群方法寻基在矩量法求解二维散射问题中的应用

Basic Functions from Group Theory in MoM for 2D EM Scattering Problems

针对横截面为正方形的散射柱,确定以方柱各边的中心点和各顶点计8个点为群变换对称点,该8个点构成8个自然对称1阶基函数。根据二维对称物体的对称特点构造出对称变换群,继而确定出该变换群的正规表示,将正规表示进行约化,根据所约化出的不可约表示,进而确定出以上述8个自然对称基的线性组合的独立归一基,计算结果表明,以该基函数级数展开来描述表面电流,具有收敛速度快、计算精度高等特点。

It is important to obtain the most well-fitted basic functions in Method of Moment (MoM). According to the symmetric feature of scattering boundary whose cross section is square, the basic function in MoM is obtained by use of Represention Theory of Finite Group. The first step is to construct the group and get the regular representations. Secondly to give the tentative functions according to the eight center symmetric positions in the boundary. Thirdly, while the regular representation is transformed into irreducible one, the orthonormal basic function which are composed of the tentative functions come into being. Numerical results show the above methods have good quality both in saving calculating time and accuracy.