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An inverse problem for the Helmholtz equation involving two semi-infinite fluids

Chakrabarti, A and Daripa, Prabir and Roy, S (2002) An inverse problem for the Helmholtz equation involving two semi-infinite fluids. In: Inverse Problems in Engineering, 10 (3). pp. 203-214.

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/1068276...


An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two fluids, and (iii) the strength of an acoustic source assumed to be situated at the interface of the two fluids. These are determined from the pressure on the interface produced by the acoustic source. The effect of the surface tension force at the interface is taken into account in this paper. The application of the proposed analytical method to solve the inverse problem is also illustrated with several examples. In particular, exact solutions of two direct problems are first derived using standard classical methods which are then used in our proposed inverse method to recover the unknowns of the corresponding inverse problems. The results are found to be in excellent agreement.

Item Type: Journal Article
Publication: Inverse Problems in Engineering
Publisher: Taylor and Francis Group
Additional Information: Copyright of this article belongs to Taylor and Francis Group.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 04 Aug 2011 05:44
Last Modified: 12 Oct 2018 14:00
URI: http://eprints.iisc.ac.in/id/eprint/38987

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