Z. H. Fan

Preconditioning Matrix Interpolation Technique for Fast Analysis of Scattering Over Broad Frequency Band

A hybrid interpolation method is proposed for the fast analysis of the radar cross-section (RCS) over a broad frequency band by use of the matrix interpolation method. In order to efficiently compute electromagnetic scattering, the general minimal residual (GMRES) iterative solver is applied to compute the coefficients of Rao-Wilton-Glisson (RWG) basis functions and the sparse approximate inversion (SAI) preconditioning technique is used to accelerate the iterative solver. Moreover, both the near field impedance and SAI preconditioning matrices are interpolated at intermediate frequencies over a relatively large frequency band with rational function interpolation technique. Therefore, a lot of time can be saved for the calculation of both the near field impedance and preconditioning matrices. Numerical results demonstrate that this hybrid method is efficient for wideband RCS calculation with high accuracy.

Solution of PMCHW Integral Equation for Transient Electromagnetic Scattering From Dielectric Body of Revolution

The transient EM scattering from a homogeneous dielectric body of revolution (BOR) is formulated in terms of the time-domain PMCHW (TD-PMCHW) integral equation. Triangular functions along the generatrix of the BOR and weighted Laguerre polynomials are used as the spatial and temporal basis functions, respectively, to expand the unknown equivalent surface electric/magnetic current densities. In this way, both the memory requirement and the CPU time can be reduced largely since the matrix equation for each Fourier mode can be solved independently. Numerical results are presented to demonstrate the feasibility of the proposed method. Moreover, the convergence is discussed for both the weighted Laguerre polynomials and the Fourier mode.

Multilevel Complex Source Beam Method for Electromagnetic Scattering Problems

This letter proposes a multilevel complex source beam (MLCSB) method for electromagnetic (EM) scattering problems. The multilevel structure is obtained with the octree grouping technique. Each basis function in the nonempty group is expanded with CSBs that tightly surround the group. The interactions between far groups are expressed with interactions of these CSBs. To accelerate the computation, the symmetry and shift invariance of the Greens function is employed. The adaptive cross approximation (ACA) algorithm is then applied to accelerate the computation of interactions of CSBs. Due to the directionality of the radiation pattern of the CSBs, the interactions of CSBs are truncated with an angle threshold. Numerical examples demonstrate the efficiency of this method.

Electromagnetic analysis of electrically large and finite periodic frequency selective surfaces

This paper describes an efficient technique to analyze the transmission and the reflection of finite size frequency selective surfaces (FSS) array. The transmission and reflection coefficients are calculated using the method of moment by comparison with the metallic plate with the same size. Numerical examples are given to demonstrate the validity and efficiency of the proposed method.

Marching-on-in-Degree Solution of the Transient Scattering From Multiple Bodies of Revolution

An efficient marching-on-in-degree (MOD) scheme is proposed to analyze the transient EM scattering from multiple conducting bodies of revolution (MBoRs) with arbitrary axis using the equivalence principle algorithm (EPA). The self-acting of each BoR is calculated by taking advantage of the rotationally symmetrical property in its local BoR coordinate system. The interaction between any two BoRs is replaced by the one between their equivalence spheres which enclose corresponding BoR with EPA. In this way, the transient scattering properties of the randomly distributed MBoRs can be obtained with high efficiency by the use of the BOR basis functions and the weighted Laguerre polynomial. Numerical results are presented to demonstrate the accuracy and efficiency of proposed algorithm.

An Effective MoM Solution With Nested Complex Source Beam Method for Electromagnetic Scattering Problems

A nested complex source beam (NCSB) method based on octree structure is proposed to accelerate the method-of-moments (MoM) solution for three-dimensional (3-D) electromagnetic scattering analysis. At the finest level, the far-field contribution of each basis function is expressed with that of complex source beams (CSBs) distributed on the equivalent sphere surface for every group. Furthermore, the far field radiated by CSBs of the source group at child level can be represented by that radiated by CSBs of the source group at parent level. Similarly, the received field of CSBs for each observation group at the parent level can be expressed with that of CSBs belong to their child level group. An equivalent relationship of CSBs between every two adjacent levels is built to obtain the nested equivalent process for NCSB method, and only the CSBs at the finest level have the direct association with the basis functions in their group. The NCSB method is shown to be O(NlogN) computational complexity for both matrix-vector product (MVP) time and memory storage by numerical examples with appropriate parameters, and numerical results demonstrate the better efficiency of the proposed method than the current multilevel CSB method.

Augmented MLFMM for solving the electromagnetic scattering problems with fine structures

MLFMM augmented with a Greens function interpolation method is proposed to efficiently solve the electromagnetic scattering problems. One well-known shortcoming of the traditional mid-frequency MLFMM method is that the finest box size must be at least 0.25 wavelength to ensure the accuracy. However, there exists a myriad of real targets having fine structure, and it usually produces a large number of unknowns in each finest box when discretizing these targets in the MLFMM implemetation, which leads to a large mount of storage of near-field interactions. In this article, a Greens function interpolation method (MLGFIM) is proposed to attack this kind of problem, the MLGFIM can make the finest box size reduced to as small as 0.1 wavelength or even smaller, and it enables a significant reduction in memory and complexity against the MLFMM. Numerical examples are presented to validate the proposed scheme.

A domain decomposition method for electromagnetic radiation of large-scale arrays

A domain decomposition method based on equivalence principle algorithm is used for analyzing and calculating radiation problems of large-scale arrays. The adaptive cross approximation method is introduced to accelerate computing the translate operator, and the repeatability of the array is removed. Numerical results demonstrate that the time consumption and the memory usage are all reduced.

Time Domain Analysis of Electromagnetic Scattering Problems by Using Integral Equation Method With Space-Delayed Temporal Basis Functions

This communication presents a new numerical method for the efficient solution of marching on in time (MOT)-based time domain integral equations (TDIE) for electromagnetic scattering from perfect electrically conducting (PEC) object with large smooth surfaces. A set of space-delayed temporal basis functions is proposed for the temporal discretization, and the curvilinear Rao-Wilson-Glisson (CRWG) basis functions for the spatial discretization. The space-delayed temporal basis functions are firstly extended to the time domain electric field integral equations (TDEFIE), then easily to the time domain combined field integral equations (TDCFIE). Numerical results demonstrate that the new method is stable and effective for the transient scattering problems from PEC objects with large smooth surfaces and a single plane wave incidence. A significant reduction of the number of spatial unknowns is achieved by using the space-delayed temporal basis functions.

Finite-element time-domain method combined with finite-element tearing and interconnecting algorithm and its application for electromagnetic band gap structure

In this paper, an unconditionally stable implicit FETD algorithm combined with the FETI method is described. The method is general enough for arbitrary geometries, and yet capable of taking advantage of periodicity. Together with the first-order ABC, the method is applied to simulate the microstrip EBG structure. Through the periodicity of this structure, memory requirements are further reduced without sacrificing accuracy. The simulation results are well agreed with the results obtained by FDTD method.