Fast Algorithms For Multilayered Green's Functions Evaluation

The problem of rigorous and efficient modeling the radiation by surfaces of arbitrary shape in planar layered media has been studied in this dissertation. It has been divided into two sub problems: The fist problem is to calculating the multilayered Green's functions efficiently with Discrete Complex Image Method (DCIM); while the second problem is to study RWG basis function expansion and singularity cancellation. An improved pole searching algorithm, which dramatically improved efficient of the DCIM algorithm has been presented. DCIM combined with this new algorithm has been successfully used to calculate multilayer Green's functions efficiently.For the first problem, the formulations of multilayered Green's functions and Discrete Complex Image Method have been first discussed in this paper. Then, the key techniques in DCIM, viz., pole searching algorithm and generalized pencil-of-function (GPOF) algorithm have been studied extensively. Based on this, an improved pole searching algorithm, which dramatically enhanced the efficiency of DCIM algorithm has been presented here and successfully used in DCIM to accelerate the calculation of the multilayer Green's function.For the second problem, the triangular patch modeling of arbitrary shape surfaces, RWG basis functions expansion of the surface currents, and the singularity cancellation method have been studied respectively. The formulations for solving the surface currents on arbitrary shape surfaces in layered medium have been deduced and programmed. The code has been used to calculate the surface current of a square plate in free space and good agreement between our results and the data from the reference has been observed.In this dissertation, the basic and crucial techniques for solving integral equation with multilayered Green's functions have been studied, e. g., layered Green's functions calculation, geometrical modeling, choosing of basis functions and testing functions, treatment of integral singularity. All the numerical results listed in this dissertation have demonstrated the validity and efficiency of our research works.