Equivalent Dipole-moment Method Research Articles

Efficient EDM-PO Method for the Scattering From Electrically Large Objects With the High-Order Impedance Boundary Condition

This work proposes an efficient hybrid method consisting of the efficient iterative method of moments–physical optics (EI-MoM-PO) and the equivalent dipole moment (EDM) with the high-order impedance boundary condition (HOIBC) to explore the electromagnetic scattering from the object with an isotropic or anisotropic surface coating. By introducing the HOIBC into the EDM method, the relationship between the equivalent electric and magnetic dipole moments is established. Therefore, the EDM method is extended to general cases. For the composite scattering from electrically large objects including MoM and PO regions, the EDM method is implemented to fill the MoM impedance matrix and to accelerate the evaluation of the coupling between the MoM and PO regions, which considerably improves the computing efficiency. The numerical results indicate that the proposed hybrid method allows for a substantial decrease in computation time. Also, they also agree well with the traditional finite element method, MoM, or MoM-PO method, which proves the validity of the proposed method.

An extended aggregate basis function method for composite structure with periodic array

AbstractThe extended aggregate basis function method (EABFM) is proposed to analyze the electromagnetic scattering by the composite structure with periodic array. The generation of the impedance matrix in the EABFM is still time consuming. The fast dipole method (FDM) and the equivalent dipole‐moment method (EDM) are applied to accelerate the fill‐in of the matrix. Several numerical examples are performed. Simulation results validate the accuracy and efficiency of the proposed method.

Efficient Electromagnetic Analysis for Complex Planar Thin-Layer Composite Objects by a Hybrid Method

The previously developed volume-surface integral equation-based domain decomposition method (VSIE-DDM) generally requires huge matrix filling time. To alleviate this issue, the equivalent dipole-moment (EDM) method is applied to the VSIE-DDM for complex electricallylarge planar thin-layer composite objects. Therefore, an efficient hybrid VSIE-DDM-EDM method is developed, in which the EDM technique remarkably saves the calculation time of the VSIE-DDM matrix. In this hybrid method, a new simplified prism vector basis-based dipole model is proposed. Compared with the Schaubert–Wilton–Glisson basis-based dipole model, the proposed model significantly reduces the number of numerical integrations within the threshold for planar thin dielectrics. Furthermore, to ensure the flexibility of the solution for a variety of electromagnetic problems, two strategies for solving equations (inner–outer iteration scheme and direct-iterative hybrid method) are, respectively, adopted. Finally, the multilevel fast multipole algorithm (MLFMA) is utilized for iteration procedure. Numerical examples are shown to validate the accuracy and efficiency of the proposed method.

Iterative dipole moment method for the interaction of multiple dielectrophoretic particles in an AC electrical field

Dielectrophoresis (DEP) for bio-particle manipulation has been drawing much attention in recent years. The equivalent dipole moment method (EDM) has widely been used to calculate DEP forces on single particle, but this method falls short to describe the interaction between neighboring particles. The Maxwell stress tensor method (MST) is theoretically rigorous for particle interaction, but its complicated numerical computation makes it difficult to implement in practice. In this paper, an iterative dipole moment method (IDM) is presented to investigate the interaction of multiple dielectrophoretic particles in a two-dimensional AC electric field. Without cumbersome numerical computation, the inter-particle forces, the particle trajectories and chain patterns calculated by the IDM method are found to be well consistent with those by the MST method for some published results and experimental observations. Furthermore, it is found that the final stable particle chain patterns strongly depend on the initial configuration of the particle distribution. An arbitrary small disturbance to the particle locations may lead to dramatically different motion trajectories and final particle chains. By tuning the frequency of AC field, the particles can be transformed between positive DEP particles and negative DEP particles, which results in different particle chains as well.

Acceleration of the Impedance Matrix Filling for Marching-on-in-Degree Method by Equivalent Dipole Moment

In this article, the equivalent dipole moment method is employed to accelerate the marching-on-in-degree method for the time-domain combined field integral equation. Each element can be viewed as a dipole model when the distance between the source and the testing basis functions is beyond a threshold distance. In this way, the impedance matrix elements of each order can be easily computed by a simple procedure, and the computational time is reduced significantly for transient electromagnetic scattering. Numerical results are presented to demonstrate the efficiency of the proposed method for electromagnetic scattering from perfect electric conductor objects.

Solutions of Broadband RCS Using AWE Technique and Equivalent Dipole Moment Method

A broadband radar cross section (RCS) calculation approach is proposed based on the asymptotic waveform evaluation (AWE) technique. The equivalent dipole moment method (EDMM) is used to accelerate the process of filling the impedance matrix and more derivative matrices. So the broadband RCS is achieved quickly by using AWE technique and EDMM. Numerical results show that the computational efficiency is improved significantly by using the method presented in this paper with ensuring the accuracy.

Analysis of transient electromagnetic scattering using time domain equivalent dipole moment method

In this paper, an efficient technique is presented for computing the matrices in time domain integral equations (TDIE). The proposed method is the extension of the frequency domain equivalent dipole moment method to the time domain. Each matrix element does not require computing the usual surface integrals involving the expansion and testing functions, which makes the matrix generation more efficient and faster than the conventional TDIE method. Numerical results about the electromagnetic scattering from perfect electric conductor(PEC) objects are given to demonstrate the accuracy and efficiency of the proposed method.

Parallelized Multilevel Fast Dipole Method For Electromagnetic Scattering From PEC Targets

Parallel implementation of the multilevel fast dipole method (MLFDM) is discussed in this article. The MLFDM is based on the equivalent dipole-moment method (EDM), in which each Rao-Wilton-Glisson (RWG) basis function is viewed as a dipole model with an equivalent dipole moment. Through expanding all the terms including R in the formulation of the EDM using a simple Taylor’s series, the MLFDM can efficiently calculate the interactions between the far groups at each level in an aggregation-translationdisaggregation form. And the complexity of matrix-vector products (MVPs) between a far-group pair, such as block i and block j, is reduced from O (NiNj ) to O (Ni + Nj ), where Ni and Nj are the number of dipoles in block i and block j, respectively. Furthermore, we show that the MLFDM is very suited for parallelization. In this article, parallelized MLFDM is implemented and employed to analyze the electromagnetic scattering from perfect electric conducting (PEC) targets.

Fast solution of volume-surface integral equation for scattering from composite conducting-dielectric targets using multilevel fast dipole method

This article presents a fast solution to the volume–surface integral equation for electromagnetic scattering from three-dimensional (3D) targets comprising both conductors and dielectric materials by using the multilevel fast dipole method (MLFDM). This scheme is based on the concept of equivalent dipole-moment method (EDM) that views the Rao–Wilton–Glisson and the Schaubert–Wilton–Glisson basis functions as dipole models with equivalent dipole moments. In the MLFDM, a simple Taylor's series expansion of the terms Rα (α = 1, −1, −2, −3) and R̂R̂ in the formulation of the EDM transforms the interaction between two equivalent dipoles into an aggregation–translation–disaggregation form naturally. Furthermore, benefiting from the multilevel grouping scheme, the matrix-vector product can be accelerated and the memory cost is reduced remarkably. Simulation results are presented to demonstrate the efficiency and accuracy of this method. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.

Fast Dipole Method for Electromagnetic Scattering From Perfect Electric Conducting Targets

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( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.5</sup> ) computational complexity and memory requirement, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of unknowns. Numerical results are presented to validate the efficiency and accuracy of this method through comparison with other rigorous solutions.

Electromagnetic Radiation from Arbitrarily Shaped Microstrip Antenna Using the Equivalent Dipole-Moment Method

The equivalent dipole-moment method (EDM) is extended and applied in the analysis of electromagnetic (EM) radiation by arbitrarily shaped microstrip antenna in this paper. The method of moments (MoM) is used to solve the volume-surface integral equation (VSIE). A strip model is applied in the treatment of the feeding probe of the microstrip antenna, in which the discretized triangular elements of the excitation source are equivalent as dipole models. The proposed approach is sufficiently versatile in handling arbitrarily shaped microstrip antenna and is easily constructed through a simple procedure. Numerical results are given to demonstrate the accuracy and efficiency of this method.

Multilevel 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&apos;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.

A FAST VOLUME-SURFACE INTEGRAL EQUATION SOLVER FOR SCATTERING FROM HIGH-CONTRAST MATERIALS

This paper presents a generalized volume-surface integral equation (GVSIE) to solve electromagnetic (EM) scattering of high contrast inhomogeneous materials. Then the method of moments (MoM) is employed to solve the GVSIE. The GVSIE technique where the domain is represented by a corresponding uniform background medium coupled with a variation, together representing the overall inhomogeneity, is solve by the method of moments (MoM) using Schaubert-Wilton-Glisson (SWG) and Rao-Wilton-Glisson (RWG) basis functions. The adaptive cross approximation (ACA) algorithm combined with the equivalent dipole-moment (EDM) method are extended to reduce memory and CPU time. A highly efiective preconditioning strategy is presented to solve the system of equations without any increase in the computational complexity. Experiments on several problems representative of scattering simulations are given to illustrate the potential of the above proposed techniques for solving EM scattering involving high contrast applications.

A Hybrid Fast Dipole Method and Adaptive Modified Characteristic Basis Function Method for Electromagnetic Scattering from Perfect Electric Conducting Targets

In this article, the fast dipole method (FDM) is combined with the adaptive modified characteristic basis function method (AMCBFM) to solve the electromagnetic scattering from perfect electric conducting (PEC) targets. The AMCBFM is an efficient method for analyzing electromagnetic problems via the size reduction of the original matrix in the method of moments (MoM) equation. However, in AMCBFM, the characteristic basis functions (CBFs) generations process and reduced matrix calculation process are still very time-consuming for containing many matrix-vector products (MVPs) and vector-matrix-vector products (VMVPs). Through a simple Taylor's series expansion, the FDM reduces the complexity of MVPs and VMVPs between the far block pair, such as block i and block j, from O(NiNj ) to O(Ni + Nj ), where Ni and Nj are the number of the low-level basis functions in blocks i and j, respectively. In addition, the equivalent dipole-moment method (EDM) is used to speed up the low-level impedance elements filling process between the near block pair, thus further accelerating the computation. Numerical results are given to demonstrate the efficiency and accuracy of the FDM-AMCBFM.

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

Electromagnetic scattering by arbitrarily shaped stratified anisotropic media using the equivalent dipole moment method

The equivalent dipole moment method, which was used to model the isotropic media, is extended and applied to the analysis of the electromagnetic scattering characteristics of arbitrarily shaped multilayer electric anisotropic media in this work. The initial motivation to put forward this method is based on the intrinsic physical properties of the electric anisotropic media whose constitutive parameter permittivity is a tensor matrix that can be modeled as equivalent electric dipole moment. This method employs the method of moments to solve the electric field volume integral equation (VIE) formulated by discretizing the scattering body into tetrahedral volume elements, in which the electrical parameters are assumed constant in each element. Then the VIE is solved directly to obtain the scattered field. Numerical results are given to validate the accuracy and efficiency of this method. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.

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

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.

A hybrid equivalent dipole moment and adaptive modified characteristic basis function method for electromagnetic scattering by multilayered dielectric bodies

In this article, the equivalent dipole moment (EDM) method is extended and applied to analyze the electromagnetic scattering of multilayered dielectric bodies. Besides the advantage of reducing the computation time, the proposed EDM method makes it unnecessary to treat the boundary condition on the surface or the interface of the multilayered dielectric body. However, the EDM method is incapable of saving memory. In this case, the adaptive modified characteristic basis function (AMCBF) method is introduced and combined with the EDM method. Numerical results are given to demonstrate the merits of this EDM-AMCBF method. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.

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

Equivalent Dipole Moment Method to Characterize Magnetic Fields Generated by Electric Appliances: Extension to Intermediate Frequencies of Up to 100 kHz

A previously proposed simple method to characterize magnetic fields near electric appliances was extended to intermediate frequencies of up to 100 kHz. The method consists of identification of the magnetic dipole moment that is equivalent to a magnetic field source of an electric appliance and simple estimation of the magnetic field distribution around the appliance. In addition, frequency characteristics of the magnetic field were taken into account by considering the harmonic components in the magnetic-field waveform for both power frequency and intermediate frequency ranges. For the application of the method, a wide-frequency range (from power frequency to 100 kHz) magnetic-field measuring instrument was developed and applied to appliances that generate intermediate frequency magnetic fields, i.e., an induction heating cooker, a TV set, and a metal detector. The results revealed that the method is adequate to quantify the magnetic field near the electric appliances at frequencies of up to 100 kHz.