| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Page(s) | S705 - S731 | |
| DOI | https://doi.org/10.1051/m2an/2020047 | |
| Published online | 26 February 2021 | |
Asymptotic behavior of acoustic waves scattered by very small obstacles
1
Magique 3D, INRIA, E2S-UPPA, LMAP UMR CNRS 5142, Pau, France
2
Department of Electrical Engineering and Computer Science, University of Liège, Liège, Belgium
* Corresponding author: sebastien.tordeux@inria.fr, sebastien.tordeux@gmail.com
Received:
3
April
2020
Accepted:
5
July
2020
The direct numerical simulation of the acoustic wave scattering created by very small obstacles is very expensive, especially in three dimensions and even more so in time domain. The use of asymptotic models is very efficient and the purpose of this work is to provide a rigorous justification of a new asymptotic model for low-cost numerical simulations. This model is based on asymptotic near-field and far-field developments that are then matched by a key procedure that we describe and demonstrate. We show that it is enough to focus on the regular part of the wave field to rigorously establish the complete asymptotic expansion. For that purpose, we provide an error estimate which is set in the whole space, including the transition region separating the near-field from the far-field area. The proof of convergence is established through Kondratiev’s seminal work on the Laplace equation and involves the Mellin transform. Numerical experiments including multiple scattering illustrate the efficiency of the resulting numerical method by delivering some comparisons with solutions computed with a finite element software.
Mathematics Subject Classification: 35C20 / 35L05 / 74J20
Key words: Acoustic wave propagation / matched asymptotic expansion method / scattering problem / Mellin transform / singularity theory
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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