Study On Fast Computation Of Impedance Matrix Of Method Of Moments

The analysis of electromagnetic scattering characteristics is an important research domain in engineering electromagnetics. The method of moments (MOM) is an efficient method for solving electromagnetic scattering problem. The computation time of electromagnetic scattering problem by the method of moments is mostly in the filling of impedance matrix and the solving of the linear system. Especially for the electromagnetic scattering problem of electrically large objects or complicated construction objects, the filling of impedance matrix elements will consume a considerable portion of the total solution time if the conventional MOM is used. So, fast and accurate computation for the impedance matrix elements is an efficient way to improve the efficiency of the method of moments. Therefore, based on the method of moments, it is important to search new efficient methods to compute the impedance matrix. In this thesis, the triangle subdivision method and the equivalent dipole-moment method are proposed to accelerate the filling efficiency of the impedance matrix.In this thesis, the electric field integral equation (EFIE), magnetic field integral equation (MFIE), combined field integral equation (CFIE) of arbitrary perfect conductor and the theory of the MOM are introduced firstly, the steps of discretizing the two-dimensional and three-dimensional integral equation are also elaborated. Secondly, the theory of triangle subdivision method is introduced in detail. This method is based on the MOM associated with the Rao-Wilton-Glisson (RWG) basis function, the perfect electric conductor surface is discretized into planar triangular patches. Then each planar triangular patch is divided into a finite number of equal small triangles. Assuming that the integrand is constant in each small triangle and the double integrals for computing impedance matrix element can be replaced by finite summations. This method avoids the calculation of double integrals in the traditional MOM, so that the filling time of the impedance matrix is reduced significantly. Finally, the equivalent dipole-moment method is introduced and used to compute the impedance matrix of arbitrary perfect conductor. In this method, if the distance between the source and the testing function locations more than a threshold distance, the RWG element at source point can be regarded as an infinitesimal dipole model, and the impedance matrix elements can be calculated through the expression of exact radiation field deduced by the equivalent dipole. Hence, the computational complexity of the impedance matrix is reduced obviously.The triangle subdivision method and the equivalent dipole-moment method are applied to calculate the radar cross section (RCS) of conductor plate and conductor sphere respectively. The results are in good agreement with that obtained by the conventional MOM method, whereas the methods presented in this thesis are more efficient.