<?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-02909750v2</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="2026-05-18T04:54:07+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Local transparent boundary conditions for wave propagation in fractal trees (ii): error and  complexity analysis</title>
            <author role="aut">
              <persName>
                <forename type="first">Patrick</forename>
                <surname>Joly</surname>
              </persName>
              <email type="md5">5e7b04780c3208cbb369ad68508f0ad3</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">patrick-joly</idno>
              <idno type="idhal" notation="numeric">4394</idno>
              <idno type="halauthorid" notation="string">11731-4394</idno>
              <idno type="IDREF">https://www.idref.fr/071471073</idno>
              <orgName ref="#struct-0"/>
              <affiliation ref="#struct-3316"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Maryna</forename>
                <surname>Kachanovska</surname>
              </persName>
              <email type="md5">4686694b3c25046dd21c5d7b4ec66d51</email>
              <email type="domain">gmail.com</email>
              <idno type="idhal" notation="string">maryna-kachanovska</idno>
              <idno type="idhal" notation="numeric">4409</idno>
              <idno type="halauthorid" notation="string">23454-4409</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-9991-9874</idno>
              <idno type="IDREF">https://www.idref.fr/253129796</idno>
              <affiliation ref="#struct-3316"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Maryna</forename>
                <surname>Kachanovska</surname>
              </persName>
              <email type="md5">4686694b3c25046dd21c5d7b4ec66d51</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2020-07-31 10:09:35</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2020-08-03 19:02:49</date>
              <date type="whenModified">2025-10-17 08:40:58</date>
              <date type="whenReleased">2020-08-04 08:45:04</date>
              <date type="whenProduced">2022</date>
              <date type="whenEndEmbargoed">2020-08-03</date>
              <ref type="file" target="https://hal.science/hal-02909750v2/document">
                <date notBefore="2020-08-03"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-02909750v2/file/main_report.pdf" id="file-2911083-2563497">
                <date notBefore="2020-08-03"/>
              </ref>
              <ref type="externalLink" target="https://hal.archives-ouvertes.fr/hal-02909750v2/file/main_report.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="317612">
                <persName>
                  <forename>Maryna</forename>
                  <surname>Kachanovska</surname>
                </persName>
                <email type="md5">4686694b3c25046dd21c5d7b4ec66d51</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-02909750</idno>
            <idno type="halUri">https://hal.science/hal-02909750</idno>
            <idno type="halBibtex">joly:hal-02909750</idno>
            <idno type="halRefHtml">&lt;i&gt;SIAM Journal on Numerical Analysis&lt;/i&gt;, 2022, 60 (2), &lt;a target="_blank" href="https://dx.doi.org/10.1137/20M1357524"&gt;&amp;#x27E8;10.1137/20M1357524&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">SIAM Journal on Numerical Analysis, 2022, 60 (2), &amp;#x27E8;10.1137/20M1357524&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-2911083-2563497"/></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="INRIA-SACLAY" corresp="INRIA">INRIA Saclay - Ile de France</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="UMA_ENSTA">Unité de Mathématiques Appliquées (UMA)</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="IP_PARIS">Institut Polytechnique de Paris</idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="INRIAARTDOI">INRIAARTDOI</idno>
            <idno type="stamp" n="ENSTA-PARIS">ENSTA-PARIS</idno>
            <idno type="stamp" n="ENSTA">Ensta</idno>
            <idno type="stamp" n="POEMS">Propagation des Ondes : Étude Mathématique et Simulation</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">Local transparent boundary conditions for wave propagation in fractal trees (ii): error and  complexity analysis</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Patrick</forename>
                    <surname>Joly</surname>
                  </persName>
                  <email type="md5">5e7b04780c3208cbb369ad68508f0ad3</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">patrick-joly</idno>
                  <idno type="idhal" notation="numeric">4394</idno>
                  <idno type="halauthorid" notation="string">11731-4394</idno>
                  <idno type="IDREF">https://www.idref.fr/071471073</idno>
                  <orgName ref="#struct-0"/>
                  <affiliation ref="#struct-3316"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Maryna</forename>
                    <surname>Kachanovska</surname>
                  </persName>
                  <email type="md5">4686694b3c25046dd21c5d7b4ec66d51</email>
                  <email type="domain">gmail.com</email>
                  <idno type="idhal" notation="string">maryna-kachanovska</idno>
                  <idno type="idhal" notation="numeric">4409</idno>
                  <idno type="halauthorid" notation="string">23454-4409</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-9991-9874</idno>
                  <idno type="IDREF">https://www.idref.fr/253129796</idno>
                  <affiliation ref="#struct-3316"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">8479</idno>
                <idno type="issn">0036-1429</idno>
                <title level="j">SIAM Journal on Numerical Analysis</title>
                <imprint>
                  <publisher>Society for Industrial and Applied Mathematics</publisher>
                  <biblScope unit="volume">60</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <date type="datePub">2022</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1137/20M1357524</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Wave equation</term>
                <term xml:lang="en">fractal</term>
                <term xml:lang="en">metric graph</term>
                <term xml:lang="en">counting function</term>
                <term xml:lang="en">Weyl asymptotics</term>
                <term xml:lang="en">Dirchlet-to-Neumann operator</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halDomain" n="math.math-sp">Mathematics [math]/Spectral Theory [math.SP]</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>This work is dedicated to a refined error analysis of the high-order transparent boundary conditions introduced in the companion work [8] for the weighted wave equation on a fractal tree. The construction of such boundary conditions relies on truncating the meromorphic series that represents the symbol of the Dirichlet-to-Neumann operator. The error induced by the truncation depends on the behaviour of the eigenvalues and the eigenfunctions of the weighted Laplacian on a self-similar metric tree. In this work we quantify this error by computing asymptotics of the eigenvalues and bounds for Neumann traces of the eigenfunctions. We prove the sharpness of the obtained bounds for a class of self-similar trees.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-3316" status="OLD">
          <idno type="RNSR">200518328E</idno>
          <idno type="ROR">https://ror.org/03gvm2667</idno>
          <orgName>Propagation des Ondes : Étude Mathématique et Simulation</orgName>
          <orgName type="acronym">POEMS</orgName>
          <date type="start">2009-01-01</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>828, boulevard des Maréchaux, 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://poems.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-135257" type="direct"/>
            <relation active="#struct-300065" type="indirect"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7231" active="#struct-441569" type="direct"/>
            <relation active="#struct-1225635" type="direct"/>
            <relation active="#struct-118511" type="indirect"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-135257" status="OLD">
          <idno type="IdRef">203564391</idno>
          <idno type="RNSR">200022595P</idno>
          <orgName>Unité de Mathématiques Appliquées</orgName>
          <orgName type="acronym">UMA</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>828, boulevard des Maréchaux 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://uma.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300065" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300065" status="OLD">
          <idno type="IdRef">028139577</idno>
          <idno type="ISNI">0000000122070120</idno>
          <idno type="ROR">https://ror.org/0309cs235</idno>
          <idno type="Wikidata">Q838454</idno>
          <orgName>École Nationale Supérieure de Techniques Avancées</orgName>
          <orgName type="acronym">ENSTA Paris</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>828, boulevard des Maréchaux 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ensta-paris.fr/fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.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="department" xml:id="struct-1225635" status="VALID">
          <idno type="ROR">https://ror.org/026839t73</idno>
          <orgName>Centre Inria de l'Institut Polytechnique de Paris</orgName>
          <date type="start">2022-11-01</date>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'Orves –Bâtiment Alan Turing –Campus de l'École Polytechnique –91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-118511" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-118511" status="VALID">
          <idno type="RNSR">200818248E</idno>
          <idno type="ROR">https://ror.org/0315e5x55</idno>
          <orgName>Centre Inria de Saclay</orgName>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/saclay</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>