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  <doc>
    <id>2598</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>55</pageFirst>
    <pageLast>56</pageLast>
    <pageNumber/>
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    <type>conferenceobject</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
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    <title language="eng">Domain decomposition method for electromagnetic scattering problems: application to EUV lithography</title>
    <parentTitle language="eng">Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices</parentTitle>
    <identifier type="doi">10.1109/NUSOD.2005.1518132</identifier>
    <author>Lin Zschiedrich</author>
    <author>Sven Burger</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <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="zschiedrich">Zschiedrich, Lin Werner</collection>
  </doc>
  <doc>
    <id>2600</id>
    <completedYear>2006</completedYear>
    <publishedYear>2006</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>12</pageFirst>
    <pageLast>32</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>188</volume>
    <type>article</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
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    <title language="eng">A new finite element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D</title>
    <parentTitle language="eng">J. Comput. Appl. Math.</parentTitle>
    <identifier type="doi">10.1016/j.cam.2005.03.047</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-7662</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Lin Zschiedrich</author>
    <author>Roland Klose</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
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  <doc>
    <id>760</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2003-11-24</completedDate>
    <publishedDate>2003-11-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">HelmPole - A finite element solver for scattering problems on unbounded domains: Implementation based on PML</title>
    <abstract language="eng">The solution of scattering problems described by the Helmholtz equation on unbounded domains is of importance for a wide variety of applications, for example in electromagnetics and acoustics. An implementation of a solver for scattering problems based on the programming language Matlab is introduced. The solver relies on the finite-element-method and on the perfectly-matched-layer-method, which allows for the simulation of scattering problems on complex geometries surrounded by inhomogeneous exterior domains. This report gives a number of detailed examples and can be understood as a user manual to the freely accessible code of the solver HelmPole.</abstract>
    <identifier type="serial">03-38</identifier>
    <identifier type="opus3-id">761</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7609</identifier>
    <author>Sven Burger</author>
    <author>Roland Klose</author>
    <author>Achim Schädle</author>
    <author>Lin Zschiedrich</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-38</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Helmholtz equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>perfectly matched layer</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="pacs" number="02.60.Cb">Numerical simulation; solution of equations</collection>
    <collection role="pacs" number="02.60.Lj">Ordinary and partial differential equations; boundary value problems</collection>
    <collection role="pacs" number="02.70.Dh">Finite-element and Galerkin methods</collection>
    <collection role="msc" number="35Q60">PDEs in connection with optics and electromagnetic theory</collection>
    <collection role="msc" number="65-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="78-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="burger">Burger, Sven</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
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    <file>https://opus4.kobv.de/opus4-zib/files/760/ZR-03-38.pdf</file>
  </doc>
  <doc>
    <id>766</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2003-12-09</completedDate>
    <publishedDate>2003-12-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal&#13;
domains in 2D</title>
    <abstract language="eng">In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.</abstract>
    <identifier type="serial">03-44</identifier>
    <identifier type="opus3-id">767</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7662</identifier>
    <identifier type="doi">10.1016/j.cam.2005.03.047</identifier>
    <enrichment key="SourceTitle">Appeared in: Journal of computational and applied mathematics, 188(2006)12-32</enrichment>
    <author>Lin Zschiedrich</author>
    <author>Roland Klose</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>perfectly matched layer</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pole condition</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="35Q60">PDEs in connection with optics and electromagnetic theory</collection>
    <collection role="msc" number="65-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/766/ZR-03-44.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/766/ZR-03-44.pdf</file>
  </doc>
  <doc>
    <id>843</id>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-01-24</completedDate>
    <publishedDate>2005-01-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fast and oblivious convolution quadrature</title>
    <abstract language="eng">We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N\, \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the convolution kernel, but instead $O(\log N)$ evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation with transparent boundary conditions.</abstract>
    <identifier type="serial">05-09</identifier>
    <identifier type="opus3-id">843</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8437</identifier>
    <enrichment key="SourceTitle">Appeared in:SIAM J. Sci. Comput. Vol. 28(2) (2005) 421-438</enrichment>
    <author>Achim Schädle</author>
    <author>Maria Lopez-Fernandez</author>
    <author>Christian Lubich</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convolution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>numerical integration</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Runge-Kutta methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Volterra integral equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>anomalous diffusion</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65R20">Integral equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/843/ZR-05-09.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/843/ZR-05-09.pdf</file>
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  <doc>
    <id>844</id>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-01-24</completedDate>
    <publishedDate>2005-01-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fast Runge-Kutta approximation of inhomogeneous parabolic equations</title>
    <abstract language="eng">The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\varepsilon$, by solving only $$O\Big(\log N\, \log \frac1\varepsilon \Big) $$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm.</abstract>
    <identifier type="serial">05-10</identifier>
    <identifier type="opus3-id">844</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8443</identifier>
    <enrichment key="SourceTitle">Appeared in: Numer. Math. 102(2005)277-291</enrichment>
    <author>Maria Lopez-Fernandez</author>
    <author>Christian Lubich</author>
    <author>Cesar Palencia</author>
    <author>Achim Schädle</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>parabolic equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Runge-Kutta methods</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65M20">Method of lines</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/844/ZR-05-10.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/844/ZR-05-10.ps</file>
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  <doc>
    <id>1916</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>729</pageFirst>
    <pageLast>796</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>4</volume>
    <type>article</type>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations</title>
    <parentTitle language="eng">Commun. Comput. Phys.</parentTitle>
    <identifier type="url">http://www.global-sci.com/openaccess/v4_729.pdf</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-10332</enrichment>
    <author>Xavier Antoine</author>
    <author>Anton Arnold</author>
    <author>Christophe Besse</author>
    <author>Matthias Ehrhardt</author>
    <author>Achim Schädle</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
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    <id>1981</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>18</pageFirst>
    <pageLast>26</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>5955</volume>
    <type>conferenceobject</type>
    <publisherName>Proc. SPIE</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Numerical Investigation of Light Scattering off Split-Ring Resonators</title>
    <parentTitle language="eng">Metamaterials</parentTitle>
    <identifier type="doi">10.1117/12.622184</identifier>
    <author>Sven Burger</author>
    <editor>T. Szoplik</editor>
    <author>Lin Zschiedrich</author>
    <editor>E. Özbay</editor>
    <author>Roland Klose</author>
    <editor>C. Soukoulis</editor>
    <author>Achim Schädle</author>
    <editor>N. Zheludev</editor>
    <author>Frank Schmidt</author>
    <author>Christian Enkrich</author>
    <author>S. Linden</author>
    <author>M. Wegener</author>
    <author>C. Soukoulis</author>
    <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="zschiedrich">Zschiedrich, Lin Werner</collection>
  </doc>
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    <id>1986</id>
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    <publishedYear>2006</publishedYear>
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    <language>eng</language>
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    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Advanced FEM Analysis of Nano-Optical Devices</title>
    <parentTitle language="eng">Proc. Symposium on Photonics Technologies for the 7th Framework Programme</parentTitle>
    <author>Sven Burger</author>
    <author>Lin Zschiedrich</author>
    <author>Achim Schädle</author>
    <author>Roland Klose</author>
    <author>Benjamin Kettner</author>
    <author>Jan Pomplun</author>
    <author>T. Pollok</author>
    <author>Frank Schmidt</author>
    <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="pollok">Pollok, Therese</collection>
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    <id>1976</id>
    <completedYear>2006</completedYear>
    <publishedYear>2006</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>72</pageFirst>
    <pageLast>82</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>6195</volume>
    <type>conferenceobject</type>
    <publisherName>Proc. SPIE</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Advanced FEM Analysis of Nano-Optical Devices</title>
    <parentTitle language="eng">Nanophotonics</parentTitle>
    <identifier type="doi">10.1117/12.662942</identifier>
    <author>Sven Burger</author>
    <editor>David L. Andrews</editor>
    <author>Achim Schädle</author>
    <editor>Jean-Michel Nunzi</editor>
    <author>Lin Zschiedrich</author>
    <editor>Andreas Ostendorf</editor>
    <author>Frank Schmidt</author>
    <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="zschiedrich">Zschiedrich, Lin Werner</collection>
  </doc>
  <doc>
    <id>1962</id>
    <completedYear>2004</completedYear>
    <publishedYear>2004</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>conferenceobject</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient Finite Element Methods for the Design of Microoptical Components</title>
    <parentTitle language="eng">Proc. Microoptics Conf. 2004</parentTitle>
    <author>Sven Burger</author>
    <author>Roland Klose</author>
    <author>Reinhard März</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <author>Lin Zschiedrich</author>
    <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="zschiedrich">Zschiedrich, Lin Werner</collection>
  </doc>
  <doc>
    <id>1963</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>164</pageFirst>
    <pageLast>173</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>5728</volume>
    <type>conferenceobject</type>
    <publisherName>Proc. SPIE</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">FEM modelling of 3D photonic crystals and photonic crystal waveguides</title>
    <parentTitle language="eng">Integrated Optics : Devices, Materials and Technologies IX</parentTitle>
    <identifier type="doi">10.1117/12.585895</identifier>
    <author>Sven Burger</author>
    <editor>Y. Sidorin</editor>
    <author>Roland Klose</author>
    <editor>Christoph Wächter</editor>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <author>Lin Zschiedrich</author>
    <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="zschiedrich">Zschiedrich, Lin Werner</collection>
  </doc>
  <doc>
    <id>1964</id>
    <completedYear>2006</completedYear>
    <publishedYear>2006</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>169</pageFirst>
    <pageLast>175</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Springer Verlag</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures</title>
    <parentTitle language="eng">Scientific Computing in Electrical Engineering</parentTitle>
    <identifier type="doi">10.1007/978-3-540-32862-9_24</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Sven Burger</author>
    <author>Roland Klose</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <author>Lin Zschiedrich</author>
    <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="zschiedrich">Zschiedrich, Lin Werner</collection>
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  <doc>
    <id>5031</id>
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    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1367</pageFirst>
    <pageLast>1390</pageLast>
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    <edition/>
    <issue>4</issue>
    <volume>29</volume>
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    <title language="eng">Transparent boundary conditions based on the pole condition for time-dependent, two-dimensional problems</title>
    <parentTitle language="eng">Numerical Methods for Partial Differential Equations</parentTitle>
    <identifier type="doi">10.1002/num.21759</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Daniel Ruprecht</author>
    <submitter>Sven Burger</submitter>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
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  <doc>
    <id>1033</id>
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    <language>eng</language>
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    <completedDate>2007-11-09</completedDate>
    <publishedDate>2007-11-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Review of Transparent and Artificial Boundary Conditions Techniques  for Linear and Nonlinear Schrödinger Equations</title>
    <abstract language="eng">In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.</abstract>
    <identifier type="serial">07-34</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1061</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10332</identifier>
    <enrichment key="SourceTitle">Appeared in: Commun. Comput. Phys. 4 (2008), 729-796</enrichment>
    <author>Xavier Antoine</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Arnold</author>
    <author>Christophe Besse</author>
    <author>Matthias Ehrhardt</author>
    <author>Achim Schädle</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-34</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schrödinger equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete convolution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>unbounded domain</value>
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    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1033/ZR_07_34.pdf</file>
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  <doc>
    <id>955</id>
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    <completedDate>2007-05-22</completedDate>
    <publishedDate>2007-05-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transparent boundary conditons for time-dependent problems</title>
    <abstract language="eng">A new approach to derive transparent boundary conditions (TBCs) for wave, Schrödinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior, and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients.</abstract>
    <identifier type="serial">07-12</identifier>
    <identifier type="opus3-id">955</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9558</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Sci. Comput., Vol. 30 (5) , 2358-2385 (2008)</enrichment>
    <author>Daniel Ruprecht</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <author>Lin Zschiedrich</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-12</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-reflecting boundary condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pole condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>wave equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schrödinger equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>drift diffusion equation</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="30E10">Approximation in the complex domain</collection>
    <collection role="msc" number="65M20">Method of lines</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/955/ZR-07-12.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/955/ZR-07-12.ps</file>
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