Improved Synthetic Basis Functions Method for Nonperiodic Scaling Structures With Arbitrary Spatial Attitudes

Synthetic basis functions method (SBFM) is an improved approach of method of moment which utilizes fewer high-order synthetic functions to replace Rao-Wilton-Glisson functions to discretize surface currents and make inner products. Thus, this approach can drastically decrease the number of unknowns and lower the requirements of PC's memory. Especially for periodic structures, computational efficiency will be improved sharply since synthetic functions defined on different subblocks can be set identical and the process of constructing synthetic functions needs to be calculated only once. However, for nonperiodic structures, this advantage no longer exists due to the diversities of synthetic functions defined on different subblocks. In that case, synthetic functions need to be calculated block by block. Targeted at this problem, an improved SBFM is proposed for nonperiodic scaling structures whose subblocks only share identical/similar contour features, but spatial attitudes, spatial positions, and geometrical sizes can be arbitrary. Based on theoretical analysis, the improved SBFM employs a special triangulating method for each subblock which makes synthetic functions defined on them reusable. In this way, synthetic functions need to be calculated only once too for nonperiodic scaling structures. Compared to traditional SBFM, this approach decreases the elapsed time of constructing synthetic functions and memory cost of synthetic functions' expansion coefficients to 1/N (N is the number of subblocks) and is of great help in the analysis of large scale targets such as complex nonperiodic arrays. Finally, accuracy of this approach is validated by both simulating and measured results.