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  <doc>
    <id>1190</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-12-14</completedDate>
    <publishedDate>2010-12-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox</title>
    <abstract language="eng">This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.</abstract>
    <identifier type="serial">10-25</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1253</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11909</identifier>
    <enrichment key="SourceTitle">Appeared in:  A. Dedner  et al. (eds.) Advances in DUNE. Springer, 2012. 101-112</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>unknown unknown</submitter>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-25</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>partial differential equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>generic programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive methods</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65Y99">None of the above, but in this section</collection>
    <collection role="msc" number="68U20">Simulation [See also 65Cxx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1190/ZR_10_25.pdf</file>
  </doc>
  <doc>
    <id>1167</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-03-22</completedDate>
    <publishedDate>2010-03-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">State Trajectory Compression for Optimal Control with Parabolic PDEs</title>
    <abstract language="eng">In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.</abstract>
    <identifier type="serial">10-05</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1228</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11676</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Sci. Comp. 34 (1): A161-A184, 2012</enrichment>
    <author>Martin Weiser</author>
    <submitter>unknown unknown</submitter>
    <author>Sebastian Götschel</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-05</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adjoint gradient computation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trajectory storage</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M29">Methods involving duality</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="94A29">Source coding [See also 68P30]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1167/ZR-10-05.pdf</file>
  </doc>
  <doc>
    <id>1856</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-05-24</completedDate>
    <publishedDate>2013-05-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Lossy Compression in Optimal Control of Cardiac Defibrillation</title>
    <abstract language="eng">This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-18566</identifier>
    <enrichment key="SourceTitle">published in J. Sci. Comput., 60(1):35-59 (2014)</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Chamakuri Nagaiah</author>
    <author>Karl Kunisch</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-26</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>monodomain model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>defibrillation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newton-CG</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trajectory storage</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>compression</value>
    </subject>
    <collection role="msc" number="35K57">Reaction-diffusion equations</collection>
    <collection role="msc" number="35Q92">PDEs in connection with biology and other natural sciences</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="68P30">Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]</collection>
    <collection role="msc" number="94A29">Source coding [See also 68P30]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Cardio">ZIB-Cardio</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1856/ZR13-26.pdf</file>
  </doc>
  <doc>
    <id>1857</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-05-24</completedDate>
    <publishedDate>2013-05-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Lossy Compression for PDE-constrained Optimization: Adaptive Error Control</title>
    <abstract language="eng">For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of&#13;
the state equation forward in time, and one backward solve of the ad-joint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many case very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were&#13;
developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-18575</identifier>
    <enrichment key="SourceTitle">to be published in Comput. Optim. Appl.</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-27</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>semilinear parabolic PDEs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newton-CG</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trajectory storage</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>lossy compression</value>
    </subject>
    <collection role="msc" number="35K58">Semilinear parabolic equations</collection>
    <collection role="msc" number="49J20">Optimal control problems involving partial differential equations</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="68P30">Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]</collection>
    <collection role="msc" number="94A29">Source coding [See also 68P30]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1857/ZR-13-27.pdf</file>
  </doc>
  <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>7690</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>197</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>9</issue>
    <volume>12</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Compression Challenges in Large Scale Partial Differential Equation Solvers</title>
    <abstract language="eng">Solvers for partial differential equations (PDEs) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that need to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to the relatively small arithmetic intensity, and increasingly due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers over the recent decades. This paper surveys data compression challenges and discusses examples of corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to the main memory. We illustrate concepts for particular methods, with examples, and give references to alternatives.</abstract>
    <parentTitle language="eng">Algorithms</parentTitle>
    <identifier type="doi">10.3390/a12090197</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2019-09-14</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-73817</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Martin Weiser</submitter>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="projects" number="HighPerMeshes">HighPerMeshes</collection>
  </doc>
  <doc>
    <id>4269</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-10-11</completedDate>
    <publishedDate>2013-10-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reducing Memory Requirements in Scientific Computing and Optimal Control</title>
    <abstract language="eng">In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which typically are double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42695</identifier>
    <enrichment key="SourceTitle">submitted to "Multiple Shooting and Time Domain Decomposition Methods", Springer Series "Contributions in Mathematical and Computational Sciences"</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-64</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trajectory storage</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh compression</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>compression</value>
    </subject>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="68P05">Data structures</collection>
    <collection role="msc" number="68P30">Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]</collection>
    <collection role="msc" number="94A29">Source coding [See also 68P30]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4269/ZR13-64.pdf</file>
  </doc>
  <doc>
    <id>1524</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-04-30</completedDate>
    <publishedDate>2012-04-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Data Enhancement for Active Thermography</title>
    <abstract language="eng">Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-15243</identifier>
    <identifier type="url">http://qirt.gel.ulaval.ca/archives/qirt2012/papers/QIRT-2012-167.pdf</identifier>
    <enrichment key="SourceTitle">Appeared in: E-book Proceedings, Ed. by Gennaro Cardone, 11th International Conference on Quantitative Infrared Thermography, Naples, 2012, 2012-ISBN 9788890648441</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Martin Weiser</author>
    <author>Christiane Maierhofer</author>
    <author>Regina Richter</author>
    <series>
      <title>ZIB-Report</title>
      <number>12-20</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>data enhancement</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>active thermography</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quantitative reconstruction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Green's functions</value>
    </subject>
    <collection role="pacs" number="81.70.-q">Methods of materials testing and analysis (for specific chemical analysis methods, see 82.80.-d)</collection>
    <collection role="pacs" number="87.63.Hg">Thermography</collection>
    <collection role="msc" number="35K05">Heat equation</collection>
    <collection role="msc" number="65M80">Fundamental solutions, Green`s function methods, etc.</collection>
    <collection role="msc" number="68U10">Image processing</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="BAM-Thermography">BAM-Thermography</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1524/ZR-12-20.pdf</file>
  </doc>
  <doc>
    <id>4611</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>263</pageFirst>
    <pageLast>287</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reducing Memory Requirements in Scientific Computing and Optimal Control</title>
    <parentTitle language="eng">Multiple Shooting and Time Domain Decomposition Methods</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0297-zib-42695</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <editor>T. Carraro</editor>
    <author>Christoph von Tycowicz</author>
    <editor>M. Geiger</editor>
    <author>Konrad Polthier</author>
    <editor>S. Koerkel</editor>
    <author>Martin Weiser</author>
    <editor>R. Rannacher</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
  </doc>
  <doc>
    <id>4613</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted>2014</thesisYearAccepted>
    <language>eng</language>
    <pageFirst>35</pageFirst>
    <pageLast>59</pageLast>
    <pageNumber>25</pageNumber>
    <edition/>
    <issue>1</issue>
    <volume>60</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Lossy Compression in Optimal Control of Cardiac Defibrillation</title>
    <abstract language="eng">This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.</abstract>
    <parentTitle language="eng">J. Sci. Comput.</parentTitle>
    <identifier type="doi">10.1007/s10915-013-9785-x</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-18566</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Chamakuri Nagaiah</author>
    <author>Karl Kunisch</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Cardio">ZIB-Cardio</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>4615</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>83</pageFirst>
    <pageLast>89</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>6</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography</title>
    <parentTitle language="eng">Nondestructive Testing of Materials and Structures</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Martin Weiser</author>
    <author>Christiane Maierhofer</author>
    <author>Regina Richter</author>
    <author>Mathias Röllig</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="BAM-Thermography">BAM-Thermography</collection>
  </doc>
  <doc>
    <id>4600</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted>2015</thesisYearAccepted>
    <language>eng</language>
    <pageFirst>131</pageFirst>
    <pageLast>155</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>62</volume>
    <type>article</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Lossy Compression for PDE-constrained Optimization: Adaptive Error Control</title>
    <abstract language="eng">For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of&#13;
 the state equation forward in time, and one backward solve of the ad-joint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many case very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were&#13;
 developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.</abstract>
    <parentTitle language="deu">Comput. Optim. Appl.</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-18575</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">http://link.springer.com/article/10.1007/s10589-014-9712-6</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ECMath-CH9">ECMath-CH9</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </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>
  <doc>
    <id>7703</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>444</pageFirst>
    <pageLast>458</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>81</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-03-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Kaskade 7 - a Flexible Finite Element Toolbox</title>
    <abstract language="eng">Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. &#13;
&#13;
We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.</abstract>
    <parentTitle language="eng">Computers and Mathematics with Applications</parentTitle>
    <identifier type="doi">10.1016/j.camwa.2020.02.011</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-02-11</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-74616</enrichment>
    <submitter>Martin Weiser</submitter>
    <author>Sebastian Götschel</author>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="DFG-RTThermo">DFG-RTThermo</collection>
    <collection role="projects" number="ECMath-CH9">ECMath-CH9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="projects" number="HighPerMeshes">HighPerMeshes</collection>
    <collection role="projects" number="ECMath-CH20">ECMath-CH20</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>7875</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>12</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation</title>
    <abstract language="eng">Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and i) characterized regarding their cellular and matrix composition or secondly ii) treated with interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate distribution of IL-1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aim to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics.</abstract>
    <parentTitle language="eng">Biofabrication</parentTitle>
    <identifier type="doi">10.1088/1758-5090/aba08f</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">26.06.2020</enrichment>
    <author>Marie-Christin Weber</author>
    <submitter>Rainald Ehrig</submitter>
    <author>Lisa Fischer</author>
    <author>Alexandra Damerau</author>
    <author>Igor Ponomarev</author>
    <author>Moritz Pfeiffenberger</author>
    <author>Timo Gaber</author>
    <author>Sebastian Götschel</author>
    <author>Jens Lang</author>
    <author>Susanna Röblitz</author>
    <author>Frank Buttgereit</author>
    <author>Rainald Ehrig</author>
    <author>Annemarie Lang</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="projects" number="BMBF-3DInJoMo">BMBF-3DInJoMo</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>6688</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Thermografie mit optimierter Anregung für die quantitative Untersuchung von Delaminationen in kohlenstofffaserverstärkten Kunststoffen</title>
    <abstract language="deu">Da kohlenstofffaserverstärkte Kunststoffe (CFK) in anspruchsvollen sicherheitsrelevanten Einsatzgebieten wie im Automobilbau und in der Luftfahrt eingesetzt werden, besteht ein zunehmender Bedarf an zerstörungsfreien Prüfmethoden. Ziel ist die Gewährleistung der Sicherheit und Zuverlässigkeit der eingesetzten Bauteile. Aktive Thermografieverfahren ermöglichen die effiziente Prüfung großer Flächen mit hoher Auflösung in wenigen Arbeitsschritten. Ein wichtiges Teilgebiet der Prüfungen ist die Ortung und Charakterisierung von Delaminationen, die sowohl bereits in der Fertigung als auch während der Nutzung eines Bauteils auftreten können, und dessen strukturelle Integrität schwächen. ;In diesem Beitrag werden CFK-Strukturen mit künstlichen und natürlichen Delaminationen mit Hilfe unterschiedlich zeitlich modulierter Strahlungsquellen experimentell untersucht. Verwendet werden dabei Anregungen mit Blitzlampen und mit frequenzmodulierten Halogenlampen. Mittels Filterfunktionen im Zeit- und Frequenzbereich wird das Kontrast-zu-Rausch-Verhältnis (CNR) der detektierten Fehlstellen optimiert. Verglichen werden anschließend die Nachweisempfindlichkeit, das CNR und die Ortsauflösung der zu charakterisierenden Delaminationen für die unterschiedlichen Anregungs- und Auswertungstechniken. Ergänzt werden die Experimente durch numerische Simulationen des dreidimensionalen Wärmetransportes.</abstract>
    <parentTitle language="deu">NDT.net Proc. DGZfP 2017</parentTitle>
    <enrichment key="PeerReviewed">no</enrichment>
    <author>Jan Müller</author>
    <submitter>Martin Weiser</submitter>
    <author>Sebastian Götschel</author>
    <author>Martin Weiser</author>
    <author>Christiane Maierhofer</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="DFG-RTThermo">DFG-RTThermo</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
  <doc>
    <id>6701</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>363</pageFirst>
    <pageLast>371</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>incollection</type>
    <publisherName>Springer</publisherName>
    <publisherPlace>Cham</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST</title>
    <abstract language="eng">In gradient-based methods for parabolic optimal control problems, it is necessary to solve both the state equation and a backward-in-time adjoint equation in each iteration of the optimization method. In order to facilitate fully parallel gradient-type and nonlinear conjugate gradient methods for the solution of such optimal control problems, we discuss the application of the parallel-in-time method PFASST to adjoint gradient computation. In addition to enabling time parallelism, PFASST provides high flexibility for handling nonlinear equations, as well as potential extra computational savings from reusing previous solutions in the optimization loop. The approach is demonstrated here for a model reaction-diffusion optimal control problem.</abstract>
    <parentTitle language="eng">Domain Decomposition Methods in Science and Engineering XXIV</parentTitle>
    <subTitle language="deu">DD 2017.</subTitle>
    <identifier type="doi">10.1007/978-3-319-93873-8_34</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-64989</enrichment>
    <enrichment key="AcceptedDate">2018-02-15</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>
    <collection role="projects" number="HPCompression">HPCompression</collection>
  </doc>
  <doc>
    <id>7428</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">In vitro and in silico modeling of cellular and matrix-related changes during the early phase of osteoarthritis</title>
    <abstract language="eng">Understanding the pathophysiological processes of osteoarthritis (OA) require adequate model systems. Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific parts of the disease. This study aimed to combine in vitro and in silico modeling to describe cellular and matrix-related changes during the early phase of OA. We developed an in vitro OA model based on scaffold-free cartilage-like constructs (SFCCs), which was mathematically modeled using a partial differential equation (PDE) system to resemble the processes during the onset of OA. SFCCs were produced from mesenchymal stromal cells and analyzed weekly by histology and qPCR to characterize the cellular and matrix-related composition. To simulate the early phase of OA, SFCCs were treated with interleukin-1β (IL-1β), tumor necrosis factor α (TNFα) and examined after 3 weeks or cultivated another 3 weeks without inflammatory cytokines to validate the regeneration potential. Mathematical modeling was performed in parallel to the in vitro experiments. SFCCs expressed cartilage-specific markers, and after stimulation an increased expression of inflammatory markers, matrix degrading enzymes, a loss of collagen II (Col-2) and a reduced cell density was observed which could be partially reversed by retraction of stimulation. Based on the PDEs, the distribution processes within the SFCCs, including those of IL-1β, Col-2 degradation and cell number reduction was simulated. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and new therapeutic strategies.</abstract>
    <parentTitle language="eng">BioRxiv</parentTitle>
    <identifier type="doi">10.1101/725317</identifier>
    <author>Marie-Christin Weber</author>
    <submitter>Rainald Ehrig</submitter>
    <author>Lisa Fischer</author>
    <author>Alexandra Damerau</author>
    <author>Igor Ponomarev</author>
    <author>Moritz Pfeiffenberger</author>
    <author>Timo Gaber</author>
    <author>Sebastian Götschel</author>
    <author>Jens Lang</author>
    <author>Susanna Röblitz</author>
    <author>Frank Buttgereit</author>
    <author>Rainald Ehrig</author>
    <author>Annemarie Lang</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="BMBF-3DInJoMo">BMBF-3DInJoMo</collection>
  </doc>
  <doc>
    <id>7381</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>2019-07-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Lossy Compression for Large Scale PDE Problems</title>
    <abstract language="eng">Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to relatively small arithmetic intensity, and increasingly so due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers during the last decades. This paper surveys data compression challenges and corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to main memory. Exemplarily, we illustrate concepts at particular methods, and give references to alternatives.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-73817</identifier>
    <identifier type="doi">10.1101/506378</identifier>
    <enrichment key="SourceTitle">algorithms 12 (9): 197, 2019</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-32</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>partial differential equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>data compression</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>floating point compression</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>lossy compression</value>
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    <collection role="msc" number="65-02">Research exposition (monographs, survey articles)</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
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    <collection role="msc" number="68P30">Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
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    <collection role="projects" number="HighPerMeshes">HighPerMeshes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7381/ZR19-32.pdf</file>
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    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
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    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <publisherName/>
    <publisherPlace/>
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    <completedDate>--</completedDate>
    <publishedDate>2019-09-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Kaskade 7 -- a Flexible Finite Element Toolbox</title>
    <abstract language="eng">Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the Dune interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. &#13;
&#13;
We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-74616</identifier>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="AcceptedDate">2020-02-11</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-48</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>generic programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>partial differential equations</value>
    </subject>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65Y99">None of the above, but in this section</collection>
    <collection role="msc" number="68U20">Simulation [See also 65Cxx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="DFG-RTThermo">DFG-RTThermo</collection>
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    <collection role="projects" number="ECMath-CH20">ECMath-CH20</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7461/ZR19-48.pdf</file>
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