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  <doc>
    <id>375</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1998-12-07</completedDate>
    <publishedDate>1998-12-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Alternative Derivation of the Exact DtN-Map on a Circle</title>
    <abstract language="eng">The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of time-harmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the boundary of a disc or sphere. The solution of the exterior domain problem is obtained via Laplace transformation techniques, where the asymptotic Sommerfeld radiation condition is reformulated accordingly.</abstract>
    <identifier type="serial">SC-98-32</identifier>
    <identifier type="opus3-id">376</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3752</identifier>
    <author>Frank Schmidt</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-32</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Helmholtz equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dirichlet-to-Neumann map</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Sommerfeld radiation condition</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65C20">Models, numerical methods [See also 68U20]</collection>
    <collection role="msc" number="65N99">None of the above, but in this section</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/375/SC-98-32.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/375/SC-98-32.pdf</file>
  </doc>
  <doc>
    <id>712</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>habilitation</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2002-11-28</completedDate>
    <publishedDate>2002-11-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms</title>
    <abstract language="eng">The work presents a new approach to the numerical solution of time-harmonic and time-dependent scattering problems. We replace Sommerfeld's radiation condition valid for the Helmholtz equation by a more general concept called pole condition. The pole condition is based on the Laplace transform of the exterior solution and allows a characterization of outgoing waves. Both new insight into the analysis of scattering problems as well as new numerical algorithms are obtained.</abstract>
    <identifier type="serial">02-45</identifier>
    <identifier type="opus3-id">713</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7128</identifier>
    <author>Frank Schmidt</author>
    <series>
      <title>ZIB-Report</title>
      <number>02-45</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pole condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Helmholtz equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Wide angle one-way equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schroedinger equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Transparent boundary conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Unbounded domains</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Fini</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="35C15">Integral representations of solutions</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="collections" number="">Habilitationen</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/712/ZR-02-45.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/712/ZR-02-45.pdf</file>
  </doc>
  <doc>
    <id>574</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2000-03-03</completedDate>
    <publishedDate>2000-03-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Discrete Nonreflecting Boundary Conditions for the Helmholtz Equation</title>
    <abstract language="eng">We derive exact discrete nonreflecting boundary conditions for time-harmonic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior problem as an initial value problem with initial data given on the boundary of the computational domain. The solution of the exterior problem is obtained via Laplace transformation techniques which supply the boundary conditions in terms of discrete Dirichlet-to-Neumann operators.</abstract>
    <identifier type="serial">00-06</identifier>
    <identifier type="opus3-id">575</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-5744</identifier>
    <enrichment key="SourceTitle">Appeared in: Proc. 5th Intern. Conf. on Mathematical and Numerical Aspects of Wave Propagation, Waves 2000, Santiago de Compostella, Spain. A. Bermudez, et al. (eds.) 2000 pp. 921-925</enrichment>
    <author>Frank Schmidt</author>
    <series>
      <title>ZIB-Report</title>
      <number>00-06</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Helmholtz equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary consitions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/574/ZR-00-06.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/574/ZR-00-06.pdf</file>
  </doc>
  <doc>
    <id>434</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-12-16</completedDate>
    <publishedDate>1999-12-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation</title>
    <abstract language="eng">We present nonlocal discrete transparent boundary conditions for a fourth-order wide-angle approximation of the two-dimensional Helmholtz equation. The boundary conditions are exact in the sense that they supply the same discrete solution on a bounded interior domain as would be obtained by considering the problem on the entire unbounded domain with zero boundary conditions at infinity. The proposed algorithm results in an unconditionally stable propagation method. Numerical examples from optics illustrate the efficiency of our approach.</abstract>
    <identifier type="serial">SC-99-45</identifier>
    <identifier type="opus3-id">434</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4345</identifier>
    <enrichment key="SourceTitle">Appeared in: J. Comput. Phys. 165 (2000) 645-659</enrichment>
    <author>Tilman Friese</author>
    <author>Frank Schmidt</author>
    <author>David Yevick</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-45</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Helmholtz equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Wide-angle approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Transparent boundary conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite-element method</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65M55">Multigrid methods; domain decomposition</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/434/SC-99-45.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/434/SC-99-45.pdf</file>
  </doc>
  <doc>
    <id>435</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-12-16</completedDate>
    <publishedDate>1999-12-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transparent Boundary Conditions for Split-Step Pade Approximations of the One-Way Helmholtz Equation</title>
    <abstract language="eng">In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by Schmidt and Deuflhard {[}Comp. Math. Appl. 29 (1995) 53-76{]} and Schmidt and Yevick {[}J. Comput. Phys. 134 (1997) 96-107{]} to propagation methods based on arbitrary Pad\'e approximations to the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method.</abstract>
    <identifier type="serial">SC-99-46</identifier>
    <identifier type="opus3-id">435</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4353</identifier>
    <enrichment key="SourceTitle">Appeared in: J. Comput. Phys. 170 (2001) 696-719</enrichment>
    <author>Frank Schmidt</author>
    <author>Tilmann Friese</author>
    <author>David Yevick</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-46</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Helmholtz equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Wide-angle approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pad/'e split step approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Transparent boundary conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite-element method</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65M55">Multigrid methods; domain decomposition</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/435/SC-99-46.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/435/SC-99-46.pdf</file>
  </doc>
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