An integral equation perturbation technique in applied mathematics-ii

Abstract

This paper is devoted to the applications of an integral equation perturbation technique to the problems of scattering by soft and rigid obstacles in acoustics, scattering by rigid inclusions and cracks in elastic medium and conducting bodies in electromagnetism, Various interesting shapes such as spheres, ellipsoids, disks and spherical caps are considered, All these scattering problems are solved when the incident wave is a time-harmonic axially symmetric plane wave,problems are solved when the incident wave is a time-harmonic axially symmetric plane wave, Formulas are presented for the far-field amplitude as well as the scattering cross section for all the above-mentioned obstacles, In the case of scattering by rigid inclusions in elastic medium we present the analysis for both P-wave and S-wave, We further derive the stress intensity factor in the case of the crack problem, For the problem of electromagnetic scattering by a conducting circular disk we also derive the value of the electric current density on the disk