Extraction of Periodicity for Quasi-Periodic Electromagnetic Surfaces Using Equivalence Principle Algorithm

Quasi-periodic electromagnetic surfaces have similar planar elements located on periodic lattices. Because the elements are different, the periodic boundary condition is not accurate for full wave modeling of quasi-periodic electromagnetic surfaces. In order to utilize the periodicity of elements to accelerate the full wave simulation, this work applies the idea of equivalence principle algorithm and projects the current of different elements onto periodic equivalence surfaces. The projection process can be written in matrix operators. For unknowns on the equivalence surfaces, the reduced basis method can be applied to reduced the number of unknowns. After extracting the periodicity or the translational invariance of the element alignment, the fast Fourier transform can be used to accelerate matrix vector production in iterative solvers for method of moments. It can reduce the computational complexity of matrix vector production from $O(N^{2})$ to $O(N\log\, N)$, where $N$ is the number of elements. Numerical examples show the algorithm can accelerate iterative solvers and has potential to solve large quasi-periodic electromagnetic surfaces.