A Fast Model Order Reduction Method for Electromagnetic Scattering of Large Periodic Arrays With Connected Elements

In this communication, a fast model order reduction (MOR) method is proposed to solve the electromagnetic scattering of large periodic arrays consisting of connected elements. Each element is enclosed by an equivalence surface (ES), and the unknowns on the element can be transferred onto the ES using the equivalence principle algorithm (EPA). The challenge arises when the ES intercept the current carrying conductor, which is hard to evaluate numerically using traditional Rao–Wilton–Glisson (RWG) basis. In this communication, a new method based on grid-robust higher order vector basis (GRHOVB) function is proposed to deal with this challenge. To reduce model order further, the characteristic basis functions (CBFs) based on $3\times3$ array are constructed on the ESs, which can analyze the strong coupling of connected elements. The proposed method is also accelerated by multilevel fast multipole algorithm (MLFMA) and sparse approximate inverse (SAI) preconditioner to solve large periodic arrays with thousands of connected elements. Numerical examples are given to show the significant advantages of the proposed method compared with commercial solver.