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  <doc>
    <id>627</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>2001-01-09</completedDate>
    <publishedDate>2001-01-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving time-harmonic scattering problems based on the condition: Theory</title>
    <abstract language="eng">The pole condition is a general concept for the theoretical analysis and the numerical solution of a variety of wave propagation problems. It says that the Laplace transform of the physical solution in radial direction has no poles in the lower complex half-plane. In the present paper we show that for the Helmholtz equation with a radially symmetric potential the pole condition is equivalent to Sommerfeld's radiation condition. Moreover, a new representation formula based on the pole condition is derived and used to prove existence, uniqueness and asymptotic properties of solutions. This lays the foundations of a promising new algorithm to solve time-harmonic scattering problems numerically and provides a new approach for analyzing existing algorithms such as the Perfectly Matched Layer (PML) method and the Bayliss-Gunzburger-Turkel (BGT) algorithm.</abstract>
    <identifier type="serial">01-01</identifier>
    <identifier type="opus3-id">628</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6279</identifier>
    <enrichment key="SourceTitle">Appeared under the title "Solving time-harmonic scattering problems based on the condition I: Theory in: SIAM Journal on Mathematical Analysis 35 (2003) 183-210</enrichment>
    <author>Thorsten Hohage</author>
    <author>Frank Schmidt</author>
    <author>Lin Zschiedrich</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Laplace transform</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="35C10">Series solutions</collection>
    <collection role="msc" number="35C15">Integral representations of solutions</collection>
    <collection role="msc" number="35C20">Asymptotic expansions</collection>
    <collection role="msc" number="65N99">None of the above, but in this section</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/627/ZR-01-01.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/627/ZR-01-01.pdf</file>
  </doc>
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