Electromagnetic scattering from cluster of spheres using diagonalized vector addition theorem

Atasoy, Halil İbrahim
Our aim is to implement an FMM (Fast Multipole Method) solver using the approach given by Chew [35] for diagonalization of vector addition theorem. Scatterer bodies will be modeled as ensemble of smaller spheres with same constitutive properties and then will be analyzed using the FMM solver. For general scattering problems, it is hard to obtain an analytical solution. There are only some special cases where exact solutions are possible. Hence, for the investigation of problems where numbers of scatterers are high, numerical methods like FMM are necessary. For the analysis of scattering problem, FMM is an effective tool. Hence, mathematical background of the method is investigated. Addition theorem is examined for the expression of the wave functions in distinct coordinate systems. Starting from the scalar addition theorem, vector addition theorem in spherical coordinates is investigated. Since, computation period spent for the calculation of the translation coefficients is high; recursive methods for the calculations are also analyzed.
Citation Formats
H. İ. Atasoy, “Electromagnetic scattering from cluster of spheres using diagonalized vector addition theorem,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.