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  <doc>
    <id>416</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>25</pageFirst>
    <pageLast>40</pageLast>
    <pageNumber>16</pageNumber>
    <edition/>
    <issue>1st Edition</issue>
    <volume>Computational Science and Its Applications</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-08-20</completedDate>
    <publishedDate>2021-08-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Industrial Applications of Optimal Control for Partial Differential Equations on Networks: Reduction and Decomposition Methods Applied to the Discrete–Continuous Control of Gas Flow in Complex Pipe Systems</title>
    <abstract language="eng">This chapter provides an exemplary road map—in a nutshell—from a given industrial application, the control of gas networks, which is far too complex for a direct approach, to a problem that can be actually handled using well-known methods in control theory. It also provides an iterative non-overlapping domain decomposition that can be interpreted as an Uzawa method. The chapter outline two strategies. The first one can be seen as a Jacobi-type approach. In the second approach, fix the integer controls s and decompose the corresponding optimality system for the entire graph into the subgraphs Gk by a another, but very similar, non-overlapping domain decomposition. The problem is the intrinsic coupling of integer controls, continuous controls, and nonlinear dynamics on a metric graph. The idea is to introduce a virtual control that aims at controlling classical in homogeneous Neumann condition including the iteration history at the interface as inhomogeneity to the Robin-type condition that appears in the decomposition.</abstract>
    <enrichment key="SubmissionStatus">in press</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Günter Leugering</author>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/416/sharda2018-contribution-leugering.pdf</file>
  </doc>
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