Accurate analysis of large-scale periodic structures using an efficient sub-entire-domain basis function method

Abstract

An efficient sub-entire-domain (SED) basis function method has been proposed to analyze large-scale periodic structures with finite sizes accurately. The SED basis function is defined on the support of each single cell of the periodic structure. After introducing dummy cells with respect to an observation cell, the real physics of SED basis function is captured accurately by solving a small-size problem. Further analysis has shown that all kinds of SED basis functions used in the periodic structure can be obtained by solving a single small problem. Hence, the original large-scale problem involving = 0 unknowns is decomposed into two small-size problems, one of which contains 9 unknowns and the other of which contains only 0 unknowns. Here, 0 is the total cell number in the periodic structure and is the number of subdomain basis functions in each unit cell. Several examples are given to test the validity and efficiency of the proposed method. Numerical results from the new method have excellent agreements with those from the conventional method of moments. However, the CPU time has been greatly reduced. Index Terms-Electromagnetic bandgap materials, frequency selective surface, metamaterials, method of moments (MoM), periodic structures, sub-entire-domain (SED) basis function.

Efficient Analysis of Rectangular-Shape Metamaterials Using P-CBFM/P-FFT Method

“…Then all types of CBFs can be obtained by solving a single small problem as shown in Fig. 3(b) [4] by considering the effects of nearby cells.…”

“…The method of using high-level basis function provides a fast and stable way to solve the largescale and ill-conditioned problems, such as macro basis function (MBF), synthetic basis function (SBF), Shannon basis functions, sub-entire domain (SED) [4], characteristic basis function (CBF) proposed by Prakash and Mittra [5]. Many studies have been carried out for improvement of the CBFM in recent years [6][7][8].…”

Analysis of Finite Periodic Dielectric Gratings by the Finite-Difference Frequency-Domain Method With the Sub-Entire-Domain Basis Functions and Wavelets

“…But because the BIE method is used on the boundary, the number of non-zero elements in the final matrix equation of the FDFD-BIE method rises rapidly, when a large object, such as a large array, is analyzed. The subentire-domain (SED) basis functions for the MoM were proposed [6,7] and used to analyze large finite periodic metal arrays [8][9][10]. In this efficient technique, the periodic property is considered, and the mutual coupling is approximately treated, so the number of unknowns can be dramatically reduced.…”

Sub-Entire-Domain Basis Function Method for Irrectangular Periodic Structures

“…Recently, some physically-based entire-domain (ED) and subentire-domain (SED) basis functions have been developed to solve the challenging problem [16][17][18][19][20][21][22][23]. For example, the Macro basis function (MBF) [16], synthetic functions (SFs) [17], characteristic basis function (CBF) [18][19][20], and sub-entire-domain (SED) basis functions [21][22][23] have been proposed.…”

“…For example, the Macro basis function (MBF) [16], synthetic functions (SFs) [17], characteristic basis function (CBF) [18][19][20], and sub-entire-domain (SED) basis functions [21][22][23] have been proposed. Among those physically-based basis functions, the SED basis functions have been proved to be efficient and can be implemented more easily [21][22][23]. But in the early records [21][22][23], problems solved by SED functions are all confined to rectangular periodic structures.…”