A Note on Matrix Decomposition for Synthetic Basis Functions Method in the Analysis of Periodic Structures

The synthetic basis functions method (SBFM) is discussed in this work and orthogonal triangle decomposition (QR decomposition) is adopted to extract independent items from solution space in the construction of synthetic functions. Just like singular value decomposition (SVD), accuracy of SBFM+QR improves with the growth of the number of synthetic functions. However, there is an interesting phenomenon for SBFM+QR: only one synthetic function is enough to get the same level of accuracy with method of moments (MoM) when a single body is concerned. Moreover, this feature can be further extended to periodic arrays. In other words, for periodic arrays, one synthetic function is enough to get high accuracy if SBFM+QR is adopted. This is meaningful for large-scale periodic arrays and may lead to benefits such as decreasing memory cost and improving efficiency.