Electromagnetic scattering by multiple three-dimensional scatterersburied under multilayered media. I. Theory

A general procedure is developed for the analysis of electromagnetic (EM) scattering by multiple three-dimensional (3D) dielectric and/or conducting objects buried under one-dimensional (1D) multilayered media. In this first part of a two-part paper, general closed-form formulations for the electric fields excited by an arbitrarily oriented electric dipole under the layered media are first presented, from which electric-field integral equations for the buried dielectric objects, pure conducting objects, and their combinations are then obtained, and the scattered electric fields in the upper space are formulated. Finally, the physical significance of the above formulations is discussed. In the second part, numerical implementations for these integral equations and the scattered fields are investigated     

Resonant frequency and Q factor of axisymmetric composite microwave cavities

Resonant frequency and unloaded Q factor of composite microwave cavities are computed using surface integral equations for axisymmetric objects. The equivalence principle is used to formulate the problem so that the unbounded space Green's function can be utilized. The numerical results are verified experimentally for many samples of conducting cavities and dielectric resonators inside conducting cavities. Also, cases with a sector of the rotational cavity are considered by introducing a conducting corner. The method allows the computation of the stored energy in each dielectric region and the unloaded Q factor.     

Extended integral equation formulation for scattering problems froma cylindrical scatterer

An extended integral equation is developed for electromagnetic scattering from a perfectly conducting cylinder and a dielectric cylinder. The conventional surface integral equations cannot yield unique solutions when the wavenumber of the electromagnetic wave is equal to an eigenwavenumber of the system. Several methods to overcome this difficulty have been presented, but each method includes some drawbacks. A numerical method is proposed in which the boundary element method is applied to the extended integral equations with the observation points lying on a closed surface inside the scatterer. It is shown that the extended integral equations have unique solutions for any given wavenumber. As examples, plane wave scattering from a perfectly conducting elliptic cylinder, a dielectric elliptic cylinder, and a dielectric rectangular cylinder is numerically analyzed     

MLFMA分析复杂载体平台上天线问题

该文分析了导体介质复合结构平台上线天线的辐射问题。利用等效原理建立EFIE-PMCHW表面积分方程组,定义线、面和连接基函数描述复杂结构上电流分布,分析了导体介质分界面处基函数的处理;利用多层快速多极子方法(MLFMA)加速迭代求解过程中的矩阵矢量相乘运算,并用于有耗媒质求解。MLFMA的运用极大地提高了求解实际电大问题的能力。数值计算结果验证了方法的正确性和高效性。     

Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. II. Implementation and results for contiguoushalf-spaces

For pt.I see ibid., vol.38, no.3, p.335-44 (1990). In pt.I, three mixed-potential electric field integral equations (MPIEs) for conducting surfaces of arbitrary shape residing in plane-stratified dielectric media with an arbitrary number of layers were formulated. One of the MPIEs (formulation C) was found to be particularly well suited for the application of the method of moments (MM). In pt.II, formulation C is specialized to the important case of a scatterer or antenna of arbitrary shape residing in contiguous half-spaces. This MPIE is solved by the MM employing a triangle-patch model of the surface of the object. Sample numerical results for several cases of interest are presented     

粗糙海面上三维金属目标的电磁散射特性分析

该文采用矩量法(MoM)计算粗糙海面上三维金属目标的电磁散射特性。计算了位于半空间媒质中的电偶极子和磁偶极子的矢量位并矢格林函数和标量位格林函数,并将其应用于矩量法中。把海水视为下半空间媒质,粗糙海面为位于上半空间中的介质表面。通过建立介质和金属混合目标的积分方程,并采用迭代方法求解矩阵方程以得到该模型的散射特性,数值结果验证了本文方法的有效性。     

A coupled surface-volume integral equation approach for thecalculation of electromagnetic scattering from composite metallic andmaterial targets

A coupled surface-volume integral equation approach is presented fur the calculation of electromagnetic scattering from conducting objects coated with materials. Free-space Green's function is used in the formulation of both integral equations. In the method of moments (MoM) solution to the integral equations, the target is discretized using triangular patches for conducting surfaces and tetrahedral cells for dielectric volume. General roof-top basis functions are used to expand the surface and volume currents, respectively. This approach is applicable to inhomogeneous material coating, and, because of the use of free-space Green's function, it can be easily accelerated using fast solvers such as the multilevel fast multipole algorithm     

Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces     

Numerical solution of time domain integral equations for arbitrarily shaped conductor/dielectric composite bodies

In this work, we present a numerical solution of the coupled time domain integral equations to obtain induced currents and scattered far fields on a three-dimensional, arbitrary shaped conducting/dielectric composite body illuminated by a Gaussian electromagnetic plane wave pulse. The coupled integral equations are derived utilizing the equivalence principle. The solution method is based on the method of moments and involves the triangular patch modeling of the composite body, in conjunction with the patch basis functions. Detailed mathematical steps along with several numerical results are presented to illustrate the efficacy of this approach.     

Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.     

Improved quadrature formulas for boundary integral equations with conducting or dielectric edge singularities

In this paper we derive new two-dimensional (2-D) quadrature formulas for the discretization of boundary integral equations in the presence of conducting or dielectric edges. The proposed formulas allow us to exactly integrate polynomials of degree less than or equal to five, multiplied by an algebraic singular factor that diverges along one side of the triangular integration domain. This is the kind of singularity that occurs when physical edges are present in both conducting and dielectric bodies. Numerical tests are performed on the presented formulas, in order to validate the achieved improvement in accuracy, and examples are given of their application to the determination of radar cross-section of 3-D metallic objects.     

Hybrid numerical method for harmonic 3-D Maxwell equations:scattering by a mixed conducting and inhomogeneous anisotropicdielectric medium

This article deals with a hybrid numerical method for solving harmonic Maxwell equations in the classical electrodynamic context. This formulation can be used with any body of arbitrary three-dimensional geometry, of perfectly conducting material or dielectric, with locally inhomogeneous and anisotropic behavior laws, and with or without dielectric losses. The mathematical formulation is presented along with applications validating it. The exterior problem is treated by the integral equation method while local equations are used for the dielectric parts of the body. A global variational formulation of the coupled problem is developed for use in discretization by the finite element method. Boundary finite elements are used for integral operators connected with the exterior problem. Localized finite elements are used for the interior problem. Difficulties of irregular frequencies, also called resonant frequencies in the perfectly conducting case, arising from the integral formulation are analyzed in detail and an efficient solution is developed     

Electromagnetic scattering from arbitrary shaped conducting bodiescoated with lossy materials of arbitrary thickness

A simple and efficient numerical technique is presented to solve the electromagnetic scattering problem of coated conducting bodies of arbitrary shape. The surface equivalence principle is used to formulate the problem in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents which represent boundary fields. The conducting structures and the dielectric materials are modeled by planar triangular patches, and the method of moments is used to solve the integral equations. Numerical results for scattering cross sections are given for various structures and compared with other available data. These results are proved accurate by a number of representative examples     

E-P-AMCBFM分析介质与PEC混合体的电磁散射

使用基于表面积分方程的矩量法来分析介质与理想导体混合体的电磁散射是计算电磁学的一大热点。对理想导体目标体表面建立电场积分方程,在介质目标体表面建立PMCHW方程组,与基于矩阵分块技术的自适应修正特征基函数法结合,对介质涂敷理想导体目标体的电磁散射进行分析,将其称之为EFIE-PMCHW-AMCBFM(E-P-AMCBFM)。并讨论不同参数如基函数阶数,矩阵块间重叠区域等对计算效率的影响,数值结果表明E-P-AMCBFM对于处理介质-理想导体混合体的电磁散射问题具有较高的精度和效率。     

A Spectral Integral Method and Hybrid SIM/FEM for Layered Media

This paper first presents a spectral integral method (SIM) for electromagnetic scattering from homogeneous dielectric and perfectly electric conducting objects straddling several layers of a multilayered medium. It then uses this SIM as an exact radiation boundary condition to truncate the computational domain in the finite-element method (FEM) to form a hybrid SIM/FEM, which is applicable to arbitrary inhomogeneous objects. Due to the high accuracy of the SIM, the sampling density on the radiation boundary requires less than five points per wavelength to achieve 1% accuracy. The efficiency and accuracy of the developed methods have been demonstrated with several numerical experiments for the TM_z case. The TE_z case can be obtained by duality     

Combined field solution for TM scattering from multiple conducting and dielectric cylinders of arbitrary cross section

A simple moment solution is given for the problem of electromagnetic scattering from multiple conducting and dielectric cylinders of arbitrary cross section. The system of conducting and dielectric cylinders is excited by a plane-wave polarized transverse magnetic to the axis of the cylinders. The equivalence principle is used to obtain three coupled integral equations for the induced electric current on the conducting cylinders and the equivalent electric and magnetic currents on the surface of dielectric cylinders. The combined field integral equation (CFIE) formulation is used. Sample numerical results are presented. The agreement with available published data is excellent.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

A numerical solution to full-vector electromagnetic scattering bythree-dimensional nonlinear bounded dielectrics

This paper deals with electromagnetic scattering by nonlinear dielectric objects. In particular, a numerical approach is developed that is aimed at determining the distributions of the electromagnetic field vector inside a three-dimensional nonlinear, inhomogeneous, isotropic scatterer illuminated by a time-periodic incident electric field vector. An integral-equation formulation for the full-vector scattering problem is considered, and the nonlinear effect is taken into account by introducing equivalent sources and a Fourier-series representation. A system of integral equations (for each harmonic vector component and for the static term) is obtained that includes the internal electric field distribution as the unknown. After discretization, the solution is reduced to solving an algebraic system of nonlinear equations. Some preliminary numerical results are reported concerning scatterers that exhibit a specific (quadratic) dependence of the dielectric permittivity on the total electric field. The harmonic components of the scattered electric field outside the objects are also computed     

Analysis of transient scattering from composite arbitrarily shapedcomplex structures

A time-domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures. The solution method is based on the method of moments (MoM) and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions. An implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain. The usual late-time instabilities associated with the time-domain integral equations are avoided by using an implicit scheme. Detailed mathematical steps are included along with representative numerical results     

Extended boundary condition integral equations for perfectly conducting and dielectric bodies: Formulation and uniqueness

The equivalence theorem is used to derive novel generalized boundary condition (GBC) integral equations for the tangential components of the electric and magnetic fields on the interfaces of a finite number of dielectric or conducting scatterers. Closed surface, plane, and line extended boundary conditions (EBC) equivalent to the GBC are introduced. The GBC integral equations can now be replaced by any of these EBC integral equations whose solutions are unique and easy to obtain numerically using the moment method. A perfectly conducting sphere and a dielectric sphere in the electrostatic field of two equal and opposite point charges are presented as simple examples of the general procedure.