Field induced in inhomogeneous spheres by external sources. The scalar case

The evaluation of acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources is based on well known volume integral equations; this is particularly true for bodies of arbitrary shape and/or composition, for which separation of variables fails. In this paper we focus the investigation to acoustic (scalar fields) in inhomogeneous spheres of arbitrary composition, i.e., with r-, theta- dependent medium parameters. The volume integral equation is solved by a hybrid (analytical - numerical) method, which takes advantage of the orthogonal properties of spherical harmonies, and, in particular, of the so called Dini's expansions of the radial functions; the optimum convergence of the former is, also, determined. The scalar case treated here, serves as a stepping stone for the solution of the more difficult electromagnetic problem.