<?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-04671832</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="2026-05-24T18:55:45+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains</title>
            <author role="aut">
              <persName>
                <forename type="first">Benjamin</forename>
                <surname>Stamm</surname>
              </persName>
              <email type="md5">ab8a982d3459a79987b86a1f6680b3fa</email>
              <email type="domain">ann.jussieu.fr</email>
              <idno type="idhal" notation="string">stamm</idno>
              <idno type="idhal" notation="numeric">1511</idno>
              <idno type="halauthorid" notation="string">30537-1511</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/B-5784-2014</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-3375-483X</idno>
              <idno type="IDREF">https://www.idref.fr/189784903</idno>
              <affiliation ref="#struct-1205957"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Lambert</forename>
                <surname>Theisen</surname>
              </persName>
              <email type="md5">83f3f0a79fe1573a841920671d385832</email>
              <email type="domain">ians.uni-stuttgart.de</email>
              <ptr type="url" target="https://thsn.dev"/>
              <idno type="idhal" notation="string">lambert-theisen</idno>
              <idno type="idhal" notation="numeric">1407641</idno>
              <idno type="halauthorid" notation="string">3214081-1407641</idno>
              <idno type="ARXIV">https://arxiv.org/a/theisen_l_1</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-5460-5425</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/AAR-2324-2021</idno>
              <idno type="VIAF">https://viaf.org/viaf/8973172126418103340002</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=ZD8cDyEAAAAJ</idno>
              <affiliation ref="#struct-1205957"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Lambert</forename>
                <surname>Theisen</surname>
              </persName>
              <email type="md5">d570b57e68bb007e83095eefbb866c89</email>
              <email type="domain">rwth-aachen.de</email>
            </editor>
            <funder>This work was supported by the German Research Foundation (DFG) under project 411724963.</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-08-16 14:08:54</date>
              <date type="whenModified">2024-12-03 13:00:08</date>
              <date type="whenReleased">2024-08-16 14:08:54</date>
              <date type="whenProduced">2022-09-15</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/2110.14982"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1439378">
                <persName>
                  <forename>Lambert</forename>
                  <surname>Theisen</surname>
                </persName>
                <email type="md5">d570b57e68bb007e83095eefbb866c89</email>
                <email type="domain">rwth-aachen.de</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04671832</idno>
            <idno type="halUri">https://hal.science/hal-04671832</idno>
            <idno type="halBibtex">stamm:hal-04671832</idno>
            <idno type="halRefHtml">&lt;i&gt;SIAM Journal on Numerical Analysis&lt;/i&gt;, 2022, 60 (5), pp.2508-2537. &lt;a target="_blank" href="https://dx.doi.org/10.1137/21M1456005"&gt;&amp;#x27E8;10.1137/21M1456005&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">SIAM Journal on Numerical Analysis, 2022, 60 (5), pp.2508-2537. &amp;#x27E8;10.1137/21M1456005&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</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 Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Benjamin</forename>
                    <surname>Stamm</surname>
                  </persName>
                  <email type="md5">ab8a982d3459a79987b86a1f6680b3fa</email>
                  <email type="domain">ann.jussieu.fr</email>
                  <idno type="idhal" notation="string">stamm</idno>
                  <idno type="idhal" notation="numeric">1511</idno>
                  <idno type="halauthorid" notation="string">30537-1511</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/B-5784-2014</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-3375-483X</idno>
                  <idno type="IDREF">https://www.idref.fr/189784903</idno>
                  <affiliation ref="#struct-1205957"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Lambert</forename>
                    <surname>Theisen</surname>
                  </persName>
                  <email type="md5">83f3f0a79fe1573a841920671d385832</email>
                  <email type="domain">ians.uni-stuttgart.de</email>
                  <ptr type="url" target="https://thsn.dev"/>
                  <idno type="idhal" notation="string">lambert-theisen</idno>
                  <idno type="idhal" notation="numeric">1407641</idno>
                  <idno type="halauthorid" notation="string">3214081-1407641</idno>
                  <idno type="ARXIV">https://arxiv.org/a/theisen_l_1</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-5460-5425</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/AAR-2324-2021</idno>
                  <idno type="VIAF">https://viaf.org/viaf/8973172126418103340002</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=ZD8cDyEAAAAJ</idno>
                  <affiliation ref="#struct-1205957"/>
                </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">5</biblScope>
                  <biblScope unit="pp">2508-2537</biblScope>
                  <date type="datePub">2022-09-15</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2110.14982</idno>
              <idno type="doi">10.1137/21M1456005</idno>
              <relatedItem target="https://doi.org/10.5281/zenodo.6576197" type="Cites" subtype="http://purl.org/coar/resource_type/c_2f33"/>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Periodic Schrödinger Equation</term>
                <term xml:lang="en">Iterative Eigenvalue Solvers</term>
                <term xml:lang="en">Preconditioner</term>
                <term xml:lang="en">Asymptotic Eigenvalue Analysis</term>
                <term xml:lang="en">Factorization Principle</term>
                <term xml:lang="en">Directional Homogenization</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halDomain" n="info.info-ce">Computer Science [cs]/Computational Engineering, Finance, and Science [cs.CE]</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 paper provides a provably quasi-optimal preconditioning strategy of the linear Schrödinger eigenvalue problem with periodic potentials for a possibly non-uniform spatial expansion of the domain. The quasi-optimality is achieved by having the iterative eigenvalue algorithms converge in a constant number of iterations for different domain sizes. In the analysis, we derive an analytic factorization of the spectrum and asymptotically describe it using concepts from the homogenization theory. This decomposition allows us to express the eigenpair as an easy-to-calculate cell problem solution combined with an asymptotically vanishing remainder. We then prove that the easy-to-calculate limit eigenvalue can be used in a shift-and-invert preconditioning strategy to bound the number of eigensolver iterations uniformly. Several numerical examples illustrate the effectiveness of this quasi-optimal preconditioning strategy.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-1205957" status="INCOMING">
          <orgName>Applied and Computational Mathematics</orgName>
          <orgName type="acronym">ACoM</orgName>
          <desc>
            <address>
              <country key="DE"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1205956" type="direct"/>
            <relation active="#struct-1205955" type="indirect"/>
            <relation active="#struct-303510" type="indirect"/>
          </listRelation>
        </org>
        <org type="department" xml:id="struct-1205956" status="INCOMING">
          <orgName>Fachgruppe Mathematik</orgName>
          <desc>
            <address>
              <country key="DE"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1205955" type="direct"/>
            <relation active="#struct-303510" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1205955" status="INCOMING">
          <orgName>Fakultät für Mathematik, Informatik und Naturwissenschaften</orgName>
          <desc>
            <address>
              <country key="DE"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-303510" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-303510" status="VALID">
          <idno type="IdRef">074130323</idno>
          <idno type="ISNI">000000010728696X</idno>
          <idno type="ROR">https://ror.org/04xfq0f34</idno>
          <idno type="Wikidata">Q273263</idno>
          <orgName>RWTH Aachen University = Rheinisch-Westfälische Technische Hochschule Aachen</orgName>
          <orgName type="acronym">RWTH Aachen</orgName>
          <date type="start">1870-01-01</date>
          <desc>
            <address>
              <addrLine>RWTH Aachen –  Templergraben 55 – 52062 Aachen (Hausanschrift) – 52056 Aachen (Postanschrift) – Deutschland</addrLine>
              <country key="DE"/>
            </address>
            <ref type="url">http://www.rwth-aachen.de/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>