Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Locating multiple multiscale acoustic scatterers

Language

English

Abstract

We develop three inverse scattering schemes for locating multiple multiscale acoustic scatterers in a very general and practical setting. For all of the three locating schemes, only one single far-field measurement is used. The number of the multiple scatterer components may be unknown, and each scatterer component is allowed to be an inhomogeneous medium with an unknown content or an impenetrable obstacle of sound-soft, sound-hard, or impedance type. Moreover, the scatterers could be multiscale; i.e., some scatterers may be of regular size, and some others may be of small size in terms of the wavelength of the detecting acoustic wave. If a scatterer component is of regular size, it is required that its shape (not necessarily its orientation, size, and location) should be from an admissible class which is known in advance. The locating schemes are based on some novel indicator functions and are computationally cheap and robust against the measurement noise. Rigorous mathematical justifications are provided for each scheme, and numerical experiments are presented to demonstrate its robustness and effectiveness.

Keywords

Indicator functions, Inverse scattering, Locating, Multiscale acoustic scatterers, Single far-field measurement

Publication Date

7-2014

Source Publication Title

Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal

Volume

12

Issue

3

Start Page

927

End Page

952

Publisher

Society for Industrial and Applied Mathematics

Peer Reviewed

1

DOI

10.1137/13093409X

Link to Publisher's Edition

http://dx.doi.org/10.1137/13093409X

ISSN (print)

15403459

ISSN (electronic)

15403467

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