Integral equation procedures for eddy current problems

Hariharan, S. I.; MacCamy, R. C.

doi:10.1016/0021-9991(82)90103-6

Cited by 31 publications

(29 citation statements)

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“…A similar problem but with plane wave incidence has been recently studied by Colton [1] and Colton and Kleinmann [2]. A rigorous analysis on forward scattering in this situation has been recently given by Hariharan and MacCamy [3]. If the metal is not made of ferromagnetic material then one will obtain an interior-exterior problem with the boundary of the conductor as an interface.…”

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“…However, for a ferromagnetic conductor one will obtain an exterior Dirichlet problem. The details of this discussion are available in [3], The analysis in what follows is also applicable to acoustic wave propagation in the situation where the scatterer is a soft material. The precise model of interest is illustrated in Fig.…”

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“…The wire which is located at x0 e carries a periodic current of the form Re(/e io"). The derivation of the associated general problem is discussed in [3], For details we refer the reader to this paper and present here the particular problem. Here up is the potential due to the wire and is prescribed by up= -^/CTIx-XqI) (x e Q + ), (1.1) and P is a non-dimensional parameter which depends on the frequency a>.…”

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“…This is a standard argument. (b) The uniqueness of problems I and II are also standard, as is the existence of 4> and (i//, C) (see for example [3,4]). Our low-frequency theory is based on the existence proofs presented in [3], To present our main result we need several lemmas.…”

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“…As an aside, we would like to point out that the result of this lemma enabled us in [3] to prove the existence of the system without the condition that the mapping radius should not equal one. This is different than the proof available in [4].…”

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Inverse scattering for an exterior Dirichlet problem

Hariharan¹

1982

Quart. Appl. Math.

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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.Introduction. In this note we are interested in the scattering due to a metallic cylinder which is in a field caused by a wire carrying a periodic current. The goal is to obtain

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