On the Naturally Induced Sources for Obstacle Scattering

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.