Applied Research On T-Matrix Method Based On Group Theory In Electromagnetic Scattering With Symmetric Structures

Big storage and long calculation time requirement are the main obstacles to the development of a numerical method. How to efficiently use geometry of scattering bodies to reduce computer storage and running time is highly significant in both theory and practice in the computational electromagnetics field. T-Matrix method was brought into computational electromagnetics by P.C Waterman in 1965. The method has the following significant advantages. Firstly, based on scalar Green’s theorem, T-matrix method can avoid the difficulties caused by cavity mode. Secondly, using cylindrical-harmonics form of Green’s function to expand the surface current on both inner and outer regions, a large amount of storage and calculation tame can be saved. Thirdly, symmetry of the scattering bodies can reflect that of T matrix. Therefore T-matrix method has been widely used in acoustic scattering, light scattering, electromagnetic scattering and elastic wave scattering.There are four research aspects in the paper around the theme that the algorithm combining T-Matrix method and group theory is applied into electromagnetic scattering problems.Firstly, to extend the research on consistency theory from T-Matrix to classical analytic solutions, this paper brings about structural equations of T-Matrix method for 2D dielectric scattering problems with TM and TE wave incident respectively. According to which for the first time, consistency issues of T-Matrix method are systematically analyzed, in other words consistency transition from T-Matrix method to analytic solutions is completed when the boundary of a dielectric scattering tends to a cylindrical one.Secondly, to expand the research on the application of GIM which is a traditional method to deal with symmetric scattering problems, the surface integral functions are showed out in this paper by way of extinction theorem and boundary conditions based on TM and TE wave incident respectively. Then we apply an algorithm combined T-Matrix method and GIM so as to reduce the running time down to 1/4 of traditional T-Matrix.Thirdly, deep-going the research on solving out special functions by group method, the integral and power series forms of Bessel functions for the first kind are obtained in this paper according to representation theory of Lie groups. Which indicate that analytic harmonics of symmetric boundary problems can be derived from group method.Lastly, as to scattering bodies whose geometry structures meet point group symmetry, in this paper group-element operators are directly act on 2D and 3D T-Matrix formulas. By analyzing we can conclude that some T matrix elements exactly equal to 0, and the other elements have symmetric or anti-symmetric relationships. Therefore numerous running time is saved in numerical computation.