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Exponential convergence of perfectly matched layers for scattering problems with periodic surfaces

Zhang, Ruming

Abstract:
The main task in this paper is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with periodic surfaces. In [5], a linear convergence is proved for the PML method for scattering problems with rough surfaces. At the end of that paper, three important questions are asked, and the third question is if exponential convergence holds locally. In our paper, we answer this question for a special case, which is scattering problems with periodic surfaces. The result can also be easily extended to locally perturbed periodic surfaces or periodic layers. Due to technical reasons, we have to exclude all the half integer valued wavenumbers. The main idea of the proof is to apply the Floquet-Bloch transform to write the problem into an equivalent family of quasi-periodic problems, and then study the analytic extension of the quasi-periodic problems with respect to the Floquet-Bloch parameters. Then the Cauchy integral formula is applied for piecewise analytic functions to avoid linear convergent points. Finally the exponential convergence is proved from the inverse Floquet-Bloch transform. ... mehr


Volltext §
DOI: 10.5445/IR/1000135099
Veröffentlicht am 07.07.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 07.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000135099
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 16 S.
Serie CRC 1173 Preprint ; 2021/30
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter PML method, scattering problems, periodic surfaces, exponential convergence, Cauchy integral theorem
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