A new fast dipole method (FDM) is proposed for the electromagnetic scattering from arbitrarily shaped three-dimensional (3D), electrically large, perfect electric conducting (PEC) targets in free space based on the concept of equivalent dipole-moment method (EDM) and the fast multipole method (FMM). The electric-field, magnetic-field and combined-field integral equations (CFIE) for this algorithm have been developed and implemented. Although the basic acceleration idea in the FDM has been borrowed from the FMM, the specific implementation of these two algorithms is completely different. In the FDM, a simple Taylor's series expansion of the distance between two interacting equivalent dipoles is used, which transforms the impedance element into another aggregation-translation-disaggregation form naturally. Furthermore, this algorithm is very simple for numerical implementation for it does not involve the calculation of a number of Bessel functions, Legendre functions for the addition theorem and complex integral operators. The FDM can achieve O(N1.5) computational complexity and memory requirement, where N is the number of unknowns. Numerical results are presented to validate the efficiency and accuracy of this method through comparison with other rigorous solutions.

Fast Dipole Method for Electromagnetic Scattering From Perfect Electric Conducting Targets

In this study, a multilevel fast dipole method (MLFDM) is proposed for the electromagnetic scattering from arbitrarily shaped three-dimensional (3D) perfect electric conducting targets to improve the equivalent dipole-moment method (EDM) The EDM views the basis functions as equivalent dipoles models and gives very extremely simplified forms for the impedance element However, it is incapable of saving memory and matrix-vector multiplication (MVM) time In the MLFDM, the multilevel grouping scheme is employed, and a simple Taylor-s series expansion of the distance between two interacting equivalent dipoles in far-group pair transforms the impedance element into an aggregation-translation-disaggregation form naturally at each level, which speeds up the MVM significantly Further more, the memory requirement can be reduced to O ( N ), where N is the number of unknowns Numerical results are presented to validate the merits of the MLFDM

Multilevel fast dipole method for electromagnetic scattering from perfect electric conducting targets

A new efficient hybrid method is proposed for calculating the electromagnetic scattering and radiation from electrically large, three-dimensional, perfect electric conductor objects. The method consists of efficient iterative method of moments-physical optics (EI-MoM-PO) and equivalent dipole moment (EDM). The EDM is adopted to fill the MoM impedance matrix and accelerate the evaluation of the coupling between MoM and PO regions, which promotes the computing efficiency. Furthermore, combined with EI-MoM-PO method, the proposed hybrid method is easier to implement and the formulations are more refined compared to the traditional MoM-PO method. Numerical results indicate that the proposed method has high accuracy and good robustness and can greatly reduce the computational time.

An Efficient Hybrid Method of Iterative MoM-PO and Equivalent Dipole-Moment for Scattering From Electrically Large Objects

The equivalent dipole-moment method (EDM) is extended and applied in the analysis of electromagnetic (EM) scattering by arbitrarily shaped perfect electric conductor (PEC) targets coated with electric anisotropic media in this paper. The scattering targets are discretized into tetrahedral volume elements in the material region and into triangle patches on the conducting surface, where the volume-surface integral equation (VSIE) is set up. Then the method of moments (MoM) is employed to solve the VSIE. In the impedance matrix, the near field interaction elements are computed by the conventional MoM while the far field interaction elements are modeled by the EDM. The proposed approach is sufficiently versatile in handling arbitrarily shaped objects coated with general electric anisotropic media and is easily constructed through a simple procedure. Numerical results are given to demonstrate the accuracy and efficiency of this method.

Electromagnetic Scattering by Arbitrarily Shaped PEC Targets Coated with Anisotropic Media Using Equivalent Dipole-Moment Method

In this article, an improved fast dipole method (IFDM) is proposed to enhance the accuracy of the conventional fast dipole method (FDM). Through expanding the terms R α and RR in the formulation of the equivalent dipole-moment method (EDM) using a simple Taylor's series, the improved FDM can represent the interaction between two dipoles as an aggregation-translation-disaggregation form more accurately than the conventional FDM. Furthermore, the complexity of matrix-vector products (MVPs) between the far-group pair, such as block i and block j, also can be reduced from O(N i N j ) to O(Ni + Nj ), where Ni and Nj are the numbers of dipoles in block i and block j, respectively. For a prescribed and relatively high accuracy, the new method leads to a significant decrease in computational effort. Numerical results about the electromagnetic scattering from perfect electric conducting (PEC) targets are given to demonstrate the merits of the IFDM.

Analysis of Electromagnetic Scattering from PEC Targets using Improved Fast Dipole Method

In this letter, the equivalent dipole-moment (EDM) method is applied to compute the matrix elements of the method of moments (MoM) via solving the volume-surface integral equation (VSIE). Besides the advantage of reducing the calculation time significantly, this extended method is unnecessary to treat the boundary condition on the surface of dielectric body and easily constructed by using a simple procedure. The proposed approach can be applied if the distance between the source and the testing basis functions is beyond a threshold distance. Numerical results validate the efficiency and accuracy of the generated matrix elements, and the radar cross-section (RCS) has been verified.

Jiade Yuan

Papers

Efficient Generation of Method of Moments Matrices Using Equivalent Dipole-Moment Method