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Title: A truly exact perfect absorbing layer for time-harmonic acoustic wave scattering problems
Authors: Yang, Zhiguo
Wang, Li-Lian
Gao, Yang
Keywords: Science::Mathematics
Issue Date: 2021
Source: Yang, Z., Wang, L. & Gao, Y. (2021). A truly exact perfect absorbing layer for time-harmonic acoustic wave scattering problems. SIAM Journal On Scientific Computing, 43(2), A1027-A1061.
Project: MOE2018-T2-1-059
Journal: SIAM Journal on Scientific Computing
Abstract: In this paper, we design a truly exact perfect absorbing layer (PAL) for domain truncation of the two-dimensional Helmholtz equation in an unbounded domain with bounded scatterers. This technique is based on a complex compression coordinate transformation in polar coordinates and a judicious substitution of the unknown field in the artificial layer. Compared with the widely used perfectly matched layer (PML) methods, the distinctive features of PAL lie in that (i) it is truly exact in the sense that the PAL-solution is identical to the original solution in the bounded domain reduced by the truncation layer; (ii) with the substitution, the PAL-equation is free of singular coefficients and the substituted unknown field is essentially nonoscillatory in the layer; and (iii) the construction is valid for general star-shaped domain truncation. By formulating the variational formulation in Cartesian coordinates, the implementation of this technique using standard spectral-element or finite-element methods can be made easy as a usual coding practice. We provide ample numerical examples to demonstrate that this method is highly accurate and robust for very high wavenumbers and thin layers. It outperforms the classical PML and the recently advocated PML using unbounded absorbing functions. Moreover, it can fix some flaws of the PML approach.
ISSN: 1064-8275
DOI: 10.1137/19M1294071
Rights: © 2021 Society for Industrial and Applied Mathematics. All rights reserved. This paper was published in SIAM Journal on Scientific Computing and is made available with permission of Society for Industrial and Applied Mathematics.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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