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Most Downloaded Articles
- Conference announcement “Inverse and Ill-Posed Problems of Mathematical Physics” dedicated to the 80th birthday of Academician M. M. Lavrentiev
- The inverse spectral problem for the Sturm–Liouville operator with discontinuous potential by Sedipkov, Aydys A.
- Chemnitz Symposium on Inverse ProblemsChemnitz, Germany, September 27–28, 2007 by Hofmann, B.
A numerical method to solve an acoustic inverse scattering problem involving ghost obstacles
11. Dipartimento di Matematica Pura e Applicata, Università di Modena e Reggio Emilia, Via Campi 213/b, 41100 Modena, Italy.
32. Dipartimento di Scienze Sociali "D. Serrani", Università Politecnica delle Marche, Piazza Martelli 8, 60121 Ancona, Italy.
53. Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", Piazzale Aldo Moro 2, 00185 Roma, Italy.
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 1, Pages 57–82, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2007.003, May 2007
- Published Online:
In this paper we study a time harmonic inverse acoustic scattering problem involving an obstacle that when hit by an incoming acoustic wave tries to appear in a location in space different from its actual location eventually with a shape and an acoustic boundary impedance different from its actual ones. We refer to this problem as inverse ghost obstacle problem and to the scatterers of this type as a special class of smart obstacles. The term "ghost" comes from the fact that the smart obstacle, when hit by the incoming wave, tries to appear as a ghost obstacle, that is as a virtual obstacle in a location in space where no real obstacle is present. We assume that the intersection between the obstacle and the ghost obstacle is empty. The obstacle tries to produce this virtual image of itself circulating on its boundary a suitable pressure current. A pressure current is a quantity whose physical dimension is pressure divided by time. The following time harmonic inverse ghost obstacle scattering problem is considered: from the knowledge of several far fields generated by the smart obstacle when hit by known time harmonic waves, of its acoustic boundary impedance and of the acoustic boundary impedance of the ghost obstacle find the location of the smart obstacle, that is find a point in the interior of the smart obstacle and eventually find the shape of the smart obstacle. The method proposed to solve this problem is a generalization of the well known Herglotz function method. We present some numerical experiments based on synthetic data that are used to test the numerical method introduced here. Some material that helps the understanding of this paper and some animations relative to the numerical experiments can be found in the website: http://www.econ.univpm.it/recchioni/w15.