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Perfectly-matched-layer truncation is exponentially accurate at high frequency

Galkowski, JE; Lafontaine, D; Spence, EA; (2022) Perfectly-matched-layer truncation is exponentially accurate at high frequency. Cornell University: Ithaca, NY, USA. Green open access

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Abstract

We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the PML solution is exponentially close, both in frequency and the tangent of the scaling angle, to the true scattering solution. Moreover, for a fixed scaling angle and large enough PML width, the PML solution is exponentially close to the true scattering solution in both frequency and the PML width. In fact, the exponential bound holds with rate of decay c (omicrontanθ − C)k where omicron is the PML width and θ is the scaling angle. More generally, the results of the paper hold in the framework of black-box scattering under the assumption of an exponential bound on the norm of the cutoff resolvent, thus including problems with strong trapping. These are the first results on the exponential accuracy of PML at high-frequency with non-trivial scatterers.

Type: Working / discussion paper
Title: Perfectly-matched-layer truncation is exponentially accurate at high frequency
Open access status: An open access version is available from UCL Discovery
Publisher version: https://doi.org/10.48550/arXiv.2105.07737
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10128041
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