Electric Fleld Integral Equation Research Articles

COMPLEX RESONANCES OF A RECTANGULAR PATCH IN A MULTILAYERED MEDIUM: A NEW ACCURATE AND EFFICIENT ANALYTICAL TECHNIQUE

A new analytical technique to study the complex resonances of a rectangular patch in a multilayered medium is introduced. The problem is formulated as an electric fleld integral equation (EFIE) in the spectral domain and discretized by means of products of Chebyshev polynomials of flrst and second kind multiplied by their orthogonal weights in a Galerkin's scheme. The method is fast convergent, i.e., few expansion functions are needed to achieve accurate results, but leads to the numerical evaluation of inflnite double integrals of oscillating and slowly decaying functions. To overcome this problem, suitable half-space contributions are pulled out of the kernels of such integrals in order to obtain exponentially decaying integrands. Moreover, the slowly converging integrals of the extracted contributions are expressed as combinations of quickly converging integrals by means of algebraic manipulations and an appropriate integration procedure in the complex plane.

SCATTERING BY A TILTED STRIP BURIED IN A LOSSY HALF-SPACE AT OBLIQUE INCIDENCE

The analysis of the scattering by a tilted perfectly conducting strip buried in a lossy half- space at oblique incidence is formulated as an electric fleld integral equation (EFIE) in the spectral domain and discretized by means of Galerkin's method with Chebyshev polynomials basis functions weighted with the edge behaviour of the surface current density on the strip. In this way, a convergence of exponential type is achieved. Moreover, a new analytical technique is introduced to rapidly evaluate the slowly converging integrals of the scattering matrix coe-cients consisting of algebraic manipulations and a suitable integration procedure in the complex plane.

A NEW EFIE METHOD BASED ON COULOMB GAUGE FOR THE LOW-FREQUENCY ELECTROMAGNETIC ANALYSIS

To solve the low-frequency breakdown inherent from the electric fleld integral equation (EFIE), an alternative new form of the EFIE is proposed by using the Coulomb-gauge Green's function of quasi-static approximation. Difierent from the commonly adopted Lorentz-gauge EFIE, the Coulomb-gauge EFIE separates the solenoidal and irrotational surface currents explicitly, which captures inductive and capacitive responses through electrodynamic and electrostatic Green's functions, respectively. By applying existing techniques such as the loop-tree decomposition, frequency normalization, and basis rearrangement, the Coulomb-gauge EFIE also can remedy the low-frequency breakdown problem. Through comparative studies between the Lorentz-gauge and Coulomb-gauge EFIE approaches from mathematical, physical and numerical aspects, the Coulomb-gauge EFIE approach shows the capability of solving low-frequency problems and achieves almost the same accuracy and computational costs compared to the Lorentz-gauge counterpart.

BLOCK MATRIX PRECONDITIONER METHOD FOR THE ELECTRIC FIELD INTEGRAL EQUATION (EFIE) FORMULATION BASED ON LOOP-STAR BASIS FUNCTIONS

In this paper, electromagnetic scattering problems are analyzed using an electric fleld integral equation (EFIE) formulation that is based on loop-star basis functions so as to avoid low-frequency instability problems. Moreover, to improve the convergence rate of iterative methods, a block matrix preconditioner (BMP) is applied to the EFIE formulation based on loop star-basis functions. Because the matrix system resulting from the conventional method of moments is a dense matrix, a sparse matrix version of each block matrix is constructed, followed by the inversion of the resultant block sparse matrix using incomplete factorization. Numerical results show that the proposed BMP is e-cient in terms of computation time and memory usage.

AN ITERATIVE SOURCE RECONSTRUCTION METHOD EXPLOITING PHASELESS ELECTRIC FIELD DATA

Conventional equivalent source reconstruction methods (SRM) require both phase and amplitude information of the acquired fleld data. However, there are situations where the phase information is not available or impractical to obtain. Hence, the development of SRM using phaseless flelds is important. In this paper, a novel iterative SRM based on phaseless electric flelds is presented. The reconstructed equivalent current source can be electric, magnetic current, or both. They can flt the physical geometry of the radiator. Electric fleld integral equation (EFIE) is employed to build the relationship between the reconstructed current source and measured flelds. It can precisely reproduce the original 3D radiation pattern with very good accuracy. To investigate the robustness and accuracy of the proposed approach, both strong and weakly-directional radiators are benchmarked.

NOVEL MULTI-DIMENSIONAL WCAWE TECHNIQUE FOR THE EFFICIENT CALCULATION OF RCS

In this paper, a novel moment-matching reduced order model technique termed the multi-dimensional well-conditioned asymptotic waveform evaluation (MDWCAWE) method is presented. The MDWCAWE method can be used to e-ciently determine the radar cross section (RCS) of arbitrarily shaped objects, in both the frequency and angular domains simultaneously. Numerical results are given in order to demonstrate the accuracy and robustness of the MDWCAWE method. All scattering problems investigated in this work are formulated using the two-dimensional volume-surface electric fleld integral equation (EFIE). We consider problems involving scattering from both dielectric dispersive and conducting objects.

AN EFFICIENT SCHEME FOR ANALYSIS OF ELECTROMAGNETIC SCATTERING FROM TARGET AND ENVIRONMENT COMPOSITE MODEL

We present an e-cient scheme for the analysis of electromagnetic scattering from target and environment composite model. In this scheme, the whole computed domain is divided into a target part and an environment part, and each part is formulated by difierent integral equations. The two parts are solved one by one until the relative residual error is less than a given value. Compared with conventional solution with pure electric fleld integral equation (EFIE), the proposed scheme has a better convergence and lower memory requirement. Additionally, the multilevel fast multipole algorithm (MLFMA) is utilized to accelerate the computations of matrix vector product. Simulated radar-cross-section (RCS) results of several examples demonstrate its validity and e-ciency.

CONICAL LINEAR SPIRAL ANTENNA FOR TRACKING, TELEMETRY AND COMMAND OF LOW EARTH ORBIT SATELLITES

Conical log spiral antennas are famous for being appro- priate for tracking, telemetry and command (TT&C) applications in low earth orbit (LEO) satellites. In this work, a conical linear (Archimedean) spiral antenna is introduced and investigated for the same purpose. The electric fleld integral equation (EFIE) technique is applied to a triangular-patch surface model of the conical equiangular linear spiral antenna. This antenna is optimized to produce the radia- tion characteristics required for TT&C applications for LEO satellites. The input impedance, polarization and radiation patterns of this an- tenna are investigated over the operating band of frequencies. Some of the obtained results especially those concerning the input impedance, radiation pattern, polarization and bandwidth are verifled experimen- tally. It is shown that the proposed antenna is quite appropriate for TT&C in LEO satellite applications.

AN EFFICIENT HIGH ORDER MULTILEVEL FAST MULTIPOLE ALGORITHM FOR ELECTROMAGNETIC SCATTERING ANALYSIS

An e-cient higher order MLFMA is developed by using an \extended-tree. With this extended-tree, the size of the box at the flnest level is reduced, and the cost associated with the aggregation and disaggregation operations is signiflcantly decreased. The sparse approximate inverse (SAI) preconditioner is utilized to accelerate the convergence of iterative solutions. The Cholesky factorization, instead of the often used QR factorization, is employed to construct the SAI preconditioner for cavity scattering analysis, by taking advantage of the symmetry of the matrix arising from electric fleld integral equation. Numerical experiments show that the higher order MLFMA is more e-cient than its low-order counterpart.

HIGHER ORDER METHOD OF MOMENTS FOR BISTATIC SCATTERING FROM 2D PEC ROUGH SURFACE WITH GEOMETRIC MODELING BY NURBS SURFACE

The higher order method of moments (HMOM) has been proposed to calculate the bistatic scattering from two-dimensional (2D) perfectly electric conducting (PEC) rough surface in this paper. The electric fleld integral equation (EFIE) is solved through the HMOM with the hierarchical higher order basis functions which are the modifled Legendre polynomials. The non-uniform rational B-spline (NURBS) surface is applied to model the plane surface related to the rough surface. Validity of this approach is shown by comparing the bistatic scattering coe-cient (BSC) to that of lower order MOM (LMOM) with the Rao-Wilton-Glisson (RWG) or rooftop basis function. This approach has fewer segments in the parametric directions than the LMOM with rooftop basis, and is more e-cient for the fewer unknowns and requires less memory than the LMOM with RWG basis. Properties of bistatic scattering from a 2D Gaussian rough surface are also exhibited and analyzed.

DISTORTION ANALYSIS OF ELECTROMAGNETIC FIELD SENSORS IN LAGUERRE FUNCTIONS SUBSPACE

A time-domain approach for distortion analysis of electromagnetic fleld senors is developed in Laguerre functions subspace. Using Laguerre convolution preservation property, it is proved that every electromagnetic fleld sensor corresponds to an equivalent discrete-time LTI system. The equivalent discrete-time system is compared to a reference system as a measure of distortion. Further, this analysis may be performed repeatedly to obtain a bandwidth-limited distortion characteristic. The method is employed to compare the distortion characteristic of an asymptotic conical dipole (ACD) to wire monopoles of various lengths. A time-domain simulation is performed in order to flnd the distortion characteristics by solving an electric fleld integral equation (EFIE) using the method of moments (MoM).

UNIAXIAL ANISOTROPIC SUBSTRATE EFFECTS ON THE RESONANCE OF AN EQUITRIANGULAR MICROSTRIP PATCH ANTENNA

Using a new combined approach, the efiect of the uniaxial anisotropic dielectrics on the resonant frequency and radiation fleld of an equitriangular patch antenna is presented in this paper. The problem is analysed in the spectral domain using the moment method and an electric fleld integral equation combined with a mathematical approach. However, the dyadic Green's functions corresponding to the proposed structure are separately developed and the Fourier transform of the basis current components are calculated mathematically using \the reference element method. Numerical results show that the change in the resonant frequency and the radiation patterns of the antenna is due primarily to a small disturbance of the substrate's nature. Then the efiect of the uniaxial anisotropic materials is a signiflcant parameter and most essential on the microstrip antenna characterization.

IMPROVING THE PERFORMANCES OF A HIGH TC SUPERCONDUCTING CIRCULAR MICROSTRIP ANTENNA WITH MULTILAYERED CONFIGURATION AND ANISO TROPIC DIELECTRICS

The moment method technique has been improved to in- vestigate the scattering properties of high Tc superconducting circular antennas with anisotropic substrate in multi-layered conflguration. In this method, the electric fleld integral equation for a current element on a grounded dielectric slab of inflnite extent was developed by basis functions involving Chebyshev polynomials. An improved analytical model is presented taking into account anisotropic substrate, super- conducting material for the circular patch and multilayered structure. To validate the theoretical results, an experimental study has been performed for a perfectly conducting circular patch on a single layer, with and without air gap. Good agreements were obtained between our theory and measurements. Efiects of temperature and thickness

FAST INHOMOGENEOUS PLANE WAVE ALGORITHM FOR ANALYSIS OF COMPOSITE BODIES OF REVOLUTION

A fast inhomogeneous plane wave algorithm is developed for the electromagnetic scattering problem from the composite bodies of revolution (BOR). Poggio-Miller-Chang-Harrington-Wu (PMCHW) approach is used for the homogeneous dielectric objects, while the electric fleld integral equation (EFIE) is used for the perfect electric conducting objects. The aggregation and disaggregation factors can be expressed analytically by using the Weyl identity. Compared with the traditional method of moments (MoM), both the memory requirement and CPU time, are reduced for large-scale composite BOR problems. Numerical results are given to demonstrate the validity and the e-ciency of the proposed method.

FINITE LENGTH OMNI-DIRECTIONAL CYLINDRICAL SPATIAL FILTERS

A flnite length cylindrical FSS is proposed as a spatial fllter for both transmitting and receiving antennas. This fllter has the advantage of not perturbing the omnidirectional property of the enclosed antenna. The proposed surface is constructed up as cylindrical array of rectangular conducting patches. The strips are arranged periodically in the `- and z-directions. The electric fleld integral equation (EFIE) approach is used for analyzing the characteristics of the proposed spatial fllter. The Rao-Wilton-Glisson (RWG) basis functions are used for current expansion on the conducting strips. The mutual efiects between the fllter and the antenna can be accurately investigated. The efiects of some dimensional parameters on the fllter characteristics, such as, the axial and angular spacing between the array elements, the length and the radius of the cylindrical surface are studied over a wide frequency range. The oblique incidence of plane waves on such a cylindrical fllter is studied with varying the direction of incidence. The performance of the proposed spatial fllter is examined when operating with nearby antennas. The efiects of such a fllter on the input impedance, VSWR, and radiation pattern of an enclosed bowtie antenna are investigated over a wide frequency range.

NUMERICAL ANALYSIS OF HUMAN HEAD INTERACTION WITH PIFA ANTENNAS IN CELLULAR MOBILE COMMUNICATIONS

This paper presents a numerical simulation of the human head coupling with a Planar Inverted-F Antenna (PIFA) structure based on the Coupled Integral Equation/Method of Moment (CIE/MoM) approach to study the efiects of the EM coupling on the antenna performance. A mix-potential integral equation (MPIE) for the surface current of PIFA structure and a volume electric fleld integral equation (VEFIE) for the head with mutual coupling terms are obtained. Finally numerical results will be presented at 900 and 1800MHz for the antenna performance parameters. The validity of the proposed method is evaluated using the XFDTD software.

DESIGN AND ANALYSIS OF WIDEBAND PLANAR MONOPOLE ANTENNAS USING THE MULTILEVEL FAST MULTIPOLE ALGORITHM

Two planar monopole antennas with wide impedance bandwidth are designed. A full-wave method of moment (MoM) based on the electric fleld integral equation (EFIE) is applied to analyze the impedance bandwidth and radiation performance of the monopoles. Meanwhile, the multilevel fast multipole algorithm (MLFMA) is employed to reduce the memory requirements and computational time. Experimental results such as the impedance bandwidth and radiation patterns are also presented. The good agreement between the experimental and numerical results well demonstrates the e-ciency and accuracy of the MLFMA code. Both the experimental and numerical results show that the two planar monopole antennas possess good input impedance and radiation performance over the AMPS, GSM900, and DCS band. As the proposed antennas can achieve such wide impedance bandwidth with relatively low proflle, they are very suitable for multi-band mobile communication systems.

FAST AND ACCURATE ANALYSIS OF LARGE METAMATERIAL STRUCTURES USING THE MULTILEVEL FAST MULTIPOLE ALGORITHM

We report fast and accurate simulations of metamaterial structures constructed with large numbers of unit cells containing split-ring resonators and thin wires. Scattering problems involving various metamaterial walls are formulated rigorously using the electric-fleld integral equation, discretized with the Rao-Wilton- Glisson basis functions. Resulting dense matrix equations are solved iteratively, where the matrix-vector multiplications are performed e-ciently with the multilevel fast multipole algorithm. For rapid solutions at resonance frequencies, convergence of the iterations is accelerated by using robust preconditioning techniques, such as the sparse-approximate-inverse preconditioner. Without resorting to homogenization approximations and periodicity assumptions, we are able to obtain accurate solutions of realistic metamaterial problems discretized with millions of unknowns.

A Fast Volume-surface Integral Equation Solver for Scattering Properties of NIMs

This paper presents a fast hybrid volume-surface integral equation approach for the computation of electromagnetic scattering from composed negative index media (NIM) such as split-ring-resonators (SRR) with wires. The volume electric fleld integral equation (EFIE) is applied to the dielectric region of this NIM, and the surface electric fleld integral equation is applied on the conducting surface. The method of moments (MoM) is used to discretize the integral equation into a matrix solution and adaptive integral method (AIM) is employed to reduce the memory requirement and CPU time for the matrix solution. The present approach is su-ciently versatile in handling scattering problems of composed NIMs, due to the combination of surface and volume electric fleld integral equations. Numerical results of calculating radar cross section (RCS) of such a NIM slab are flnally presented to demonstrate the accuracy and e-ciency of this technique. DOI: 10.2529/PIERS061003050010