Schwinger-Lippman volume integral equation method for green´s function evaluation in an inhomogeneous sphere by an inner source using dini´s series expansion

The fields induced in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them are evaluated through a Schwinger-Lippman volume integral equation. In the case of an inhomogeneous sphere, the radial part of the unknown Green´s function can be expanded in a double Dini´s series, which allows analytical evaluation of the involved cumbersome integrals. The case treated here can be extended to more difficult situations, involving inhomogeneous density, as well as to the corresponding electromagnetic problem, to the elastic problem or even to the electromagnetic problem for cylindrical configuration. Finally, numerical results are given for various inhomogeneous compressibility distributions.