title: Field induced in inhomogeneous spheres by external sources. I. The scalar case.
abstract: 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 the investigation focuses on acoustic (scalar fields) in inhomogeneous spheres of arbitrary composition, i.e., with r-, theta- or even phi-dependent medium parameters. The volume integral equation is solved by a hybrid (analytical-numerical) method, which takes advantage of the orthogonal properties of spherical harmonics, and, in particular, of the so-called Dini's expansions of the radial functions, whose convergence is optimized. The numerical part comes at the end; it involves the evaluation of certain definite integrals and the matrix inversion for the expansion coefficients of the solution. The scalar case treated here serves as a steppingstone for the solution of the more difficult electromagnetic problem.
authors.affiliation: Institute of Communication and Computer Systems, National Technical University of Athens, Zografou, Greece.
authors.forename: Gerassimos C
authors.initials: GC
authors.lastname: Kokkorakis
authors.forename: John G
authors.initials: JG
authors.lastname: Fikioris
authors.forename: George
authors.initials: G
authors.lastname: Fikioris