A multilevel fast spectral domain algorithm for electromagnetic analysis of infinite periodic arrays with large unit cells

摘要

A multilevel fast spectral domain algorithm (MLFSDA) is introduced for the efficient evaluation of the matrix vector productsdue to the boundary integral (BI) operator within a hybrid finite element - BI (FEBI) method for the analysis of infinite periodicarrays. The MLFSDA utilizes the diagonalization property of the spectral domain (SD) BI representation and handles the large numbersof Floquet modes required for large (with respect to wavelength) periodic unit cells by similar hierarchical techniques as appliedin the multilevel fast multipole method/algorithm (MLFMM/MLFMA). With the capability of the MLFSDA to handle very large periodic unit cells, itbecomes possible to model finite antennas and scatterers with the infinite periodic array model. For a cavity-backedantenna element and for a semi-finite array of 4 cavity-backed antenna elements in the finite direction, the dependence of the input impedanceson the unit cell sizes is investigated and it is found that array resonances disappear for reasonably large unit cell dimensions.Finally, a semi-finite array of antipodal Vivaldi antenna elements is considered and simulation results for infinite periodic, finite, andsemi-finite array configurations are compared to measured data.