Solving time-harmonic scattering problems based on the pole condition: Convergence of the PML method

Please always quote using this URN: urn:nbn:de:0297-zib-6494
  • In this paper we study the PML method for Helmholtz-type scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a \textbf{P}erfectly \textbf{M}atched sponge \textbf{L}ayer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral eqaution techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution.

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Metadaten
Author:Thorsten Hohage, Frank Schmidt, Lin Zschiedrich
Document Type:ZIB-Report
Tag:PML; pole condition; transparent boundary conditions
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N12 Stability and convergence of numerical methods
Date of first Publication:2001/09/26
Series (Serial Number):ZIB-Report (01-23)
Published in:Appeared under the title "Solving time-hamonic scattering problems based on the pole condition II: Convergence of the PML method" in: SIAM Journal on Mathematical Analysis 35 (2003) 547-560