Commun. Comput. Phys., 1 (2006), pp. 974-983.


On the Naturally Induced Sources for Obstacle Scattering

Perrin S. Meyer 1, Marcos Capistran 2, Yu Chen 3*

1 Meyer Sound, 2832 San Pablo Avenue, Berkeley, CA 94702-2204, USA.
2 Universidad Autonoma del Estado de Morelos, Av. Universidad No. 1001, Col. Chamilpa, 62210 Cuernavaca, Morelos, Mexico.
3 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1110, USA.

Received 14 November 2005; Accepted (in revised version) 8 May 2006

Abstract

We introduce the equivalent sources for the Helmholtz equation and establish their connections to the naturally induced sources for the sound-soft, sound-hard, and impedance obstacles for the inverse scattering problems of the Helmholtz equation. As two applications, we employ the naturally induced sources to improve the boundary integral equation formulations for the obstacle scattering problems, and develop a unified, straightforward approach to establishing boundary conditions governing the domain derivatives of scattered waves for the soft, hard, and impedance obstacles.


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Key words: Naturally induced sources; obstacle scattering; domain derivatives.


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Correspondence to: Yu Chen , Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1110, USA. Email: yuchen@cims.nyu.edu
 

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