Serveur d'exploration sur l'Université de Trèves

Attention, ce site est en cours de développement !
Attention, site généré par des moyens informatiques à partir de corpus bruts.
Les informations ne sont donc pas validées.

Computation of POD basis functions for fluid flows with lanczos methods

Identifieur interne : 001123 ( Istex/Corpus ); précédent : 001122; suivant : 001124

Computation of POD basis functions for fluid flows with lanczos methods

Auteurs : M. Fahl

Source :

RBID : ISTEX:81EFFF56F28DF02683ED4ED6166727B24DD84AF5

Abstract

The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows. Supposing an ensemble of solutions of the time-dependent Navier-Stokes equations at fixed time instants (snapshots) is given, the aim is to compute a few global basis functions to represent the main dynamics of the flow. The POD basis functions can be computed via a truncated singular value decomposition of the data matrix given by the snapshots, where Lanczos methods can be used to calculate the POD basis functions efficiently.

Url:
DOI: 10.1016/S0895-7177(01)00051-6

Links to Exploration step

ISTEX:81EFFF56F28DF02683ED4ED6166727B24DD84AF5

Le document en format XML

<record>
<TEI wicri:istexFullTextTei="biblStruct">
<teiHeader>
<fileDesc>
<titleStmt>
<title>Computation of POD basis functions for fluid flows with lanczos methods</title>
<author>
<name sortKey="Fahl, M" sort="Fahl, M" uniqKey="Fahl M" first="M." last="Fahl">M. Fahl</name>
<affiliation>
<mods:affiliation>Universität Trier, FB IV—Mathematik D-54286 Trier, Germany</mods:affiliation>
</affiliation>
<affiliation>
<mods:affiliation>E-mail: fahl@uni-trier.de</mods:affiliation>
</affiliation>
</author>
</titleStmt>
<publicationStmt>
<idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:81EFFF56F28DF02683ED4ED6166727B24DD84AF5</idno>
<date when="2001" year="2001">2001</date>
<idno type="doi">10.1016/S0895-7177(01)00051-6</idno>
<idno type="url">https://api.istex.fr/document/81EFFF56F28DF02683ED4ED6166727B24DD84AF5/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001123</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001123</idno>
</publicationStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title level="a">Computation of POD basis functions for fluid flows with lanczos methods</title>
<author>
<name sortKey="Fahl, M" sort="Fahl, M" uniqKey="Fahl M" first="M." last="Fahl">M. Fahl</name>
<affiliation>
<mods:affiliation>Universität Trier, FB IV—Mathematik D-54286 Trier, Germany</mods:affiliation>
</affiliation>
<affiliation>
<mods:affiliation>E-mail: fahl@uni-trier.de</mods:affiliation>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series>
<title level="j">Mathematical and Computer Modelling</title>
<title level="j" type="abbrev">MCM</title>
<idno type="ISSN">0895-7177</idno>
<imprint>
<publisher>ELSEVIER</publisher>
<date type="published" when="2001">2001</date>
<biblScope unit="volume">34</biblScope>
<biblScope unit="issue">1–2</biblScope>
<biblScope unit="page" from="91">91</biblScope>
<biblScope unit="page" to="107">107</biblScope>
</imprint>
<idno type="ISSN">0895-7177</idno>
</series>
<idno type="istex">81EFFF56F28DF02683ED4ED6166727B24DD84AF5</idno>
<idno type="DOI">10.1016/S0895-7177(01)00051-6</idno>
<idno type="PII">S0895-7177(01)00051-6</idno>
</biblStruct>
</sourceDesc>
<seriesStmt>
<idno type="ISSN">0895-7177</idno>
</seriesStmt>
</fileDesc>
<profileDesc>
<textClass></textClass>
<langUsage>
<language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front>
<div type="abstract" xml:lang="en">The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows. Supposing an ensemble of solutions of the time-dependent Navier-Stokes equations at fixed time instants (snapshots) is given, the aim is to compute a few global basis functions to represent the main dynamics of the flow. The POD basis functions can be computed via a truncated singular value decomposition of the data matrix given by the snapshots, where Lanczos methods can be used to calculate the POD basis functions efficiently.</div>
</front>
</TEI>
<istex>
<corpusName>elsevier</corpusName>
<author>
<json:item>
<name>M. Fahl</name>
<affiliations>
<json:string>Universität Trier, FB IV—Mathematik D-54286 Trier, Germany</json:string>
<json:string>E-mail: fahl@uni-trier.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>Singular value decomposition</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>Lanczos method</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>Fluid flow</value>
</json:item>
</subject>
<language>
<json:string>eng</json:string>
</language>
<originalGenre>
<json:string>Full-length article</json:string>
</originalGenre>
<abstract>The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows. Supposing an ensemble of solutions of the time-dependent Navier-Stokes equations at fixed time instants (snapshots) is given, the aim is to compute a few global basis functions to represent the main dynamics of the flow. The POD basis functions can be computed via a truncated singular value decomposition of the data matrix given by the snapshots, where Lanczos methods can be used to calculate the POD basis functions efficiently.</abstract>
<qualityIndicators>
<score>6.008</score>
<pdfVersion>1.2</pdfVersion>
<pdfPageSize>526 x 760 pts</pdfPageSize>
<refBibsNative>true</refBibsNative>
<keywordCount>4</keywordCount>
<abstractCharCount>540</abstractCharCount>
<pdfWordCount>5271</pdfWordCount>
<pdfCharCount>30901</pdfCharCount>
<pdfPageCount>17</pdfPageCount>
<abstractWordCount>84</abstractWordCount>
</qualityIndicators>
<title>Computation of POD basis functions for fluid flows with lanczos methods</title>
<pii>
<json:string>S0895-7177(01)00051-6</json:string>
</pii>
<refBibs>
<json:item>
<host>
<author></author>
</host>
</json:item>
<json:item>
<author>
<json:item>
<name>J. Peterson</name>
</json:item>
</author>
<host>
<volume>10</volume>
<pages>
<last>786</last>
<first>777</first>
</pages>
<issue>4</issue>
<author></author>
<title>SIAM J. Sci. Comput.</title>
</host>
<title>The reduced basis method for incompressible viscous flow calculations</title>
</json:item>
<json:item>
<host>
<author></author>
<title>Reduced basis method for optimal control of unsteady viscous flows</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
<title>On suboptimal control strategies for the Navier-Stokes equations</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
</host>
</json:item>
<json:item>
<author>
<json:item>
<name>L. Sirovich</name>
</json:item>
</author>
<host>
<volume>45</volume>
<pages>
<last>571</last>
<first>561</first>
</pages>
<issue>3</issue>
<author></author>
<title>Quart. Appl. Math.</title>
</host>
<title>Turbulence and the dynamics of coherent structures, Part I: Coherent structures</title>
</json:item>
<json:item>
<host>
<author></author>
<title>Galerkin proper orthogonal decomposition methods for parabolic problems</title>
</host>
</json:item>
<json:item>
<author>
<json:item>
<name>K. Kunisch</name>
</json:item>
<json:item>
<name>S. Volkwein</name>
</json:item>
</author>
<host>
<volume>102</volume>
<pages>
<last>371</last>
<first>345</first>
</pages>
<issue>2</issue>
<author></author>
<title>J. Optim. Theory Appl.</title>
</host>
<title>Control of Burgers' equation by a reduced order approach using proper orthogonal decomposition</title>
</json:item>
<json:item>
<host>
<author></author>
<title>Reduced order controllers for spatially distributed systems via proper orthogonal decomposition</title>
</host>
</json:item>
<json:item>
<author>
<json:item>
<name>C. Eckart</name>
</json:item>
<json:item>
<name>G. Young</name>
</json:item>
</author>
<host>
<volume>1</volume>
<pages>
<last>218</last>
<first>211</first>
</pages>
<author></author>
<title>Psychometrika</title>
</host>
<title>The approximation of one matrix by another of lower rank</title>
</json:item>
<json:item>
<host>
<author></author>
<title>Modeling and control of physical processes using proper orthogonal decomposition</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
<title>Proper orthgonal decomposition for reduced basis feedback controllers for parabolic equations</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
<title>Evaluation of material integrity using reduced order computational methodology</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
</host>
</json:item>
<json:item>
<author>
<json:item>
<name>P.C. Hansen</name>
</json:item>
</author>
<host>
<author></author>
<title>SIAM</title>
</host>
<title>Rank-deficient and discrete ill-posed problems</title>
</json:item>
<json:item>
<host>
<author></author>
</host>
</json:item>
<json:item>
<host>
<author></author>
</host>
</json:item>
<json:item>
<author>
<json:item>
<name>Y. Saad</name>
</json:item>
</author>
<host>
<volume>17</volume>
<pages>
<last>706</last>
<first>687</first>
</pages>
<issue>5</issue>
<author></author>
<title>SIAM J. Numer. Anal.</title>
</host>
<title>On the rates of convergence of the Lanczos and the block-Lanczos methods</title>
</json:item>
<json:item>
<author>
<json:item>
<name>D.C. Sorensen</name>
</json:item>
</author>
<host>
<volume>13</volume>
<pages>
<last>385</last>
<first>357</first>
</pages>
<issue>1</issue>
<author></author>
<title>SIAM J. Matrix Anal. Appl.</title>
</host>
<title>Implicit application of polynomial filters in a k-step Arnoldi method</title>
</json:item>
<json:item>
<host>
<author></author>
<title>Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
<title>Reduced order model feedback control design: Numerical implementation in a thin shell model</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
<title>Proper orthogonal decomposition based control of transverse beam vibrations: Experimental implementation</title>
</host>
</json:item>
<json:item>
<host>
<author></author>
<title>Reduced order model compensator control of species transport in a cvd reactor</title>
</host>
</json:item>
<json:item>
<author>
<json:item>
<name>M. Rajaee</name>
</json:item>
<json:item>
<name>S.K.F. Karlsson</name>
</json:item>
<json:item>
<name>L. Sirovich</name>
</json:item>
</author>
<host>
<volume>258</volume>
<pages>
<last>29</last>
<first>1</first>
</pages>
<author></author>
<title>J. Fluid Mech.</title>
</host>
<title>Low-dimensional description of free-shear-flow coherent structures and their dynamical behavior</title>
</json:item>
</refBibs>
<genre>
<json:string>research-article</json:string>
</genre>
<host>
<volume>34</volume>
<pii>
<json:string>S0895-7177(00)X0109-4</json:string>
</pii>
<pages>
<last>107</last>
<first>91</first>
</pages>
<issn>
<json:string>0895-7177</json:string>
</issn>
<issue>1–2</issue>
<genre>
<json:string>journal</json:string>
</genre>
<language>
<json:string>unknown</json:string>
</language>
<title>Mathematical and Computer Modelling</title>
<publicationDate>2001</publicationDate>
</host>
<categories>
<wos>
<json:string>science</json:string>
<json:string>mathematics, applied</json:string>
<json:string>computer science, software engineering</json:string>
<json:string>computer science, interdisciplinary applications</json:string>
</wos>
<scienceMetrix>
<json:string>natural sciences</json:string>
<json:string>mathematics & statistics</json:string>
<json:string>numerical & computational mathematics</json:string>
</scienceMetrix>
</categories>
<publicationDate>2001</publicationDate>
<copyrightDate>2001</copyrightDate>
<doi>
<json:string>10.1016/S0895-7177(01)00051-6</json:string>
</doi>
<id>81EFFF56F28DF02683ED4ED6166727B24DD84AF5</id>
<score>1.656456</score>
<fulltext>
<json:item>
<extension>pdf</extension>
<original>true</original>
<mimetype>application/pdf</mimetype>
<uri>https://api.istex.fr/document/81EFFF56F28DF02683ED4ED6166727B24DD84AF5/fulltext/pdf</uri>
</json:item>
<json:item>
<extension>zip</extension>
<original>false</original>
<mimetype>application/zip</mimetype>
<uri>https://api.istex.fr/document/81EFFF56F28DF02683ED4ED6166727B24DD84AF5/fulltext/zip</uri>
</json:item>
<istex:fulltextTEI uri="https://api.istex.fr/document/81EFFF56F28DF02683ED4ED6166727B24DD84AF5/fulltext/tei">
<teiHeader>
<fileDesc>
<titleStmt>
<title level="a">Computation of POD basis functions for fluid flows with lanczos methods</title>
</titleStmt>
<publicationStmt>
<authority>ISTEX</authority>
<publisher>ELSEVIER</publisher>
<availability>
<p>ELSEVIER</p>
</availability>
<date>2001</date>
</publicationStmt>
<notesStmt>
<note>Supported by the “Deutsche Forchungsgemeinschaft” through the Graduiertenkolleg “Mathematische Optimierung” at the University of Trier.</note>
<note>The author wishes to thank the referees for their corrections and suggestions.</note>
</notesStmt>
<sourceDesc>
<biblStruct type="inbook">
<analytic>
<title level="a">Computation of POD basis functions for fluid flows with lanczos methods</title>
<author xml:id="author-1">
<persName>
<forename type="first">M.</forename>
<surname>Fahl</surname>
</persName>
<email>fahl@uni-trier.de</email>
<affiliation>Universität Trier, FB IV—Mathematik D-54286 Trier, Germany</affiliation>
</author>
</analytic>
<monogr>
<title level="j">Mathematical and Computer Modelling</title>
<title level="j" type="abbrev">MCM</title>
<idno type="pISSN">0895-7177</idno>
<idno type="PII">S0895-7177(00)X0109-4</idno>
<imprint>
<publisher>ELSEVIER</publisher>
<date type="published" when="2001"></date>
<biblScope unit="volume">34</biblScope>
<biblScope unit="issue">1–2</biblScope>
<biblScope unit="page" from="91">91</biblScope>
<biblScope unit="page" to="107">107</biblScope>
</imprint>
</monogr>
<idno type="istex">81EFFF56F28DF02683ED4ED6166727B24DD84AF5</idno>
<idno type="DOI">10.1016/S0895-7177(01)00051-6</idno>
<idno type="PII">S0895-7177(01)00051-6</idno>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc>
<creation>
<date>2001</date>
</creation>
<langUsage>
<language ident="en">en</language>
</langUsage>
<abstract xml:lang="en">
<p>The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows. Supposing an ensemble of solutions of the time-dependent Navier-Stokes equations at fixed time instants (snapshots) is given, the aim is to compute a few global basis functions to represent the main dynamics of the flow. The POD basis functions can be computed via a truncated singular value decomposition of the data matrix given by the snapshots, where Lanczos methods can be used to calculate the POD basis functions efficiently.</p>
</abstract>
<textClass>
<keywords scheme="keyword">
<list>
<head>Keywords</head>
<item>
<term>Proper orthogonal decomposition</term>
</item>
<item>
<term>Singular value decomposition</term>
</item>
<item>
<term>Lanczos method</term>
</item>
<item>
<term>Fluid flow</term>
</item>
</list>
</keywords>
</textClass>
</profileDesc>
<revisionDesc>
<change when="2001">Published</change>
</revisionDesc>
</teiHeader>
</istex:fulltextTEI>
<json:item>
<extension>txt</extension>
<original>false</original>
<mimetype>text/plain</mimetype>
<uri>https://api.istex.fr/document/81EFFF56F28DF02683ED4ED6166727B24DD84AF5/fulltext/txt</uri>
</json:item>
</fulltext>
<metadata>
<istex:metadataXml wicri:clean="Elsevier, elements deleted: tail">
<istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration>
<istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType>
<istex:document>
<converted-article version="4.5.2" docsubtype="fla">
<item-info>
<jid>MCM</jid>
<aid>01000516</aid>
<ce:pii>S0895-7177(01)00051-6</ce:pii>
<ce:doi>10.1016/S0895-7177(01)00051-6</ce:doi>
<ce:copyright type="unknown" year="2001"></ce:copyright>
</item-info>
<head>
<ce:article-footnote>
<ce:label></ce:label>
<ce:note-para>Supported by the “Deutsche Forchungsgemeinschaft” through the Graduiertenkolleg “Mathematische Optimierung” at the University of Trier.</ce:note-para>
</ce:article-footnote>
<ce:article-footnote>
<ce:label>☆☆</ce:label>
<ce:note-para>The author wishes to thank the referees for their corrections and suggestions.</ce:note-para>
</ce:article-footnote>
<ce:title>Computation of POD basis functions for fluid flows with lanczos methods</ce:title>
<ce:author-group>
<ce:author>
<ce:given-name>M.</ce:given-name>
<ce:surname>Fahl</ce:surname>
<ce:e-address>fahl@uni-trier.de</ce:e-address>
</ce:author>
<ce:affiliation>
<ce:textfn>Universität Trier, FB IV—Mathematik D-54286 Trier, Germany</ce:textfn>
</ce:affiliation>
</ce:author-group>
<ce:abstract>
<ce:section-title>Abstract</ce:section-title>
<ce:abstract-sec>
<ce:simple-para>The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows. Supposing an ensemble of solutions of the time-dependent Navier-Stokes equations at fixed time instants (snapshots) is given, the aim is to compute a few global basis functions to represent the main dynamics of the flow. The POD basis functions can be computed via a truncated singular value decomposition of the data matrix given by the snapshots, where Lanczos methods can be used to calculate the POD basis functions efficiently.</ce:simple-para>
</ce:abstract-sec>
</ce:abstract>
<ce:keywords>
<ce:section-title>Keywords</ce:section-title>
<ce:keyword>
<ce:text>Proper orthogonal decomposition</ce:text>
</ce:keyword>
<ce:keyword>
<ce:text>Singular value decomposition</ce:text>
</ce:keyword>
<ce:keyword>
<ce:text>Lanczos method</ce:text>
</ce:keyword>
<ce:keyword>
<ce:text>Fluid flow</ce:text>
</ce:keyword>
</ce:keywords>
</head>
</converted-article>
</istex:document>
</istex:metadataXml>
<mods version="3.6">
<titleInfo>
<title>Computation of POD basis functions for fluid flows with lanczos methods</title>
</titleInfo>
<titleInfo type="alternative" contentType="CDATA">
<title>Computation of POD basis functions for fluid flows with lanczos methods</title>
</titleInfo>
<name type="personal">
<namePart type="given">M.</namePart>
<namePart type="family">Fahl</namePart>
<affiliation>Universität Trier, FB IV—Mathematik D-54286 Trier, Germany</affiliation>
<affiliation>E-mail: fahl@uni-trier.de</affiliation>
<role>
<roleTerm type="text">author</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="research-article" displayLabel="Full-length article"></genre>
<originInfo>
<publisher>ELSEVIER</publisher>
<dateIssued encoding="w3cdtf">2001</dateIssued>
<copyrightDate encoding="w3cdtf">2001</copyrightDate>
</originInfo>
<language>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
<languageTerm type="code" authority="rfc3066">en</languageTerm>
</language>
<physicalDescription>
<internetMediaType>text/html</internetMediaType>
</physicalDescription>
<abstract lang="en">The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows. Supposing an ensemble of solutions of the time-dependent Navier-Stokes equations at fixed time instants (snapshots) is given, the aim is to compute a few global basis functions to represent the main dynamics of the flow. The POD basis functions can be computed via a truncated singular value decomposition of the data matrix given by the snapshots, where Lanczos methods can be used to calculate the POD basis functions efficiently.</abstract>
<note>Supported by the “Deutsche Forchungsgemeinschaft” through the Graduiertenkolleg “Mathematische Optimierung” at the University of Trier.</note>
<note>The author wishes to thank the referees for their corrections and suggestions.</note>
<subject>
<genre>Keywords</genre>
<topic>Proper orthogonal decomposition</topic>
<topic>Singular value decomposition</topic>
<topic>Lanczos method</topic>
<topic>Fluid flow</topic>
</subject>
<relatedItem type="host">
<titleInfo>
<title>Mathematical and Computer Modelling</title>
</titleInfo>
<titleInfo type="abbreviated">
<title>MCM</title>
</titleInfo>
<genre type="journal">journal</genre>
<originInfo>
<dateIssued encoding="w3cdtf">200107</dateIssued>
</originInfo>
<identifier type="ISSN">0895-7177</identifier>
<identifier type="PII">S0895-7177(00)X0109-4</identifier>
<part>
<date>200107</date>
<detail type="volume">
<number>34</number>
<caption>vol.</caption>
</detail>
<detail type="issue">
<number>1–2</number>
<caption>no.</caption>
</detail>
<extent unit="issue pages">
<start>1</start>
<end>242</end>
</extent>
<extent unit="pages">
<start>91</start>
<end>107</end>
</extent>
</part>
</relatedItem>
<identifier type="istex">81EFFF56F28DF02683ED4ED6166727B24DD84AF5</identifier>
<identifier type="DOI">10.1016/S0895-7177(01)00051-6</identifier>
<identifier type="PII">S0895-7177(01)00051-6</identifier>
<recordInfo>
<recordContentSource>ELSEVIER</recordContentSource>
</recordInfo>
</mods>
</metadata>
<serie></serie>
</istex>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001123 | SxmlIndent | more

Ou

HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 001123 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Rhénanie
   |area=    UnivTrevesV1
   |flux=    Istex
   |étape=   Corpus
   |type=    RBID
   |clé=     ISTEX:81EFFF56F28DF02683ED4ED6166727B24DD84AF5
   |texte=   Computation of POD basis functions for fluid flows with lanczos methods
}}

Wicri

This area was generated with Dilib version V0.6.31.
Data generation: Sat Jul 22 16:29:01 2017. Site generation: Wed Feb 28 14:55:37 2024