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  <doc>
    <id>776</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-04-23</completedDate>
    <publishedDate>2004-04-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Affine conjugate adaptive Newton methods for nonlinear elastomechanics</title>
    <abstract language="eng">The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.</abstract>
    <identifier type="serial">04-01</identifier>
    <identifier type="opus3-id">777</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7768</identifier>
    <enrichment key="SourceTitle">Appeared in: Opt. Meth. Softw. 22(3): 413-431 (2007)</enrichment>
    <author>Martin Weiser</author>
    <author>Peter Deuflhard</author>
    <author>Bodo Erdmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>affine conjugate Newton methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonconvex minimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear elastomechnics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cranio-maxillofacial surgery</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>soft tissue simulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multilev</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="74B20">Nonlinear elasticity</collection>
    <collection role="msc" number="74G65">Energy minimization</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>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="FacialSurgery">FacialSurgery</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/776/ZR-04-01.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/776/ZR-04-01.pdf</file>
  </doc>
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