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  <doc>
    <id>5039</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>2014-03-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive sampling strategies for efficient parameter scans in nano-photonic device simulations</title>
    <abstract language="eng">Rigorous optical simulations are an important tool in optimizing scattering properties of nano-photonic devices and are used, for example, in solar cell optimization. The finite element method (FEM)  yields rigorous, time-harmonic, high accuracy solutions of the full  3D vectorial Maxwell's equations [1] and furthermore allows for great  flexibility and accuracy in the geometrical modeling of these often  complex shaped 3D nano-structures. A major drawback of frequency domain  methods is the limitation of  single frequency evaluations. For example the accurate computation of  the short circuit current density of an amorphous silicon / micro-crystalline multi-junction thin film solar cell may require the solution of Maxwell's equations for over a hundred different  wavelengths if  an equidistant sampling strategy is employed. Also in optical metrology, wavelength scans are frequently used to reconstruct unknown geometrical and material properties of optical systems numerically from measured &#13;
scatterometric data.&#13;
In  our contribution we present several adaptive numerical integration and sampling  routines and study their efficiency in the context of the determination of generation rate profiles  of solar cells. We show that these strategies lead to a reduction in  the computational effort without loss of accuracy. We discuss the employment of tangential information in a Hermite interpolation scheme  to achieve similar accuracy on coarser grids. We explore the usability of these strategies for scatterometry and solar cell simulations.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.1117/12.2036363</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-50395</identifier>
    <enrichment key="SourceTitle">Appeared in Proceedings of the SPIE Volume 8980</enrichment>
    <author>Martin Hammerschmidt</author>
    <submitter>Martin Hammerschmidt</submitter>
    <author>Jan Pomplun</author>
    <author>Sven Burger</author>
    <author>Frank Schmidt</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-20</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optical simulations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optical metrology</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>parameter scans</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>solar cells</value>
    </subject>
    <collection role="pacs" number="40.00.00">ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="burger">Burger, Sven</collection>
    <collection role="persons" number="hammerschmidt">Hammerschmidt, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5039/zib_report_adaptivity.pdf</file>
  </doc>
  <doc>
    <id>5724</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>2016-02-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs</title>
    <abstract language="eng">Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for  the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-57249</identifier>
    <identifier type="doi">10.1117/12.2212482</identifier>
    <enrichment key="SourceTitle">Appeared in: Proc. SPIE 9756</enrichment>
    <author>Martin Hammerschmidt</author>
    <submitter>Martin Hammerschmidt</submitter>
    <author>Carlo Barth</author>
    <author>Jan Pomplun</author>
    <author>Sven Burger</author>
    <author>Christiane Becker</author>
    <author>Frank Schmidt</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-06</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rigorous optical modeling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>photonic crystals</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reduced basis method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>parameter estimation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optical metrology</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="pacs" number="40.00.00">ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS</collection>
    <collection role="msc" number="46-XX">FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx)</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="78-XX">OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80)</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="burger">Burger, Sven</collection>
    <collection role="persons" number="hammerschmidt">Hammerschmidt, Martin</collection>
    <collection role="projects" number="ECMath-SE6">ECMath-SE6</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5724/zibreport_fixed.pdf</file>
  </doc>
</export-example>
