<?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-04911125</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="2026-05-04T09:04:35+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Structural schemes for Hamiltonian systems</title>
            <author role="aut">
              <persName>
                <forename type="first">Stéphane</forename>
                <surname>Clain</surname>
              </persName>
              <idno type="halauthorid">1570-0</idno>
              <affiliation ref="#struct-94655"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Emmanuel</forename>
                <surname>Franck</surname>
              </persName>
              <email type="md5">275c9eb4fa9df177346d393edaaae8ce</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">emmanuel-franck</idno>
              <idno type="idhal" notation="numeric">2593</idno>
              <idno type="halauthorid" notation="string">11406-2593</idno>
              <idno type="IDREF">https://www.idref.fr/166942642</idno>
              <affiliation ref="#struct-1194409"/>
              <affiliation ref="#struct-93707"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Victor</forename>
                <surname>Michel-Dansac</surname>
              </persName>
              <email type="md5">83874dfd9a2f5b3d6ffcc218506a4f05</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">victormichel-dansac</idno>
              <idno type="idhal" notation="numeric">2407</idno>
              <idno type="halauthorid" notation="string">35073-2407</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3859-8517</idno>
              <idno type="IDREF">https://www.idref.fr/19781283X</idno>
              <affiliation ref="#struct-1194409"/>
              <affiliation ref="#struct-93707"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Victor</forename>
                <surname>Michel-Dansac</surname>
              </persName>
              <email type="md5">83874dfd9a2f5b3d6ffcc218506a4f05</email>
              <email type="domain">inria.fr</email>
            </editor>
            <funder ref="#projanr-153168"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-01-24 15:57:18</date>
              <date type="whenWritten">2025-01</date>
              <date type="whenModified">2025-06-04 08:38:32</date>
              <date type="whenReleased">2025-01-24 16:52:25</date>
              <date type="whenProduced">2025-01</date>
              <date type="whenEndEmbargoed">2025-01-24</date>
              <ref type="file" target="https://hal.science/hal-04911125v1/document">
                <date notBefore="2025-01-24"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04911125v1/file/Clain_Franck_Michel-Dansac.pdf" id="file-4911125-4264243">
                <date notBefore="2025-01-24"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2501.13515"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="192831">
                <persName>
                  <forename>Victor</forename>
                  <surname>Michel-Dansac</surname>
                </persName>
                <email type="md5">83874dfd9a2f5b3d6ffcc218506a4f05</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04911125</idno>
            <idno type="halUri">https://hal.science/hal-04911125</idno>
            <idno type="halBibtex">clain:hal-04911125</idno>
            <idno type="halRefHtml">2025</idno>
            <idno type="halRef">2025</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4911125-4264243"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <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="IRMA">Institut de Recherche Mathématique Avancée</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="UNIV-STRASBG">Université de Strasbourg</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</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="SITE-ALSACE">Archive ouverte du site Alsace</idno>
            <idno type="stamp" n="IRMAMOCO" corresp="IRMA">Modélisation et contrôle</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="UNIVOAK">UNIVOAK</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Structural schemes for Hamiltonian systems</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Stéphane</forename>
                    <surname>Clain</surname>
                  </persName>
                  <idno type="halauthorid">1570-0</idno>
                  <affiliation ref="#struct-94655"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Emmanuel</forename>
                    <surname>Franck</surname>
                  </persName>
                  <email type="md5">275c9eb4fa9df177346d393edaaae8ce</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">emmanuel-franck</idno>
                  <idno type="idhal" notation="numeric">2593</idno>
                  <idno type="halauthorid" notation="string">11406-2593</idno>
                  <idno type="IDREF">https://www.idref.fr/166942642</idno>
                  <affiliation ref="#struct-1194409"/>
                  <affiliation ref="#struct-93707"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Victor</forename>
                    <surname>Michel-Dansac</surname>
                  </persName>
                  <email type="md5">83874dfd9a2f5b3d6ffcc218506a4f05</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">victormichel-dansac</idno>
                  <idno type="idhal" notation="numeric">2407</idno>
                  <idno type="halauthorid" notation="string">35073-2407</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3859-8517</idno>
                  <idno type="IDREF">https://www.idref.fr/19781283X</idno>
                  <affiliation ref="#struct-1194409"/>
                  <affiliation ref="#struct-93707"/>
                </author>
              </analytic>
              <monogr>
                <imprint>
                  <date type="datePub">2025-01-23</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2501.13515</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Structural method</term>
                <term xml:lang="en">Compact schemes</term>
                <term xml:lang="en">Hamiltonian systems</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We present an adaptation of the so-called structural method [see Clain, Machado and Malheiro, 2023] for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem into two sets of equations: the physical equations, which describe the local dynamics of the system, and the structural equations, which only involve the discretization on a very compact stencil. They have desirable properties, such as unconditional stability or high-order accuracy. We first give a general description of the scheme for the scalar case (which corresponds to e.g. spring-mass interactions or pendulum motion), before extending the technique to the vector case (treating e.g. the $n$-body system). The scheme is also written in the case of a non-separable system (e.g. a charged particle in an electromagnetic field). We give numerical evidence of the method's efficiency, its capacity to preserve invariant quantities such as the total energy, and draw comparisons with the traditional symplectic methods.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-94655" status="VALID">
          <orgName>Center for Mathematics [Coimbra]</orgName>
          <orgName type="acronym">CMUC</orgName>
          <desc>
            <address>
              <addrLine>Department of Mathematics - Apartado 3008, EC Santa Cruz, 3001-501 Coimbra</addrLine>
              <country key="PT"/>
            </address>
            <ref type="url">http://www.mat.uc.pt/~cmuc/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300707" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-1194409" status="VALID">
          <idno type="RNSR">202424531P</idno>
          <idno type="ROR">https://ror.org/03de2ht59</idno>
          <orgName>Apprentissage automatique pour des méthodes numériques optimisées</orgName>
          <orgName type="acronym">MACARON</orgName>
          <date type="start">2024-04-01</date>
          <date type="end">2028-03-31</date>
          <desc>
            <address>
              <addrLine>Centre Inria de l'Université de Lorraine , 615 Rue du Jardin-Botanique, 54600 Villers-lès-Nancy</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-93707" type="direct"/>
            <relation active="#struct-199013" type="indirect"/>
            <relation name="UMR7501" active="#struct-441569" type="indirect"/>
            <relation active="#struct-129671" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-93707" status="VALID">
          <idno type="IdRef">026571641</idno>
          <idno type="ISNI">0000000121732313</idno>
          <idno type="RNSR">199212569B</idno>
          <idno type="ROR">https://ror.org/02hwgty18</idno>
          <idno type="Wikidata">Q3152101</idno>
          <orgName>Institut de Recherche Mathématique Avancée</orgName>
          <orgName type="acronym">IRMA</orgName>
          <date type="start">2009-01-01</date>
          <desc>
            <address>
              <addrLine>7 rue René-Descartes, 67084 Strasbourg Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://irma.math.unistra.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-199013" type="direct"/>
            <relation name="UMR7501" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300707" status="VALID">
          <idno type="IdRef">026430339</idno>
          <idno type="ISNI">0000 0000 9511 4342</idno>
          <idno type="ROR">https://ror.org/04z8k9a98</idno>
          <idno type="Wikidata">Q368643</idno>
          <orgName>Universidade de Coimbra = University of Coimbra [Portugal]</orgName>
          <orgName type="acronym">UC</orgName>
          <date type="start">1290-01-01</date>
          <desc>
            <address>
              <addrLine>Rua LargaEdifício Faculdade de Medicina (R/Ch. Esq.)3004-504 Coimbra</addrLine>
              <country key="PT"/>
            </address>
            <ref type="url">http://www.uc.pt/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-199013" status="VALID">
          <idno type="IdRef">131056549</idno>
          <idno type="ROR">https://ror.org/00pg6eq24</idno>
          <orgName>Université de Strasbourg</orgName>
          <orgName type="acronym">UNISTRA</orgName>
          <desc>
            <address>
              <addrLine>4 rue Blaise Pascal - CS 90032 - 67081 Strasbourg cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.unistra.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="laboratory" xml:id="struct-129671" status="VALID">
          <idno type="RNSR">198618246Y</idno>
          <idno type="ROR">https://ror.org/03fcjvn64</idno>
          <orgName>Centre Inria de l'Université de Lorraine</orgName>
          <desc>
            <address>
              <addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/nancy</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>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-153168" status="VALID">
          <idno type="anr">ANR-24-CE46-7505</idno>
          <orgName>SMEAGOL</orgName>
          <desc>Méthode structurelle – Application à des systèmes hyperboliques généraux</desc>
          <date type="start">2024</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>