As a first result in the development of a full wave integral equation solver for 3D structures in multilayered media, a dedicated solution for scattering problems on arbitrarily shaped, heterogeneous dielectric objects is proposed. The solution is based on a mixed potential volume integral equation formulation and solved using the method of moments. The dielectric objects are staircase approximated, using a cuboidal mesh. The unknown current distribution is expanded in generalized 3D rooftop basis functions. As a consequence, separation of horizontal and vertical dependencies can be exploited to the utmost, resulting in a full analytical and thus computational very efficient evaluation of the reaction integrals. The validity of this approach is demonstrated by calculating the well known, full resonant radar cross section (RCS) of dielectric and metallic spheres.
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