Fast spectral domain algorithm for hybrid finite element/boundary integral modelling of doubly periodic structures

A fast integral equation algorithm is used for an efficient evaluation of the boundary integral (BI) termination in hybrid finite element (FE)/BI methods, as applied to three-dimensional doubly periodic structures. The method is referred to as a fast spectral domain algorithm (FSDA) since it uses the spectral Green's function representation to evaluate the matrix-vector products carried out within an iterative solver. The FSDA avoids explicit generation of the usual fully populated method of moments matrix. Instead, at each iteration, the actual current distribution is summed up in the spectral domain, and the spectral Floquet mode series (in the evaluation of the BI) is carried out only once per testing function. Thus, the FSDA leads to substantial central processing unit time and memory savings when applied within the FE/BI method for the analysis of infinite periodic structures. This is demonstrated by validation and timing results for a variety of array configurations, which are compared with results obtained using a conventional BI formulation and a BI formulation based on the adaptive integral method.