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  <doc>
    <id>864</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-05-20</completedDate>
    <publishedDate>2005-05-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology</title>
    <abstract language="eng">Adaptive numerical methods in space and time are introduced and studied for multiscale cardiac reaction-diffusion models in three dimensions. The evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated with both the anisotropic Bidomain and Monodomain models, coupled with either a variant of the simple FitzHugh-Nagumo model or the more complex phase-I Luo-Rudy ionic model. The simulations are performed with the {\sc kardos} library, that employs adaptive finite elements in space and adaptive linearly implicit methods in time. The numerical results show that this adaptive method successfully solves these complex cardiac reaction-diffusion models on three-dimensional domains of moderate sizes. By automatically adapting the spatial meshes and time steps to the proper scales in each phase of the heartbeat, the method accurately resolves the evolution of the intra- and extra-cellular potentials, gating variables and ion concentrations during the excitation, plateau and recovery phases.</abstract>
    <identifier type="serial">05-30</identifier>
    <identifier type="opus3-id">864</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8649</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM Journal on Scientific Computing vol. 28, issue 3, 2006, pp. 942-962</enrichment>
    <author>Piero Colli Franzone</author>
    <author>Peter Deuflhard</author>
    <author>Bodo Erdmann</author>
    <author>Jens Lang</author>
    <author>Luca Franco Pavarino</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-30</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction-diffusion equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cardiac Bidomain and Monodomain models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive time integration</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="ccs" number="G.4">MATHEMATICAL SOFTWARE</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="92B05">General biology and biomathematics</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/864/ZR-05-30.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/864/ZR-05-30.ps</file>
  </doc>
  <doc>
    <id>2131</id>
    <completedYear>2002</completedYear>
    <publishedYear>2002</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace>Ulm, Germany</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible</title>
    <parentTitle language="eng">proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-6403</enrichment>
    <author>Bodo Erdmann</author>
    <author>C. Kober</author>
    <author>Jens Lang</author>
    <author>Peter Deuflhard</author>
    <author>J. Zeilhofer</author>
    <author>Robert Sader</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
  </doc>
  <doc>
    <id>2267</id>
    <completedYear>2003</completedYear>
    <publishedYear>2003</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>49</pageFirst>
    <pageLast>57</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>1</volume>
    <type>bookpart</type>
    <publisherName>Universität Jena</publisherName>
    <publisherPlace>Germany</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Effiziente und zuverlässige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers</title>
    <parentTitle language="eng">Berichte des IZWR - Interdisziplinäres Zentrum für Wissenschaftliches Rechnen</parentTitle>
    <author>Jens Lang</author>
    <editor>Walter Alt</editor>
    <author>Bodo Erdmann</author>
    <editor>Martin Hermann</editor>
    <author>Cornelia Kober</author>
    <author>Peter Deuflhard</author>
    <author>Robert Sader</author>
    <author>Hans-Florian Zeilhofer</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
  </doc>
  <doc>
    <id>182</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1995-05-31</completedDate>
    <publishedDate>1995-05-31</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Algorithms in Dynamical Process Simulation</title>
    <abstract language="eng">Dynamical simulation of industrially relevant processes strongly advises the use of algorithms, which are {\em adaptive} both in time and in space discretization. The paper presents two alternatives: (a) a fully adaptive method of lines approach, which is based on finite difference methods and essentially applicable to 1D problems; (b) a fully adaptive Rothe method, which is based on a fast multilevel finite element method and applicable to 1D up to 3D.</abstract>
    <identifier type="serial">SC-95-16</identifier>
    <identifier type="opus3-id">182</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-1823</identifier>
    <enrichment key="SourceTitle">Appeared in: Topics in Industrial Mathematics. Proc. 8th Conf. of the European Consortium for Mathematics in Industry (ECMI 94). H. Neunzert (ed.) Wiley; Teubner 1996, pp. 122-137</enrichment>
    <author>Peter Deuflhard</author>
    <author>Jens Lang</author>
    <author>Ulrich Nowak</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-95-16</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/182/SC-95-16.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/182/SC-95-16.pdf</file>
  </doc>
  <doc>
    <id>1994</id>
    <completedYear>2006</completedYear>
    <publishedYear>2006</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>942</pageFirst>
    <pageLast>962</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>28</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology</title>
    <parentTitle language="eng">SIAM J. Sc. Comp.</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8649</enrichment>
    <author>Piero Colli Franzone</author>
    <author>Peter Deuflhard</author>
    <author>Bodo Erdmann</author>
    <author>Jens Lang</author>
    <author>Luca Franco Pavarino</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
  </doc>
  <doc>
    <id>2089</id>
    <completedYear>1996</completedYear>
    <publishedYear>1996</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>122</pageFirst>
    <pageLast>137</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Wiley &amp; Teubner</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Recent Progress in Dynamical Process Simulation</title>
    <parentTitle language="eng">Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94)</parentTitle>
    <author>Peter Deuflhard</author>
    <editor>H. Neunzert</editor>
    <author>Jens Lang</author>
    <author>Ulrich Nowak</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
  </doc>
  <doc>
    <id>640</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2001-07-03</completedDate>
    <publishedDate>2001-07-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible</title>
    <abstract language="eng">By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method.</abstract>
    <identifier type="serial">01-14</identifier>
    <identifier type="opus3-id">641</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6403</identifier>
    <enrichment key="SourceTitle">Appeared in: Proc. of 9th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, Ulm, Germany, 2002, CD-ROM</enrichment>
    <author>Bodo Erdmann</author>
    <author>Cornelia Kober</author>
    <author>Jens Lang</author>
    <author>Robert Sader</author>
    <author>Hans-Florian Zeilhofer</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-14</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mandible</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sensitivity analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive grid refinement</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="74B10">Linear elasticity with initial stresses</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/640/ZR-01-14.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/640/ZR-01-14.pdf</file>
  </doc>
</export-example>
