<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>7149</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2019-01-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs</title>
    <abstract language="eng">To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE constrained optimization. In order to develop an efficient fully time-parallel algorithm we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and adjoint equations simultaneously. We also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a non-linear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-71490</identifier>
    <enrichment key="AcceptedDate">2019-09-18</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="SourceTitle">SIAM J. Sci. Comput. 41(6):C603-C626, 2019</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Michael L. Minion</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-04</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>PDE-constrained optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>parallel-in-time methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>PFASST</value>
    </subject>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65M55">Multigrid methods; domain decomposition</collection>
    <collection role="msc" number="65M70">Spectral, collocation and related methods</collection>
    <collection role="msc" number="65Y05">Parallel computation</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="projects" number="DFG-RTThermo">DFG-RTThermo</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7149/ZR-19-04.pdf</file>
  </doc>
  <doc>
    <id>7547</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>C603</pageFirst>
    <pageLast>C626</pageLast>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>41</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs</title>
    <abstract language="eng">To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. We also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.</abstract>
    <parentTitle language="eng">SIAM J. Sci. Comput.</parentTitle>
    <identifier type="doi">10.1137/19M1239313</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-71490</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Michael L. Minion</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="projects" number="DFG-RTThermo">DFG-RTThermo</collection>
  </doc>
</export-example>
