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  <doc>
    <id>1094</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-10-24</completedDate>
    <publishedDate>2008-10-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Properties of Reduced Reversible Markov Chains</title>
    <abstract language="eng">The enormous time lag between fast atomic motion and complex pro- tein folding events makes it almost impossible to compute molecular dy- namics on a high resolution. A common way to tackle this problem is to model the system dynamics as a Markov process. Yet for large molec- ular systems the resulting Markov chains can hardly be handled due to the curse of dimensionality. Coarse graining methods can be used to re- duce the dimension of a Markov chain, but it is still unclear how far the coarse grained Markov chain resembles the original system. In order to answer this question, two different coarse-graining methods were analysed and compared: a classical set-based reduction method and an alternative subspace-based approach, which is based on membership vectors instead of sets. On the basis of a small toy system, it could be shown, that in con- trast to the subset-based approach, the subspace-based reduction method preserves the Markov property as well as the essential dynamics of the original system.</abstract>
    <identifier type="serial">08-42</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1130</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10941</identifier>
    <author>Fiete Haack</author>
    <submitter>unknown unknown</submitter>
    <advisor>Marcus Weber</advisor>
    <series>
      <title>ZIB-Report</title>
      <number>08-42</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov Chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>PCCA+</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Conformation dynamics</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="60J22">Computational methods in Markov chains [See also 65C40]</collection>
    <collection role="msc" number="62-07">Data analysis</collection>
    <collection role="msc" number="65C40">Computational Markov chains</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1094/ZR_08_42.pdf</file>
  </doc>
  <doc>
    <id>1096</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-11-10</completedDate>
    <publishedDate>2008-11-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Plausibility Check of an Asymptotic Column Model for Deep Convective Clouds</title>
    <abstract language="eng">By use of asymptotic analysis Carqué et al. [ZIB-Report 08-03] derived an asymptotic column model for deep convective clouds based on the three dimensional compressible flow equations and a bulk microphysics parameterization. In the present study we check the plausibility of the reduced model equations by comparing implications of the model for the scaling of various terms in the governing equations with those extracted from large eddy simulation data based on the computational model UCLA-LES1.1. This code solves an anelastic system of equations with complete droplet based microphysics and LES closures. We observe that the simulation data corroborate the basic assumptions of the asymptotic analysis and the main conclusions implied by the asymptotically reduced model. The code output reflects the scales of space and time: The deep convective clouds show an anisotropic structure where the horizontal scale is considerably narrower than the vertical scale; with a period of about 20 min, from emergence to breakup, the life cycle of one particular deep convective cloud corresponds exactly to the reference time of the reduced model. The characteristic properties of dynamics as predicted by the reduced model are also reflected in the simulation data: The horizontal flow is controlled by the pressure field; the vertical velocity develops freely independent of pressure over the depth of the convective column; the vertical velocity is directly determined by the buoyancy induced by the potential temperature deviation relative to the background stratification. With respect to grid resolution we observe that refining the spatial step size of the equidistant computational grid from 125 m to 62.5 m does not influence the results: Even with the coarser grid the relevant physical phenomena are sufficiently resolved. Somewhat surprisingly, the Coriolis term involving vertical velocity and acting on the horizontal (east-west) velocity component appears at leading order in the asymptotics. Accordingly, we expected to find a nontrivial impact of this Coriolis effect on the horizontal flow velocity components within columns of updrafts. However, switching the term on and off in subsequent simulations did not sizeably affect the results.</abstract>
    <identifier type="serial">08-44</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1133</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10967</identifier>
    <author>Gunter Carqué</author>
    <submitter>unknown unknown</submitter>
    <author>Heiko Schmidt</author>
    <author>Bjorn Stevens</author>
    <author>Rupert Klein</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>atmospheric moist convection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>deep convection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>precipitating clouds</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>asymptotic analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Large Eddy Simulation</value>
    </subject>
    <collection role="ddc" number="550">Geowissenschaften</collection>
    <collection role="pacs" number="92.60.-e">Properties and dynamics of the atmosphere; meteorology (see also 92.40.Zg Hydrometeorology, hydroclimatology)</collection>
    <collection role="pacs" number="92.60.Nv">Cloud physics and chemistry</collection>
    <collection role="msc" number="76M45">Asymptotic methods, singular perturbations</collection>
    <collection role="msc" number="76U05">Rotating fluids</collection>
    <collection role="msc" number="86A10">Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1096/ZR_08_44.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1096/ZR-08-44.ps</file>
  </doc>
  <doc>
    <id>1098</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-12-01</completedDate>
    <publishedDate>2008-12-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Development and test of a numerical model for pulse thermography in civil engineering</title>
    <abstract language="eng">Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.</abstract>
    <identifier type="serial">08-45</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1135</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10980</identifier>
    <enrichment key="SourceTitle">Appeared in: Heat and Mass Transfer: Volume 46, Issue 11(2010), Page 1419</enrichment>
    <author>Martin Weiser</author>
    <submitter>unknown unknown</submitter>
    <author>Mathias Röllig</author>
    <author>Ralf Arndt</author>
    <author>Bodo Erdmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-45</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>KARDOS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pulse thermography</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>civil engineering</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>inverse solution</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="pacs" number="44.05.+e">Analytical and numerical techniques</collection>
    <collection role="pacs" number="44.20.+b">Boundary layer heat flow</collection>
    <collection role="msc" number="65M50">Mesh generation and refinement</collection>
    <collection role="msc" number="80M10">Finite element methods</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/1098/ZR_08_45.pdf</file>
  </doc>
  <doc>
    <id>1100</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-12-10</completedDate>
    <publishedDate>2008-12-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity</title>
    <abstract language="eng">We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.</abstract>
    <identifier type="serial">09-01</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1139</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11007</identifier>
    <enrichment key="SourceTitle">A rev. vers. appeared u. the title "An interior point algorithm with inexact step computation in function space for state constrained optimal control" in: Numerische Mathematik 119(2): 373-407(2011)</enrichment>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <author>Andreas Günther</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptivity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M05">Methods based on necessary conditions</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1100/ZR_09_01.pdf</file>
  </doc>
  <doc>
    <id>1071</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-03-26</completedDate>
    <publishedDate>2008-03-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The minimization of an L^{\infty}-functional subject to an elliptic PDE and state constraints</title>
    <abstract language="eng">We study the optimal control of a maximum-norm objective functional subject to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L^{\infty}-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.</abstract>
    <identifier type="serial">08-17</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1100</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10714</identifier>
    <enrichment key="SourceTitle">Appeared under the title "The Minimization of a maximum-norm functional subject to an elliptic PDE and state constraints" in: Z. angew. Math. Mech., 89(7): 536-551, 2009</enrichment>
    <author>Uwe Prüfert</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-17</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M30">Other methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1071/ZR_08_17.pdf</file>
  </doc>
  <doc>
    <id>1077</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-07-09</completedDate>
    <publishedDate>2008-07-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Mehr Mathematik wagen in der Medizin</title>
    <abstract language="deu">Der Artikel gibt einen Einblick in das reiche Feld der Zusammenarbeit zwischen Mathematik und Medizin. Beispielhaft werden drei Erfolgsmodelle dargestellt: Medizinische Bildgebung, mathematische Modellierung und Biosignalverarbeitung im Bereich der Dynamik des Herzens sowie mathematische Modellierung und Simulation in der Krebstherapie Hyperthermie und der Mund-Kiefer-Gesichts-Chirurgie. In allen Fällen existiert ein Gleichklang der Interessen von Medizin und Mathematik: Beide Disziplinen wollen die Resultate schnell und zuverlässig. Für die Klinik heißt das, dass notwendige Rechnungen in möglichst kurzer Zeit, und zwar auf dem PC, ablaufen müssen und dass die Resultate so genau und belastbar sein müssen, dass medizinische Entscheidungen darauf aufbauen können. Für die Mathematik folgt daraus, dass höchste Anforderungen an die Effizienz der verwendeten Algorithmen und die darauf aufbauende Software in Numerik und Visualisierung zu stellen sind. Jedes Kapitel endet mit einer Darstellung der Perspektive des jeweiligen Gebietes. Abschließend werden mögliche Handlungsoptionen für Politik und Wirtschaft diskutiert.</abstract>
    <identifier type="serial">08-25</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1111</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10776</identifier>
    <enrichment key="SourceTitle">Ersch. in: Produktionsfaktor Mathematik : wie Mathematik Technik und Wirtschaft bewegt / Martin Grötschel, Klaus Lucas, Volker Mehrmann (Hrsg.) Berlin : Springer, 2009. (acatech diskutiert) ISBN 978-3-540-89434-6 S. 435-459</enrichment>
    <author>Peter Deuflhard</author>
    <submitter>unknown unknown</submitter>
    <author>Olaf Dössel</author>
    <submitter>unknown unknown</submitter>
    <author>Alfred Louis</author>
    <author>Stefan Zachow</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-25</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="zachow">Zachow, Stefan</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1077/ZR_08_25.pdf</file>
  </doc>
  <doc>
    <id>1079</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-07-10</completedDate>
    <publishedDate>2008-07-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Perturbation Result for Dynamical Contact Problems</title>
    <abstract language="eng">This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.</abstract>
    <identifier type="serial">08-27</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1113</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10793</identifier>
    <enrichment key="SourceTitle">Appeared in: Numer. Math. Theor. Meth. Appl. 2 (2009)</enrichment>
    <author>Corinna Klapproth</author>
    <submitter>unknown unknown</submitter>
    <author>Peter Deuflhard</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-27</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dynamical contact problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>(visco-)elasticity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Signorini condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newmark method</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="35L85">Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]</collection>
    <collection role="msc" number="74H55">Stability</collection>
    <collection role="msc" number="74M15">Contact</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1079/ZR_08_27.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1079/ZR_08_27.ps</file>
  </doc>
  <doc>
    <id>1087</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-08-25</completedDate>
    <publishedDate>2008-08-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An efficient analysis of rare events in canonical ensemble dynamics</title>
    <abstract language="eng">For an analysis of a molecular system from a computational statistical thermodynamics point of view, extensive molecular dynamics simulations are very inefficient. During this procedure, at lot of redundant data is generated. Whereas the algorithms spend most of the computing time for a sampling of configurations within the basins of the potential energy landscape of the molecular system, the important information about the long-time behaviour of the molecules is given by transition regions and barriers between the basins, which are sampled rarely only. Thinking of molecular dynamics trajectories, researchers try to figure out which kind of dynamical model is suitable for an efficient simulation. This article suggests to change the point of view from extensive simulation of molecular dynamics trajectories to more efficient sampling strategies of the conformation dynamics approach.</abstract>
    <identifier type="serial">08-36</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1123</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10871</identifier>
    <author>Marcus Weber</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>08-36</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Moleküldynamik</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Kanonische Gesamtheit</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Metastabilität</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>canonical ensemble</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <collection role="ddc" number="500">Naturwissenschaften und Mathematik</collection>
    <collection role="pacs" number="02.70.Hm">Spectral methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1087/ZR_08_36.pdf</file>
  </doc>
  <doc>
    <id>1101</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-12-10</completedDate>
    <publishedDate>2008-12-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient Constraints</title>
    <abstract language="eng">In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.</abstract>
    <identifier type="serial">08-47</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1138</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11014</identifier>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <author>Winnifried Wollner</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-47</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>necessary optimality conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convergence of the central path</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gradient constrained optimization</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M05">Methods based on necessary conditions</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1101/ZR_08_47.pdf</file>
  </doc>
  <doc>
    <id>1104</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-12-12</completedDate>
    <publishedDate>2008-12-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Buoyancy-reversal in cloud-top mixing layers</title>
    <abstract language="eng">A theoretical and numerical small-scale study of the evaporative cooling phenomenon that might appear in the stratocumulus-topped boundary layers is presented. An ideal configuration of a cloud-top mixing layer is considered as defined by two nonturbulent horizontal layers, stably stratified and with buoyancy reversal within a certain range of mixture fractions due to the evaporative cooling. Linear stability analysis of the shear-free configuration is employed to provide a new interpretation of the buoyancy reversal parameter, namely, in terms of a time-scale ratio between the unstable and the stable modes of the system. An incompressible high-order numerical algorithm to perform direct numerical simulation of the configuration is described and two-dimensional simulations of single-mode perturbations are discussed. These simulations confirm the role of the different parameters identified in the linear stability analysis and show that convoluted flow patterns can be generated by the evaporative cooling even for the low levels of buoyancy reversal found in stratocumulus clouds. They also show that there is no enhancement of entrainment of upper layer fluid in the shear-free configuration, and mixing enhancement by the evaporative cooling is restricted to the lower layer.</abstract>
    <identifier type="serial">08-50</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1142</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11046</identifier>
    <author>Juan Pedro Mellado</author>
    <submitter>unknown unknown</submitter>
    <author>Bjorn Stevens</author>
    <author>Heiko Schmidt</author>
    <author>Norbert Peters</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-50</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Stratocumulus Wolken</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>freie Konvektion</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>turbulente Strömungen</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stratocumulus</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>free convection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>free turbulent flows</value>
    </subject>
    <collection role="ddc" number="550">Geowissenschaften</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1104/ZR_08_50.pdf</file>
  </doc>
  <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>1312</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-06-16</completedDate>
    <publishedDate>2011-06-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Convergence Analysis of Smoothing Methods for Optimal Control of Stationary Variational Inequalities</title>
    <abstract language="eng">In the article an optimal control problem subject to a stationary variational inequality&#13;
is investigated. The optimal control problem is complemented with pointwise control constraints.&#13;
The convergence of a smoothing scheme is analyzed. There, the variational inequality&#13;
is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal&#13;
control problem converge to solutions of the original one. Passing to the limit in the&#13;
optimality system of the regularized problem allows to prove C-stationarity of local solutions of the original problem.&#13;
Moreover, convergence rates with respect to the regularization parameter for the error in the control are obtained.&#13;
These rates coincide with rates obtained by numerical experiments, which are included in the paper.</abstract>
    <identifier type="serial">11-23</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-13125</identifier>
    <author>Anton Schiela</author>
    <submitter>Anton Schiela</submitter>
    <author>Daniel Wachsmuth</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-23</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Variational inequalities</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>control constraints</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>path-following</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>C-stationarity</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1312/ZR-11-23.pdf</file>
  </doc>
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