Numerical simulation of electromagnetic scattering by a large three-dimensional (3D) object is a rather challenging problem mainly because of its high computational complexity. Fortunately, many realistic objects exhibit certain special features that can be exploited to speed up the numerical analysis. There have been many successful examples in this aspect. For example, an infinitely large periodic structure can be analyzed by considering only a unit cell in conjunction with the Floquet representation of the fields. In the case of a finite periodic structure, one can arrange the final numerical system in such a way that it exhibits a circulant block structure, which permits the use of the fast Fourier transform (FFT) to efficiently compute the matrix-vector product.
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