Solving time-harmonic scattering problems based on the condition: Theory

Please always quote using this URN: urn:nbn:de:0297-zib-6279
  • 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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Thorsten Hohage, Frank Schmidt, Lin Zschiedrich
Document Type:ZIB-Report
Tag:Laplace transform; Sommerfeld radiation condition; transparent boundary conditions
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Cxx Representations of solutions / 35C10 Series solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Cxx Representations of solutions / 35C15 Integral representations of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Cxx Representations of solutions / 35C20 Asymptotic expansions
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N99 None of the above, but in this section
Date of first Publication:2001/01/09
Series (Serial Number):ZIB-Report (01-01)
Published in: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