In this paper, we develop numerical methods for using vector spherical and spheroidal waves in the hybrid method to calculate the multiple scattering of objects of complex shapes, based on the rigorous solutions of Maxwell equations in the form of Foldy-Lax multiple scattering equations (FL). The steps in the hybrid method are: (1) calculating the T-matrix of each single object using vector spherical/spheroidal waves and (2) vector spherical/spheroidal waves addition theorem. We utilize the commercial software HFSS to calculate the scattered fields of a complex object on the circumscribing sphere or spheroid for multiple incidences and polarizations. The T-matrix of spherical waves or spheroidal waves are then obtained from these scattered fields. To perform wave transformations (i.e. addition theorem) for vector spherical/spheroidal waves, we develop robust numerical methods. Numerical results are illustrated for T-matrices and numerical vector addition theorems.
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