Fast spectral domain algorithm for hybrid finite element/boundary integral modeling of infinite periodic arrays

Abstract

Finite element (FE)/boundary integral (BI) modeling of infinite periodic arrays (antennas and frequency selective surfaces (FSSs)) has become very attractive. Originally, the fully three-dimensional (3D) modeling flexibility of the approach was obtained for the cost of high central processing unit (CPU) time requirements of the BI termination. However, this issue has been relieved by the utilization of fast integral equation methods (FIEMs) such as the adaptive integral method (AIM). A basic principle of AIM and other FIEMs is that the speed-up is obtained by fast evaluation of the far interactions within the BI whereas the near interactions are still calculated in a conventional manner. Based on this strategy, considerable speed-ups can only by achieved for relatively large numbers of BI unknowns. This problem can be overcome by the fast spectral domain algorithm (FSDA) which is based on the well-known spectral domain formulation of convolution type integral equations. FSDA avoids explicit generation of any BI matrix elements. Instead, at each iteration of the employed iterative equation solver the actual current distribution is summed up in the spectral domain and the spectral Floquet mode series for evaluation of the BI is carried out only once per testing function. We present the formulation of FSDA within the framework of a hybrid FE/BI approach for infinite periodic structures. Validation, convergence and timing data are also given.