A New Guideline for the Allocation of Multipoles in the Multiple Multipole Method for Two Dimensional Scattering from Dielectrics

A new guideline for proper allocation of multipoles in the multiple multipole method (MMP) is proposed. In an ‘a posteriori’ approach, subspace fitting (SSF) is used to find the best location of multipole expansions for the two dimensional dielectric scattering problem. It is shown that the best location of multipole expansions (regarding their global approximating power) coincides with the medial axis of the object. The subspace analysis is performed for various scenarios including objects with different shapes and sizes relative to the wavelength, different permittivities and both TEz and TMz polarizations. Numerical examples for both TEz and TMz cases are also presented. The results are in a very good agreement with the finite element method (FEM) results. Two challenging test cases are presented. First, a large object compared to the wavelength and second, a small object with field singularities close to the boundary. Accuracy of the final MMP results shows the effectiveness of the new allocation rule.