Perfectly-Matched-Layer Truncation is Exponentially Accurate at High Frequency - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2023

Perfectly-Matched-Layer Truncation is Exponentially Accurate at High Frequency

Jeffrey Galkowski
Euan Spence

Résumé

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(wtanθ−C)k where w 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.

Dates et versions

hal-04284815 , version 1 (14-11-2023)

Identifiants

Citer

Jeffrey Galkowski, David Lafontaine, Euan Spence. Perfectly-Matched-Layer Truncation is Exponentially Accurate at High Frequency. SIAM Journal on Mathematical Analysis, 2023, 55 (4), pp.3344-3394. ⟨10.1137/21M1443716⟩. ⟨hal-04284815⟩
36 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More