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  <doc>
    <id>359</id>
    <completedYear>2020</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>28</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
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    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2020-11-29</completedDate>
    <publishedDate>2020-11-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems</title>
    <abstract language="eng">In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis is done entirely on the continuous level. A distinguishing feature of the method is that the decomposed optimality system can be interpreted as an optimality system of a local "virtual" optimal control problem. Thus, the iterative time-domain decomposition of the optimality system can be interpreted as an iterative  parallel scheme for virtual optimal control problems on the subintervals. A typical example and further comments are given to show the range of potential applications. Moreover, we provide some numerical experiments to give a first interpretation of the role of the parameters involved in the iterative process.</abstract>
    <parentTitle language="deu">SIAM Journal on Control and Optimization</parentTitle>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Richard Krug</author>
    <author>Günter Leugering</author>
    <author>Alexander Martin</author>
    <author>Martin Schmidt</author>
    <author>Dieter Weninger</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Time-domain decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Semilinear hyperbolic systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convergence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>A posteriori error estimates</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B07</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/359/time-domain-decomp_preprint.pdf</file>
  </doc>
  <doc>
    <id>427</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-10-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Space-time-domain decomposition for optimal control problems governed by linear hyperbolic systems</title>
    <abstract language="eng">In this article, we combine a domain decomposition method in space and time for optimal control problems with PDE-constraints described by Lagnese and Leugering to a simultaneous space-time decomposition applied to optimal control problems for systems of linear hyperbolic equations with distributed control. We thereby extend the recent work by Krug et al. and answer a long standing open question as to whether the combination of time- and space domain decomposition for the method under consideration can be put into one single convergent iteration procedure. The algorithm is designed for a semi-elliptic system of equations obtained from the hyperbolic optimality system by the way of reduction to the adjoint state. The focus is on the relation to the classical procedure introduced by Lions for elliptic problems.</abstract>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Günter Leugering</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Space- and time-domain decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear hyperbolic systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convergence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>A posteriori error estimates</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/427/space_time_domain_decomp.pdf</file>
  </doc>
  <doc>
    <id>415</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>18</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-08-20</completedDate>
    <publishedDate>2021-08-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Space-Time-Domain Decomposition for Optimal Control Problems Governed by Linear Hyperbolic Systems</title>
    <abstract language="eng">In this article, we combine a domain decomposition method in space and time for optimal control problems with PDE-constraints described by Lagnese and Leugering to a simultaneous space-time decomposition applied to optimal control problems for systems of linear hyperbolic equations with distributed control. We thereby extend the recent work by Krug et al. and answer a long standing open question as to whether the combination of time- and space domain decomposition for the method under consideration can be put into one single convergent iteration procedure. The algorithm is designed for a semi-elliptic system of equations obtained from the hyperbolic optimality system by the way of reduction to the adjoint state. The focus is on the relation to the classical procedure introduced by Lions for elliptic problems.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
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    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Günter Leugering</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Space- and time-domain decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear hyperbolic systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convergence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>A posteriori error estimates</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/415/space-time-domain-decompostion.pdf</file>
  </doc>
</export-example>
