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An Alternative Derivation of the Exact DtN-Map on a Circle

Please always quote using this URN: urn:nbn:de:0297-zib-3752
  • 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.

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Metadaten
Author:Frank Schmidt
Document Type:ZIB-Report
Tag:Dirichlet-to-Neumann map; Helmholtz equation; Sommerfeld radiation condition
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C20 Models, numerical methods [See also 68U20]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N99 None of the above, but in this section
Date of first Publication:1998/12/07
Series (Serial Number):ZIB-Report (SC-98-32)
ZIB-Reportnumber:SC-98-32
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