CBFM-based p-FFT method: A new algorithm for solving large-scale finite periodic arrays scattering problems

In this paper, a novel p-FFT method based on characteristic basis function method (CBFM) has been proposed and implemented to solve electromagnetic scattering by large scaled finite periodic arrays. The CBFs can be constructed by solving the integral equations associated with one unit cell at plane wave incidence from different incident angles and with different polarizations. Then, the unit cell can be considered as an element in solving the whole array problem. When characterizing an array of a very large number of unit cells with a large number of CBFs per unit cell, the resultant linear equation system is too large to be directly solved. The p-FFT method can be integrated by utilizing the CBFs to accelerate the solution to large scale array problems and to reduce memory requirements. The proposed method can be used to solve both 2D and 3D array problems. Numerical examples are shown to demonstrate the high accuracy and efficiency of the proposed new method. Large scale array problems are considered at the end of the paper.