Sub-entire Domain Basis Function Research Articles

Scattering Analysis of Finite Periodic Array in the Vicinity of Arbitrary Object Using Hybrid Macro Basis Function Method

A hybrid macro basis function (MBF) method is proposed to analyze the finite periodic array in the vicinity of an arbitrary object. The array cells and object are modeled using the low order basis functions firstly. Afterwards, the MBFs defined on the cells are constructed using the modified accurate subentire domain basis function method. The MBFs on the object can be obtained using the characteristic basis function method. The total number of MBFs defined on the array cells and object is far less than that of the low order bases. Another advantage of the proposed method is that multiple excitations can be efficiently computed. Simulation results show that good agreement between the proposed method and other techniques is reached. In addition, computational efficiency is validated.

Fast Subentire-Domain Basis Functions Method for Analysis of Composite Finite Periodic Structures With Dielectric-Conductor Cells

The subentire-domain (SED) basis functions method based on the multiple plane waves (MPWs) has achieved the efficient analysis of the scattering problem of the large-scale finite periodic structures (LFPSs) with interconnected perfect electric conducting cells. However, for the composite LFPSs with dielectric-conductor cells, the enormous unknowns in dielectric volume become a huge burden to construct matrix equations and obtain the SED basis functions. In addition, it is hard to manually set the match points of the volume meshes on the boundaries between adjacent cells. In this letter, the fast SED basis functions method has been proposed to analyze the composite LFPSs with dielectric-conductor cells. In the fast SED basis functions method, the discontinuous Galerkin technique has been employed to guarantee the continuity of the current on the boundaries of the adjacent cells without the match points. Moreover, the fast dipole method has been introduced to accelerate the calculation of the coupling among the SED basis functions. In the scattering and the radiation problems, the MPWs and the ports excited in turn have been applied to construct SED basis functions. Numerical experiments prove the accuracy and the efficiency of the fast SED basis functions method.

Rapid Subentire-Domain Basis Functions Method Based on Adaptive Artificial Neural Networks

The subentire-domain (SED) basis functions method has shown its efficiency in solving the electromagnetic problem of large-scale finite periodic structures (LFPSs). However, calculating the expansion coefficients of SED basis functions is very time-consuming due to the consideration of the mutual coupling between all the elements in LFPSs, even after accelerated by conjugate-gradient fast Fourier transform (CG-FFT) and/or fast multipole method (FMM). In this article, based on the physics locations of observation cells, the adaptive artificial neural networks (AANNs) have been employed to rapidly predict the expansion coefficients of SED basis functions on interior cells, edge cells, and corner cells. By involving the AANNs, the mutual coupling between all the elements can be accounted into the neural networks without the construction of the mutual coupling matrix, and the expansion coefficients of SED basis functions can be obtained rapidly. Numerical experiments prove the accuracy and efficiency of the AANN-assisted SED basis functions method.

Analysis of finite frequency selective surfaces backed by dielectric substrate using sub-entire-domain basis function method

Purpose – Analysis of the frequency selective surface (FSS) is of great significance. In the method of moments, when the electric size of the FSS increases, huge in-core memory and CPU time are required. The purpose of this paper is to efficiently analyze the finite FSS backed by dielectric substrate utilizing sub-entire-domain (SED) basis function method. Design/methodology/approach – Different types of SED basis functions are generated according to the locations of the cells in the entire structure, and a reduced system is constructed and solved. The couplings of all cells of the FSS are taken into account by using Green’s function and Galerkin’s test procedure. The spatial Green’s function is obtained with the discrete complex image method. The reflection and transmission coefficients of the FSS are calculated using the far field of the FSS and the metallic plate with the same size. Findings – Moderate problems of the finite FSS backed by dielectric substrate are solved with the SED basis function method. The original problem can be simplified to two smaller problems. It enables a significant reduction to the matrix size and storage, and efficient analysis of FSS can be performed. The band-stop type of FSS can be composed of periodic conductive patch cells on the dielectric substrate, and shows total reflection property at the resonant frequency. Originality/value – The SED basis function method is mostly used to analyze periodic PEC structures in free space. The layered medium Green’s function is successfully employed and several dielectric substrate backed finite FSSs are discussed in this paper. The calculation of reflection and transmission coefficients, which are more effective rather than far field scattering of the FSS, are described.

A Fast Analysis of Scattering From Large-Scale Finite Periodic Microstrip Patch Arrays Arranged on a Non-Orthogonal Lattice Using Sub-Entire Domain Basis Functions

A sub-entire domain (SED) basis function method, which was first introduced for modeling large-scale finite periodic PEC structures in free space, has been extended for fast characterization of electromagnetic scattering from an electrically large planar finite periodic microstrip patch array. The microstrip array may have a nonrectangular layout and non-orthogonal lattice configurations (e.g., hexagons or quadrangles). Based on the mixed potential integral equation, and utilizing the proposed SED basis function algorithm, the original large-scale finite periodic array of microstrip patches can be efficiently simulated by decomposing it into two problems with matrix equations of small dimensions. The first is to construct the SED basis functions for the corresponding microstrip arrays with orthogonal/non-orthogonal lattices. Three kinds of the SED basis functions are constructed, including those related to the edge patch elements, the interior patch elements, and the corner patch elements. The second is to solve the system equation with significantly reduced problem dimension as compared to the original larger problem. Based on the obtained SED basis functions, the reduced matrix equation of small size can be generated by the Galerkin procedure, and solved by use of the LU (lower-upper) decomposition-based direct solver, which results in a fast solution. The accuracy and efficiency of the developed algorithms are demonstrated by numerical tests that include the scattering from several large-scale finite periodic arrays of microstrip patches with rectangular, non-orthogonal lattices.

ANALYSIS OF FINITE PERIODIC DIELECTRIC GRATINGS BY THE FINITE-DIFFERENCE FREQUENCY-DOMAIN METHOD WITH THE SUB-ENTIRE-DOMAIN BASIS FUNCTIONS AND WAVELETS

In this paper, the flnite-difierence frequency-domain (FDFD) method, boundary integral equation (BIE) method and sub-entire-domain (SED) basis functions are combined to analyze scatterings from flnite periodic dielectric gratings. The wavelet method is used to reduce the number of inner product operations in calculating the mutual-impedance elements between the SED basis functions. In the numerical examples, the RCS curves obtained by the method in this paper are in good agreement with those obtained by the classical full-domain FDFD method, but the computational times are largely reduced and no large matrix equation needs to be stored and solved in the former.

SUB-ENTIRE-DOMAIN BASIS FUNCTION METHOD FOR IRRECTANGULAR PERIODIC STRUCTURES

The Sub-Entire-Domain (SED) basis function method has been applied to solve electromagnetic problems of irrectangular periodic structures with finite sizes efficiently. Three typical irrectangular periodic structures such as parallelogrammic periodic structures, triangular periodic structures, and trapeziform periodic structures are investigated using the SED basis function method. Just as the SED basis functions for rectangular periodic structures, the new SED basis functions for irrectangular periodic structures are defined on the support of each single cell, and the corresponding dummy cells are introduced to obtain the new SED basis functions. Using the proposed SED basis function method, the original large-scale problem is decomposed into two small-size problems. One is the determination of new SED basis functions, and the other is to solve the whole problem using MoM and SED basis functions. Numerical examples are given to prove the validity and efficiency of the new method.

An Extended Simplified Sub-Entire Domain Basis Function Method for Finite-Sized Periodic Structures

In this paper, an extended simplified sub-entire domain (ExSSED) basis function method is presented. Its advantage is that it can further reduce the number of unknowns over the original one. Several numerical examples are given to validate its accuracy. Good agreement between the results using the proposed method and those by the method of moments and original simplified sub-entire domain basis function method is achieved.

An Extended Sub-Entire Domain Basis Function Method for Finite Periodic Structures

In this letter, an extended accurate sub-entire domain basis function method is proposed, in which the number of unknowns is further reduced than the original one. The solution time is shorter because the number of unknowns is reduced. Several examples are given, which show that numerical results given by the proposed method are in good agreement with those given by the method of moments and by the original one. Meanwhile, the CPU time is reduced by the proposed method.

Scattering Analysis of Large-Scale Periodic Structures Using the Sub-Entire Domain Basis Function Method and Characteristic Function Method

In this paper, the sub-entire domain basis function method and characteristic function (CF) method are used to analyze scattering of large-scale periodic structures. The former can dramatically reduce the number of unknows. To reduce the time for impedance matrix generation, the CF method can be used when the distance between the source function and the testing function positions is big enough. Finally, some simulation examples are given to validate the method.

Fast algorithms for large-scale periodic structures using subentire domain basis functions

Two efficient algorithms are proposed to analyze a large-scale periodic structure with finite size using the subentire-domain (SED) basis functions and the conjugate-gradient fast Fourier transform (CG-FFT). The SED basis function is defined on the support of each single element of the periodic structure. In a simplified SED (SSED)-CG-FFT algorithm, all elements of the periodic structure share the same SED basis function. As a consequence, SSED-CG-FFT can be performed in the whole periodic structure. However, SSED-CG-FFT becomes less accurate if the gap between two unit elements is very small, where the single SED basis function cannot capture the strong mutual coupling. In order to consider the mutual coupling, an accurate SED (ASED)-CG-FFT algorithm is proposed. In this algorithm, nine types of SED basis functions are employed to distinguish interior cells, edge cells, and corner cells. As a consequence, ASED-CG-FFT can be performed in all interior cells of the periodic structure. Comparing with the conventional method of moments with subdomain basis functions, the proposed algorithms are more efficient in both the computational complexity and the memory requirement. Numerical results are given to test the validity and efficiency of the proposed methods.

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

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 N=N/sub 0/M unknowns is decomposed into two small-size problems, one of which contains 9M unknowns and the other of which contains only N/sub 0/ unknowns. Here, N/sub 0/ is the total cell number in the periodic structure and M 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.