<?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-00545865v2</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="2026-05-22T20:10:40+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A boundary matching micro/macro decomposition for kinetic equations</title>
            <author role="aut">
              <persName>
                <forename type="first">Mohammed</forename>
                <surname>Lemou</surname>
              </persName>
              <idno type="halauthorid">133553-0</idno>
              <affiliation ref="#struct-75"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Florian</forename>
                <surname>Méhats</surname>
              </persName>
              <email type="md5">0ef769c7b91618412070af71785cd149</email>
              <email type="domain">univ-rennes1.fr</email>
              <idno type="idhal" notation="string">florian-mehats</idno>
              <idno type="idhal" notation="numeric">832682</idno>
              <idno type="halauthorid" notation="string">133542-832682</idno>
              <affiliation ref="#struct-75"/>
              <affiliation ref="#struct-2519"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Florian</forename>
                <surname>Méhats</surname>
              </persName>
              <email type="md5">0ef769c7b91618412070af71785cd149</email>
              <email type="domain">univ-rennes1.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2010-12-14 10:35:54</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2011-02-21 17:39:28</date>
              <date type="whenWritten">2010</date>
              <date type="whenModified">2025-04-01 12:52:05</date>
              <date type="whenReleased">2011-02-21 19:11:20</date>
              <date type="whenProduced">2011</date>
              <date type="whenEndEmbargoed">2011-02-21</date>
              <ref type="file" target="https://hal.science/hal-00545865v2/document">
                <date notBefore="2011-02-21"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00545865v2/file/note-MMbord.pdf" id="file-567748-665285">
                <date notBefore="2011-02-21"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1012.2976"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="109685">
                <persName>
                  <forename>Florian</forename>
                  <surname>Méhats</surname>
                </persName>
                <email type="md5">0ef769c7b91618412070af71785cd149</email>
                <email type="domain">univ-rennes1.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00545865</idno>
            <idno type="halUri">https://hal.science/hal-00545865</idno>
            <idno type="halBibtex">lemou:hal-00545865</idno>
            <idno type="halRefHtml">&lt;i&gt;Comptes Rendus. Mathématique&lt;/i&gt;, 2011, 349 (7-8), pp.479-484. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.crma.2011.02.002"&gt;&amp;#x27E8;10.1016/j.crma.2011.02.002&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Comptes Rendus. Mathématique, 2011, 349 (7-8), pp.479-484. &amp;#x27E8;10.1016/j.crma.2011.02.002&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-567748-665285"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-RENNES1">Université de Rennes 1</idno>
            <idno type="stamp" n="IRMAR">Institut de Recherche Mathématique de Rennes</idno>
            <idno type="stamp" n="UR2-HB">Université Rennes 2 - Haute Bretagne</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="INSA-RENNES">Institut National des Sciences Appliquées de Rennes</idno>
            <idno type="stamp" n="INRIA-RENNES">INRIA Rennes - Bretagne Atlantique</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="UNAM">l'unam - université nantes angers le mans</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="IRMAR-AN">Analyse numérique</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="UR1-HAL">Publications labos UR1 dans HAL-Rennes 1</idno>
            <idno type="stamp" n="UR1-MATH-STIC">UR1 - publications Maths-STIC</idno>
            <idno type="stamp" n="AGREENIUM">Archive ouverte en agrobiosciences</idno>
            <idno type="stamp" n="UNIV-RENNES2">Université Rennes 2</idno>
            <idno type="stamp" n="TEST-UNIV-RENNES">TEST Université de Rennes</idno>
            <idno type="stamp" n="TEST-UR-CSS">TEST Université de Rennes CSS</idno>
            <idno type="stamp" n="UNIV-RENNES">Université de Rennes</idno>
            <idno type="stamp" n="INRIA-RENGRE">INRIA-RENGRE</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="UR1-MATH-NUM">Pôle UnivRennes - Mathématiques - Numérique </idno>
            <idno type="stamp" n="INSTITUT-AGRO">Institut Agro</idno>
            <idno type="stamp" n="IRMAR-ANM">Equipe Analyse numérique et modélisation - IRMAR</idno>
            <idno type="stamp" n="IRMAR-ANUM" corresp="IRMAR">Equipe Analyse numérique et modélisation - IRMAR</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">A boundary matching micro/macro decomposition for kinetic equations</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Mohammed</forename>
                    <surname>Lemou</surname>
                  </persName>
                  <idno type="halauthorid">133553-0</idno>
                  <affiliation ref="#struct-75"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Florian</forename>
                    <surname>Méhats</surname>
                  </persName>
                  <email type="md5">0ef769c7b91618412070af71785cd149</email>
                  <email type="domain">univ-rennes1.fr</email>
                  <idno type="idhal" notation="string">florian-mehats</idno>
                  <idno type="idhal" notation="numeric">832682</idno>
                  <idno type="halauthorid" notation="string">133542-832682</idno>
                  <affiliation ref="#struct-75"/>
                  <affiliation ref="#struct-2519"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">11990</idno>
                <idno type="issn">1631-073X</idno>
                <idno type="eissn">1778-3569</idno>
                <title level="j">Comptes Rendus. Mathématique</title>
                <imprint>
                  <publisher>Académie des sciences (Paris)</publisher>
                  <biblScope unit="volume">349</biblScope>
                  <biblScope unit="issue">7-8</biblScope>
                  <biblScope unit="pp">479-484</biblScope>
                  <date type="datePub">2011</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.crma.2011.02.002</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</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 introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distribution fonction $f$ in all its domain as the sum of a Maxwellian adapted to the boundary (which is not the usual Maxwellian associated with $f$) and a reminder kinetic part. This Maxwellian is defined such that its "incoming" velocity moments coincide with the "incoming" velocity moments of the distribution function. Important consequences of this strategy are the following. i) No artificial boundary condition is needed in the micro/macro models and the exact boundary condition on $f$ is naturally transposed to the macro part of the model. ii) It provides a new class of the so-called 'Asymptotic preserving' (AP) numerical schemes: such schemes are consistent with the original kinetic equation for all fixed positive value of the Knudsen number $\eps$, and if $\eps \to 0 $ and the numerical parameters are fixed, then these schemes degenerate into consistent numerical schemes for the various corresponding asymptotic fluid or diffusive models. Here, the strategy provides AP schemes not only inside the physical domain but also in the space boundary layers. We provide a numerical test in the case of a diffusion limit of the one-group transport equation, and show that our AP scheme recovers the boundary layer and a good approximation of the theoretical boundary value, which is usually computed from to the so-called Chandrasekhar function.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-75" status="OLD">
          <idno type="IdRef">028233107</idno>
          <idno type="RNSR">199612396W</idno>
          <idno type="ROR">https://ror.org/05y76vp22</idno>
          <orgName>Institut de Recherche Mathématique de Rennes</orgName>
          <orgName type="acronym">IRMAR</orgName>
          <date type="start">1996-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, bâtiments 22 et 23, 263 avenue du Général Leclerc, CS 7420535042  RENNES Cédex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://irmar.univ-rennes1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-105160" type="direct"/>
            <relation active="#struct-117606" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-247362" type="direct"/>
            <relation active="#struct-406201" type="direct"/>
            <relation name="UMR6625" active="#struct-441569" type="direct"/>
            <relation active="#struct-1090536" type="direct"/>
            <relation active="#struct-1042499" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-2519" status="OLD">
          <idno type="RNSR">200418360U</idno>
          <orgName>Invariant Preserving SOlvers</orgName>
          <orgName type="acronym">IPSO</orgName>
          <date type="start">2004-12-06</date>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/ipso</ref>
          </desc>
          <listRelation>
            <relation active="#struct-75" type="direct"/>
            <relation active="#struct-105160" type="indirect"/>
            <relation active="#struct-117606" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-247362" type="indirect"/>
            <relation active="#struct-406201" type="indirect"/>
            <relation name="UMR6625" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1090536" type="indirect"/>
            <relation active="#struct-1042499" type="indirect"/>
            <relation active="#struct-419153" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-105160" status="VALID">
          <idno type="IdRef">26693823X</idno>
          <idno type="ROR">https://ror.org/015m7wh34</idno>
          <orgName>Université de Rennes</orgName>
          <orgName type="acronym">UR</orgName>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, 263 avenue Général Leclerc, CS 74205, 35042 RENNES CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-rennes.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-117606" status="VALID">
          <idno type="ROR">https://ror.org/04xaa4j22</idno>
          <orgName>Institut National des Sciences Appliquées - Rennes</orgName>
          <orgName type="acronym">INSA Rennes</orgName>
          <desc>
            <address>
              <addrLine>20, avenue des Buttes de Coësmes - CS 70839 - 35708 Rennes cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-rennes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-247362" status="VALID">
          <idno type="ROR">https://ror.org/03rxtdc22</idno>
          <orgName>École normale supérieure - Rennes</orgName>
          <orgName type="acronym">ENS Rennes</orgName>
          <desc>
            <address>
              <addrLine>Campus de Ker Lann - avenue Robert Schuman - 35170 Bruz</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-rennes.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-406201" status="VALID">
          <idno type="IdRef">054447658</idno>
          <idno type="ISNI">0000000121522279</idno>
          <idno type="ROR">https://ror.org/01m84wm78</idno>
          <orgName>Université de Rennes 2</orgName>
          <orgName type="acronym">UR2</orgName>
          <desc>
            <address>
              <addrLine>Place du recteur Henri Le Moal - CS 24307 - 35043 Rennes cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-rennes2.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>
        <org type="institution" xml:id="struct-1090536" status="OLD">
          <idno type="ROR">https://ror.org/01s3fs709</idno>
          <orgName>INSTITUT AGRO Agrocampus Ouest</orgName>
          <date type="start">2020-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>65 rue de Saint Brieuc CS 84215 35042 Rennes CEDEX</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1042499" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-1042499" status="VALID">
          <idno type="IdRef">260373249</idno>
          <idno type="ROR">https://ror.org/01dkyve95</idno>
          <orgName>Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement</orgName>
          <orgName type="acronym">Institut Agro</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.institut-agro.fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-419153" status="VALID">
          <idno type="RNSR">198018249C</idno>
          <idno type="ROR">https://ror.org/04040yw90</idno>
          <orgName>Centre Inria de l'Université de Rennes</orgName>
          <desc>
            <address>
              <addrLine>Campus de beaulieu35042 Rennes cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/rennes</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>
      </listOrg>
    </back>
  </text>
</TEI>