Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle

Ivanyshyn, Olha and Johansson, Tomas (2007). Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle. Journal of Integral Equations and Applications, 19 (3), pp. 289-308.

Abstract

The problem considered is that of determining the shape of a planar acoustically sound-soft obstacle from knowledge of the far-field pattern for one time-harmonic incident field. Two methods, which are based on the solution of a pair of integral equations representing the incoming wave and the far-field pattern, respectively, are proposed and investigated for finding the unknown boundary. Numerical resultsare included which show that the methods give accurate numerical approximations in relatively few iterations.

Publication DOI: https://doi.org/10.1216/jiea/1190905488
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: Copyright © 2007 Rocky Mountain Mathematics Consortium
Uncontrolled Keywords: far field pattern ,ill-posed ,inverse scattering ,Newton method ,sound-soft ,Tikhonov regularization.
Published Date: 2007-01
Authors: Ivanyshyn, Olha
Johansson, Tomas ( 0000-0001-9066-7922)

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