In the field of electromagnetism, the characteristic mode (CM) method has been applied to theoretical analysis and engineering design of electromagnetic scattering and radiation due to its clear physical meaning and complete theory. In this article, the CMs are used as the entire-domain basis functions for solving electromagnetic scattering and radiation problems of large-scale, arbitrary arrangement of repetitive structures.

Firstly, the CM method for solving the scattering problems of nonconnected repetitive structures is reviewed, and the source mode is introduced to compensate the accuracy when analyzing radiation problems. Secondly, for connected repetitive structures, the buffer region is proposed to guarantee the current continuity on the surface of the conductor, and half-SWG basis functions are used for dielectric connected structures. Thirdly, a series of acceleration methods are proposed to improve the computational efficiency. To generate the reduced matrix fast, the translation invariance of repetitive structures and interpolation technology are utilized to fill the matrix entries. Multilevel Fast Multipole Algorithm (MLFMA) is also used to accelerate the matrix–vector products (MVPs) between the impedance matrix and the eigenvectors. At last, a hybrid MPI–OPENMP parallel scheme is proposed for solving large-scale finite array. The numerical examples have shown that the proposed method has a good accuracy and efficiency. It provides a strong tool for designing and optimizing antenna arrays and other EM repetitive structures.