstract><qualityIndicators><score>6.896</score><pdfVersion>1.3</pdfVersion><pdfPageSize>593.887 x 782.362 pts</pdfPageSize><refBibsNative>true</refBibsNative><abstractCharCount>1055</abstractCharCount><pdfWordCount>9279</pdfWordCount><pdfCharCount>53413</pdfCharCount><pdfPageCount>22</pdfPageCount><abstractWordCount>158</abstractWordCount></qualityIndicators><title>A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model</title><refBibs><json:item><host><author></author><title>Trust‐region methods for flow control based on reduced order modeling</title></host></json:item><json:item><host><author></author><title>Trust‐region proper orthogonal decomposition for flow control</title></host></json:item><json:item><host><author></author><title>Conn AR, Gould NIM, Toint PL. Trust‐region Methods. 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No. CCF‐0635162;</note><note>Natural Environment Research Council - No. NE/C51829X/1;</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model</title><author xml:id="author-1"><persName><forename type="first">X.</forename><surname>Chen</surname></persName><affiliation>Department of Mathematics, Florida State University, Tallahassee, FL, 32306, U.S.A.</affiliation></author><author xml:id="author-2"><persName><forename type="first">I. M.</forename><surname>Navon</surname></persName><affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.</affiliation><affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.===</affiliation></author><author xml:id="author-3"><persName><forename type="first">F.</forename><surname>Fang</surname></persName><affiliation>Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, London, SW7 2AZ, U.K.</affiliation></author></analytic><monogr><title level="j">International Journal for Numerical Methods in Fluids</title><title level="j" type="abbrev">Int. J. Numer. Meth. 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Our purpose in this paper is to solve an inverse problem for the above model controlling its initial conditions in presence of observations being assimilated in a time interval (window of assimilation). We then attempt to obtain a reduced‐order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4‐D VAR. Different approaches of POD implementation of the reduced inverse problem are compared, including a dual‐weighed method for snapshot selection coupled with a trust‐region POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dual‐weighing choice of snapshots is combined with POD adaptivity of the trust‐region type. Results of ad‐hoc adaptivity of the POD 4‐D VAR turn out to yield less accurate results than trust‐region POD when compared with high‐fidelity model. Directions of future research are finally outlined. Copyright © 2009 John Wiley & Sons, Ltd.</p></abstract><textClass xml:lang="en"><keywords scheme="keyword"><list><head>keywords</head><item><term>proper orthogonal decomposition</term></item><item><term>4‐D VAR</term></item><item><term>shallow water equations</term></item><item><term>dual weighting</term></item><item><term>trust‐region method</term></item><item><term>inverse problem</term></item></list></keywords></textClass><textClass><keywords scheme="Journal Subject"><list><head>article-category</head><item><term>Research Article</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2009-05-21">Received</change><change when="2009-08-27">Registration</change><change when="2011-02-20">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/91F2F75600EBD0F72EEAE10E0E1BD988895990BB/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>John Wiley & Sons, Ltd.</publisherName><publisherLoc>Chichester, UK</publisherLoc></publisherInfo><doi registered="yes">10.1002/(ISSN)1097-0363</doi><issn type="print">0271-2091</issn><issn type="electronic">1097-0363</issn><idGroup><id type="product" value="FLD"></id></idGroup><titleGroup><title type="main" xml:lang="en" sort="INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS">International Journal for Numerical Methods in Fluids</title><title type="short">Int. 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M.</givenNames><familyName>Navon</familyName></personName><contactDetails><email>inavon@fsu.edu</email></contactDetails></creator><creator xml:id="au3" creatorRole="author" affiliationRef="#af3"><personName><givenNames>F.</givenNames><familyName>Fang</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="af1" countryCode="US" type="organization"><unparsedAffiliation>Department of Mathematics, Florida State University, Tallahassee, FL, 32306, U.S.A.</unparsedAffiliation></affiliation><affiliation xml:id="af2" countryCode="US" type="organization"><unparsedAffiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.</unparsedAffiliation></affiliation><affiliation xml:id="af3" countryCode="GB" type="organization"><unparsedAffiliation>Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, London, SW7 2AZ, U.K.</unparsedAffiliation></affiliation></affiliationGroup><keywordGroup xml:lang="en" type="author"><keyword xml:id="kwd1">proper orthogonal decomposition</keyword><keyword xml:id="kwd2">4‐D VAR</keyword><keyword xml:id="kwd3">shallow water equations</keyword><keyword xml:id="kwd4">dual weighting</keyword><keyword xml:id="kwd5">trust‐region method</keyword><keyword xml:id="kwd6">inverse problem</keyword></keywordGroup><fundingInfo><fundingAgency>NSF</fundingAgency><fundingNumber>ATM‐0201808</fundingNumber><fundingNumber>CCF‐0635162</fundingNumber></fundingInfo><fundingInfo><fundingAgency>Natural Environment Research Council</fundingAgency><fundingNumber>NE/C51829X/1</fundingNumber></fundingInfo><abstractGroup><abstract type="main" xml:lang="en"><title type="main">Abstract</title><p>We consider a limited‐area finite‐element discretization of the shallow‐water equations model. Our purpose in this paper is to solve an inverse problem for the above model controlling its initial conditions in presence of observations being assimilated in a time interval (window of assimilation). We then attempt to obtain a reduced‐order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4‐D VAR. Different approaches of POD implementation of the reduced inverse problem are compared, including a dual‐weighed method for snapshot selection coupled with a trust‐region POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dual‐weighing choice of snapshots is combined with POD adaptivity of the trust‐region type. Results of <i>ad‐hoc</i> adaptivity of the POD 4‐D VAR turn out to yield less accurate results than trust‐region POD when compared with high‐fidelity model. Directions of future research are finally outlined. Copyright © 2009 John Wiley & Sons, Ltd.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>DUAL‐WEIGHTED TRUST‐REGION ADAPTIVE POD 4D‐VAR</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model</title></titleInfo><name type="personal"><namePart type="given">X.</namePart><namePart type="family">Chen</namePart><affiliation>Department of Mathematics, Florida State University, Tallahassee, FL, 32306, U.S.A.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">I. M.</namePart><namePart type="family">Navon</namePart><affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.</affiliation><affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306‐4120, U.S.A.===</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">F.</namePart><namePart type="family">Fang</namePart><affiliation>Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, London, SW7 2AZ, U.K.</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">2011-02-20</dateIssued><dateCaptured encoding="w3cdtf">2009-05-21</dateCaptured><dateValid encoding="w3cdtf">2009-08-27</dateValid><copyrightDate encoding="w3cdtf">2011</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">11</extent><extent unit="tables">1</extent><extent unit="references">61</extent></physicalDescription><abstract lang="en">We consider a limited‐area finite‐element discretization of the shallow‐water equations model. Our purpose in this paper is to solve an inverse problem for the above model controlling its initial conditions in presence of observations being assimilated in a time interval (window of assimilation). We then attempt to obtain a reduced‐order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4‐D VAR. Different approaches of POD implementation of the reduced inverse problem are compared, including a dual‐weighed method for snapshot selection coupled with a trust‐region POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dual‐weighing choice of snapshots is combined with POD adaptivity of the trust‐region type. Results of ad‐hoc adaptivity of the POD 4‐D VAR turn out to yield less accurate results than trust‐region POD when compared with high‐fidelity model. Directions of future research are finally outlined. Copyright © 2009 John Wiley & Sons, Ltd.</abstract><note type="funding">NSF - No. ATM‐0201808; No. CCF‐0635162; </note><note type="funding">Natural Environment Research Council - No. NE/C51829X/1; </note><subject lang="en"><genre>keywords</genre><topic>proper orthogonal decomposition</topic><topic>4‐D VAR</topic><topic>shallow water equations</topic><topic>dual weighting</topic><topic>trust‐region method</topic><topic>inverse problem</topic></subject><relatedItem type="host"><titleInfo><title>International Journal for Numerical Methods in Fluids</title></titleInfo><titleInfo type="abbreviated"><title>Int. J. Numer. Meth. 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