A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model
Identifieur interne : 000A17 ( Main/Exploration ); précédent : 000A16; suivant : 000A18A dual‐weighted trust‐region adaptive POD 4D‐VAR applied to a finite‐element shallow‐water equations model
Auteurs : X. Chen [États-Unis] ; I. M. Navon [États-Unis] ; F. Fang [Royaume-Uni]Source :
- 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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Chen</name><affiliation wicri:level="1"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Department of Mathematics, Florida State University, Tallahassee, FL, 32306</wicri:regionArea><wicri:noRegion>32306</wicri:noRegion></affiliation></author><author><name sortKey="Navon, I M" sort="Navon, I M" uniqKey="Navon I" first="I. M." last="Navon">I. M. 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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><affiliations><list><country><li>Royaume-Uni</li><li>États-Unis</li></country></list><tree><country name="États-Unis"><noRegion><name sortKey="Chen, X" sort="Chen, X" uniqKey="Chen X" first="X." last="Chen">X. Chen</name></noRegion><name sortKey="Navon, I M" sort="Navon, I M" uniqKey="Navon I" first="I. M." last="Navon">I. M. Navon</name><name sortKey="Navon, I M" sort="Navon, I M" uniqKey="Navon I" first="I. M." last="Navon">I. M. Navon</name></country><country name="Royaume-Uni"><noRegion><name sortKey="Fang, F" sort="Fang, F" uniqKey="Fang F" first="F." last="Fang">F. Fang</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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