<?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-00661977</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="2026-05-24T22:48:05+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Toward an Optimized Global-in-Time Schwarz Algorithm for Diffusion Equations with Discontinuous and Spatially Variable Coefficients, Part 1: The Constant Coefficients Case</title>
            <author role="crp">
              <persName>
                <forename type="first">Florian</forename>
                <surname>Lemarié</surname>
              </persName>
              <email type="md5">c8365871732835642ac178194e4253ab</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">florian-lemarie</idno>
              <idno type="idhal" notation="numeric">4170</idno>
              <idno type="halauthorid" notation="string">20330-4170</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-6341-402X</idno>
              <idno type="IDREF">https://www.idref.fr/134023188</idno>
              <orgName ref="#struct-300009"/>
              <affiliation ref="#struct-44839"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Laurent</forename>
                <surname>Debreu</surname>
              </persName>
              <email type="md5">2c38e8dc75b00e25490682ad4540b711</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">laurent-debreu</idno>
              <idno type="idhal" notation="numeric">1710</idno>
              <idno type="halauthorid" notation="string">355-1710</idno>
              <idno type="IDREF">https://www.idref.fr/153106743</idno>
              <orgName ref="#struct-300009"/>
              <affiliation ref="#struct-44839"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Eric</forename>
                <surname>Blayo</surname>
              </persName>
              <email type="md5">7a05828a167b333e2dbd7351bfcce27f</email>
              <email type="domain">univ-grenoble-alpes.fr</email>
              <idno type="idhal" notation="string">eric-blayo</idno>
              <idno type="idhal" notation="numeric">11065</idno>
              <idno type="halauthorid" notation="string">5106-11065</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8742-5655</idno>
              <idno type="IDREF">https://www.idref.fr/085599050</idno>
              <affiliation ref="#struct-44839"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Florian</forename>
                <surname>Lemarié</surname>
              </persName>
              <email type="md5">c8365871732835642ac178194e4253ab</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2012-01-22 19:00:47</date>
              <date type="whenModified">2025-09-27 18:48:42</date>
              <date type="whenReleased">2012-01-22 19:06:06</date>
              <date type="whenProduced">2013</date>
              <date type="whenEndEmbargoed">2012-01-22</date>
              <ref type="file" target="https://hal.science/hal-00661977v1/document">
                <date notBefore="2012-01-22"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00661977v1/file/Lemarie_ETNA1_2011.pdf" id="file-661977-581325">
                <date notBefore="2012-01-22"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="130955">
                <persName>
                  <forename>Florian</forename>
                  <surname>Lemarié</surname>
                </persName>
                <email type="md5">c8365871732835642ac178194e4253ab</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00661977</idno>
            <idno type="halUri">https://hal.science/hal-00661977</idno>
            <idno type="halBibtex">lemarie:hal-00661977</idno>
            <idno type="halRefHtml">&lt;i&gt;Electronic Transactions on Numerical Analysis&lt;/i&gt;, 2013, 40, pp.148-169</idno>
            <idno type="halRef">Electronic Transactions on Numerical Analysis, 2013, 40, pp.148-169</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-661977-581325"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UGA">HAL Grenoble Alpes</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="UNIV-GRENOBLE1">Université Joseph Fourier - Grenoble I</idno>
            <idno type="stamp" n="UNIV-PMF_GRENOBLE">Université Pierre-Mendès-France - Grenoble II</idno>
            <idno type="stamp" n="INPG">Institut polytechnique de Grenoble</idno>
            <idno type="stamp" n="INRIA-RHA">INRIA Grenoble - Rhône-Alpes</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="LJK">Laboratoire Jean Kuntzmann</idno>
            <idno type="stamp" n="LJK_MAD" corresp="LJK">Département Modèles et Algorithmes Déterministes</idno>
            <idno type="stamp" n="LJK_MAD_MOISE" corresp="LJK_MAD">MOISE</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="UGA-TEST-QUATER">UGA-TEST-QUATER</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="INRIA-RENGRE">INRIA-RENGRE</idno>
            <idno type="stamp" n="INRIA-300009">Inria 300009</idno>
            <idno type="stamp" n="TEST-UGA">TEST-UGA</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">Toward an Optimized Global-in-Time Schwarz Algorithm for Diffusion Equations with Discontinuous and Spatially Variable Coefficients, Part 1: The Constant Coefficients Case</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Florian</forename>
                    <surname>Lemarié</surname>
                  </persName>
                  <email type="md5">c8365871732835642ac178194e4253ab</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">florian-lemarie</idno>
                  <idno type="idhal" notation="numeric">4170</idno>
                  <idno type="halauthorid" notation="string">20330-4170</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-6341-402X</idno>
                  <idno type="IDREF">https://www.idref.fr/134023188</idno>
                  <orgName ref="#struct-300009"/>
                  <affiliation ref="#struct-44839"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Laurent</forename>
                    <surname>Debreu</surname>
                  </persName>
                  <email type="md5">2c38e8dc75b00e25490682ad4540b711</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">laurent-debreu</idno>
                  <idno type="idhal" notation="numeric">1710</idno>
                  <idno type="halauthorid" notation="string">355-1710</idno>
                  <idno type="IDREF">https://www.idref.fr/153106743</idno>
                  <orgName ref="#struct-300009"/>
                  <affiliation ref="#struct-44839"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Eric</forename>
                    <surname>Blayo</surname>
                  </persName>
                  <email type="md5">7a05828a167b333e2dbd7351bfcce27f</email>
                  <email type="domain">univ-grenoble-alpes.fr</email>
                  <idno type="idhal" notation="string">eric-blayo</idno>
                  <idno type="idhal" notation="numeric">11065</idno>
                  <idno type="halauthorid" notation="string">5106-11065</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8742-5655</idno>
                  <idno type="IDREF">https://www.idref.fr/085599050</idno>
                  <affiliation ref="#struct-44839"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">777</idno>
                <idno type="issn">1068-9613</idno>
                <title level="j">Electronic Transactions on Numerical Analysis</title>
                <imprint>
                  <publisher>Kent State University Library</publisher>
                  <biblScope unit="volume">40</biblScope>
                  <biblScope unit="pp">148-169</biblScope>
                  <date type="datePub">2013</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">optimized Schwarz methods</term>
                <term xml:lang="en">waveform relaxation</term>
                <term xml:lang="en">alternating and parallel Schwarz methods</term>
              </keywords>
              <classCode scheme="classification">MSC: 65M55, 65F10, 65N22, 35K15</classCode>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</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>In this paper we present a global-in-time non-overlapping Schwarz method applied to the one dimensional unsteady diffusion equation. We address specifically the problem with discontinuous diffusion coefficients, our approach is therefore especially designed for subdomains with heterogeneous properties. We derive efficient interface conditions by solving analytically the minmax problem associated with the search for optimized conditions in a Robin-Neumann case and in a two-sided Robin-Robin case. The performance of the proposed schemes are illustrated by numerical experiments</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-44839" status="OLD">
          <idno type="RNSR">200618276U</idno>
          <orgName>Modelling, Observations, Identification for Environmental Sciences</orgName>
          <orgName type="acronym">MOISE</orgName>
          <date type="start">2007-01-01</date>
          <date type="end">2014-12-31</date>
          <desc>
            <address>
              <addrLine>Laboratoire Jean Kuntzmann B. P. 53 38041 Grenoble Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/moise</ref>
          </desc>
          <listRelation>
            <relation active="#struct-2497" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-24474" type="direct"/>
            <relation active="#struct-3886" type="indirect"/>
            <relation active="#struct-51016" type="indirect"/>
            <relation active="#struct-89889" type="direct"/>
            <relation name="UMR5224" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-2497" status="VALID">
          <idno type="RNSR">199218244V</idno>
          <idno type="ROR">https://ror.org/00n8d6z93</idno>
          <orgName>Centre Inria de l'Université Grenoble Alpes</orgName>
          <desc>
            <address>
              <addrLine>Inovallée655 avenue de l'Europe38330 Montbonnot</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/grenoble</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-24474" status="OLD">
          <idno type="IdRef">184945011</idno>
          <idno type="ISNI">0000 0004 0383 676X</idno>
          <idno type="RNSR">200711891Z</idno>
          <idno type="ROR">https://ror.org/04ett5b41</idno>
          <orgName>Laboratoire Jean Kuntzmann</orgName>
          <orgName type="acronym">LJK</orgName>
          <date type="start">2007-01-01</date>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment IMAG, CS 40700, F-38058 Grenoble Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://ljk.imag.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-3886" type="direct"/>
            <relation active="#struct-51016" type="direct"/>
            <relation active="#struct-89889" type="direct"/>
            <relation name="UMR5224" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-3886" status="OLD">
          <idno type="IdRef">02640432X</idno>
          <idno type="ROR">https://ror.org/02f7wz369</idno>
          <orgName>Université Pierre Mendès France - Grenoble 2</orgName>
          <orgName type="acronym">UPMF</orgName>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.upmf-grenoble.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-51016" status="OLD">
          <idno type="IdRef">026404796</idno>
          <idno type="ROR">https://ror.org/02aj0kh94</idno>
          <orgName>Université Joseph Fourier - Grenoble 1</orgName>
          <orgName type="acronym">UJF</orgName>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ujf-grenoble.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-89889" status="OLD">
          <idno type="IdRef">026388804</idno>
          <idno type="ROR">https://ror.org/05sbt2524</idno>
          <orgName>Institut polytechnique de Grenoble - Grenoble Institute of Technology</orgName>
          <orgName type="acronym">Grenoble INP</orgName>
          <date type="start">2007-01-01</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>46 avenue Félix Viallet 38031 Grenoble Cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.grenoble-inp.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>
    </back>
  </text>
</TEI>