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9 July 2001 Fields induced in inhomogeneous spheres by external sources: the scalar case
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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 harmonics, 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.
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Gerassimos C. Kokkorakis, John G. Fikioris, and George Fikioris "Fields induced in inhomogeneous spheres by external sources: the scalar case", Proc. SPIE 4467, Complex Mediums II: Beyond Linear Isotropic Dielectrics, (9 July 2001);

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