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A Generalized Surface Integral Equation Formulation for Analysis of Complex Electromagnetic Systems

A novel method is presented to analyze the electromagnetic characteristics of systems consisting of a large number of scatterers with different shapes and materials. In the method, nearly located scatterers are grouped together, while large bulk materials are divided into subblocks with adequate sizes. A scatterer group or a subblock forms a basic block of the system, and each block is contained with a virtual reference surface. A generalized transition matrix defined on the reference surface is used to characterize the electromagnetic characteristics of the block. The generalized transition matrix relates the rotated tangential components of the scattered fields or the equivalence sources to the rotated tangential components of the incident fields directly. The generalized transition matrix can be calculated for each block independently using proper methods according to its structure and material. Surface integral equations are established on all the virtual reference surfaces, which can be solved by moment method to get the electromagnetic characteristics of the whole system. Characteristic basis functions and synthetic basis functions can be applied to further reduce the unknown number, while fast multipole method can be used to accelerate the evaluation of interactions. Two-dimensional examples are provided to verify the method.