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

05/17/2021
by   Jeffrey Galkowski, et al.
0

We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We show that for any fixed perfectly-matched-layer (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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/12/2022

Asymptotic expansions of high-frequency multiple scattering iterations for sound hard scattering problems

We consider the two-dimensional high-frequency plane wave scattering pro...
research
07/12/2022

The hp-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect

We consider approximation of the variable-coefficient Helmholtz equation...
research
02/25/2021

Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method

Over the last ten years, results from [Melenk-Sauter, 2010], [Melenk-Sau...
research
11/02/2022

Higher order convergence of perfectly matched layers in 3D bi-periodic surface scattering problems

The perfectly matched layer (PML) is a very popular tool in the truncati...
research
12/21/2021

Super-localized Orthogonal Decomposition for high-frequency Helmholtz problems

We propose a novel variant of the Localized Orthogonal Decomposition (LO...
research
07/21/2019

Convergence analysis of the PML method for time-domain electromagnetic scattering problems

In this paper, a perfectly matched layer (PML) method is proposed to sol...
research
11/25/2019

A sharp relative-error bound for the Helmholtz h-FEM at high frequency

For the h-finite-element method (h-FEM) applied to the Helmholtz equatio...

Please sign up or login with your details

Forgot password? Click here to reset