<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00784187</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-20T03:01:26+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem</title>
            <author role="aut">
              <persName>
                <forename type="first">Frédéric</forename>
                <surname>Legoll</surname>
              </persName>
              <email type="md5">1e978b6a8f49ff9bf4ad9c907ff1c57f</email>
              <email type="domain">enpc.fr</email>
              <idno type="idhal" notation="string">frederic-legoll</idno>
              <idno type="idhal" notation="numeric">171652</idno>
              <idno type="halauthorid" notation="string">29758-171652</idno>
              <idno type="IDREF">https://www.idref.fr/090175077</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2334-5058</idno>
              <affiliation ref="#struct-241874"/>
              <affiliation ref="#struct-388745"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">William</forename>
                <surname>Minvielle</surname>
              </persName>
              <idno type="idhal" notation="numeric">767815</idno>
              <idno type="halauthorid" notation="string">688765-767815</idno>
              <idno type="IDREF">https://www.idref.fr/191798983</idno>
              <affiliation ref="#struct-241874"/>
              <affiliation ref="#struct-51621"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Frederic</forename>
                <surname>Legoll</surname>
              </persName>
              <email type="md5">1e978b6a8f49ff9bf4ad9c907ff1c57f</email>
              <email type="domain">enpc.fr</email>
            </editor>
            <funder ref="#projanr-38050"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-02-04 08:35:42</date>
              <date type="whenWritten">2013-01-31</date>
              <date type="whenModified">2026-01-28 15:12:03</date>
              <date type="whenReleased">2013-02-04 08:35:42</date>
              <date type="whenProduced">2015</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1302.0038"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="119613">
                <persName>
                  <forename>Frederic</forename>
                  <surname>Legoll</surname>
                </persName>
                <email type="md5">1e978b6a8f49ff9bf4ad9c907ff1c57f</email>
                <email type="domain">enpc.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00784187</idno>
            <idno type="halUri">https://hal.science/hal-00784187</idno>
            <idno type="halBibtex">legoll:hal-00784187</idno>
            <idno type="halRefHtml">&lt;i&gt;Discrete and Continuous Dynamical Systems - Series S&lt;/i&gt;, 2015, 8 (1), pp.1-27. &lt;a target="_blank" href="https://dx.doi.org/10.3934/dcdss.2015.8.1"&gt;&amp;#x27E8;10.3934/dcdss.2015.8.1&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Discrete and Continuous Dynamical Systems - Series S, 2015, 8 (1), pp.1-27. &amp;#x27E8;10.3934/dcdss.2015.8.1&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="CERMICS" corresp="ENPC">Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique</idno>
            <idno type="stamp" n="UR-NAVIER" corresp="ENPC">Laboratoire Navier</idno>
            <idno type="stamp" n="NAVIER-IRM" corresp="UR-NAVIER">IRM</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="MULTI-ECHELLE" corresp="UR-NAVIER">MULTI-ECHELLE</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="IFSTTAR">Ifsttar</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="UNIV-EIFFEL">Université Gustave Eiffel</idno>
            <idno type="stamp" n="IFSTTAR-UNIVEIFFEL">Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Frédéric</forename>
                    <surname>Legoll</surname>
                  </persName>
                  <email type="md5">1e978b6a8f49ff9bf4ad9c907ff1c57f</email>
                  <email type="domain">enpc.fr</email>
                  <idno type="idhal" notation="string">frederic-legoll</idno>
                  <idno type="idhal" notation="numeric">171652</idno>
                  <idno type="halauthorid" notation="string">29758-171652</idno>
                  <idno type="IDREF">https://www.idref.fr/090175077</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2334-5058</idno>
                  <affiliation ref="#struct-241874"/>
                  <affiliation ref="#struct-388745"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">William</forename>
                    <surname>Minvielle</surname>
                  </persName>
                  <idno type="idhal" notation="numeric">767815</idno>
                  <idno type="halauthorid" notation="string">688765-767815</idno>
                  <idno type="IDREF">https://www.idref.fr/191798983</idno>
                  <affiliation ref="#struct-241874"/>
                  <affiliation ref="#struct-51621"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">20877</idno>
                <idno type="issn">1937-1632</idno>
                <idno type="eissn">1937-1179</idno>
                <title level="j">Discrete and Continuous Dynamical Systems - Series S</title>
                <imprint>
                  <publisher>American Institute of Mathematical Sciences</publisher>
                  <biblScope unit="volume">8</biblScope>
                  <biblScope unit="issue">1</biblScope>
                  <biblScope unit="pp">1-27</biblScope>
                  <date type="datePub">2015</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1302.0038</idno>
              <idno type="doi">10.3934/dcdss.2015.8.1</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider a nonlinear convex stochastic homogenization problem, in a stationary setting. In practice, the deterministic homogenized energy density can only be approximated by a random apparent energy density, obtained by solving the corrector problem on a truncated domain. We show that the technique of antithetic variables can be used to reduce the variance of the computed quantities, and thereby decrease the computational cost at equal accuracy. This leads to an efficient approach for approximating expectations of the apparent homogenized energy density and of related quantities. The efficiency of the approach is numerically illustrated on several test cases. Some elements of analysis are also provided.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-241874" status="OLD">
          <idno type="RNSR">201421206U</idno>
          <orgName>MATHematics for MatERIALS</orgName>
          <orgName type="acronym">MATHERIALS</orgName>
          <date type="start">2014-01-01</date>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/matherials</ref>
          </desc>
          <listRelation>
            <relation active="#struct-51621" type="direct"/>
            <relation active="#struct-301545" type="direct"/>
            <relation active="#struct-86790" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-388745" status="OLD">
          <orgName>Modélisation et expérimentation multi-échelle pour les solides hétérogènes</orgName>
          <orgName type="acronym">multi-échelle</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>École des Ponts ParisTech6-8 avenue Blaise Pascal- Cité DescartesChamps-sur-MarneF-77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://navier.enpc.fr/Multi-echelle</ref>
          </desc>
          <listRelation>
            <relation active="#struct-204904" type="direct"/>
            <relation active="#struct-222110" type="indirect"/>
            <relation active="#struct-301545" type="indirect"/>
            <relation name="UMR8205" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-51621" status="OLD">
          <idno type="IdRef">151174822</idno>
          <idno type="ISNI">0000000403826254</idno>
          <idno type="RNSR">200320607R</idno>
          <idno type="ROR">https://ror.org/03wct8w46</idno>
          <idno type="Wikidata">Q51781803</idno>
          <orgName>Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique</orgName>
          <orgName type="acronym">CERMICS</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cermics.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-86790" status="OLD">
          <orgName>Inria Paris-Rocquencourt</orgName>
          <date type="end">2016-03-30</date>
          <desc>
            <address>
              <addrLine>INRIA Rocquencourt : Domaine de Voluceau, Rocquencourt B.P. 105 78153 le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris-rocquencourt</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-204904" status="OLD">
          <idno type="IdRef">144736829</idno>
          <idno type="RNSR">200718421X</idno>
          <orgName>Laboratoire Navier</orgName>
          <orgName type="acronym">navier umr 8205</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Ecole des Ponts ParisTech 6 / 8 avenue Blaise Pascal 77455 CHAMPS SUR MARNE</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://navier.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-222110" type="direct"/>
            <relation active="#struct-301545" type="direct"/>
            <relation name="UMR8205" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-222110" status="OLD">
          <idno type="ROR">https://ror.org/02xwvzv71</idno>
          <orgName>Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux</orgName>
          <orgName type="acronym">IFSTTAR</orgName>
          <date type="start">2011-01-01</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>14-20 Boulevard Newton - Cité Descartes, Champs sur Marne - F-77447 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ifsttar.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-38050" status="VALID">
          <idno type="anr">ANR-11-LABX-0022</idno>
          <idno type="program">Laboratoires d'excellence</idno>
          <orgName>MMCD</orgName>
          <desc>Modélisation et Expérimentation Multi-Echelles des Matériaux pour la Cons-truction Durable</desc>
          <date type="start">2011</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>