Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Inverse scattering for an exterior Dirichlet problem


Author: S. I. Hariharan
Journal: Quart. Appl. Math. 40 (1982), 273-286
MSC: Primary 78A45; Secondary 35J05
DOI: https://doi.org/10.1090/qam/678198
MathSciNet review: 678198
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Abstract: In this paper we consider scattering due to a metallic cylinder which is in the field of a wire carrying a periodic current. The aim of the paper is to obtain information such as the location and shape of the cylinder with a knowledge of a far-field measurement in between the wire and the cylinder. The same analysis is applicable in acoustics in the situation that the cylinder is a soft-wall body and the wire is a line source. The associated direct problem in this situation is an exterior Dirichlet problem for the Helmholtz equation in two dimensions. We present an improved low-frequency estimate for the solution of this problem using integral equation methods, and our calculations on inverse scattering are accurate to this estimate. The far-field measurements are related to the solutions of boundary integral equations in the low-frequency situation. These solutions can be expressed in terms of mapping function which maps the exterior of the unknown curve onto the exterior of a unit disk. The coefficients of the Laurent expansion of the conformal transformations can be related to the far-field coefficients. The first far-field coefficient leads to the calculation of the distance between the source and the cylinder. The other coefficients are determined by placing the source in a different location and using the corresponding new far-field measurements.


References [Enhancements On Off] (What's this?)

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  • [3] S. I. Hariharan and R. C. MacCamy, Integral equation procedures for eddy current problems, J. Comput. Phys. 45 (1982), no. 1, 80–99. MR 650426, https://doi.org/10.1016/0021-9991(82)90103-6
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DOI: https://doi.org/10.1090/qam/678198
Article copyright: © Copyright 1982 American Mathematical Society


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