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A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms

Please always quote using this URN: urn:nbn:de:0297-zib-7128
  • 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.

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Metadaten
Author:Frank Schmidt
Document Type:Habilitation
Tag:Fini; Helmholtz equation; Pole condition; Schroedinger equation; Transparent boundary conditions; Unbounded domains; Wide angle one-way equation
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Cxx Representations of solutions / 35C15 Integral representations of solutions
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:2002/11/28
Series (Serial Number):ZIB-Report (02-45)
ZIB-Reportnumber:02-45
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