Homogeneous Dielectric Bodies Research Articles

Volume integral operators in electromagnetic scattering by homogeneous anisotropic dielectric bodies

Volume integral operators in electromagnetic scattering by homogeneous anisotropic dielectric bodies

Fast Computation of Electromagnetic Scattering From Dielectric Objects Using Quadrilateral Piecewise Sinusoidal Basis and Characteristic Basis Function Method

A method of moments (MoM)-based procedure is developed to calculate the scattering from homogeneous dielectric bodies. The technique uses quadrilaterals for the approximation of geometry and piecewise sinusoidal (PS) basis functions for the approximation of surface currents. The notable advantage of the PS basis is its radiated fields can be expressed in closed-form. The proposed approach therefore circumvents the need to use Green’s function in formulating the integral equations. Combined with a simple testing procedure, the matrix filling time is reduced and the concern of singularity is removed. To further reduce the computational complexity and enhance the performance, a characteristic basis function method (CBFM) is implemented and embellished with a new characteristic basis function (CBF) generation strategy. Specifically, a cubical surface bounding the entire target is first specified and discretized. A set of auxiliary sources are then defined in a manner similar to that done for a scattering body. These auxiliary sources are defined once and shared by different blocks. In comparison to the traditional plane wave spectrum (PWS) method, the CBFs generated by the new approach are valid not only for plane wave excitations but also for localized excitations. Numerical results are provided to validate the efficacy of the proposed algorithm.

Theory of Characteristic Modes for Nonsymmetric Surface Integral Operators

The theory of characteristic modes is formulated with nonsymmetric surface integral operators for perfect electric conductors, impedance surfaces, and homogeneous dielectric bodies. For nonsymmetric (nonself-adjoint) operators, the eigenvectors are not orthogonal with respect to the weighted inner product defined with the weighting operator of the generalized eigenvalue equation. Rather, this orthogonality holds between the eigenvectors of the original equation and the adjoint equation, including adjoint operators. This implies that the modal expansion, used to express any scattering or radiation solution as a linear combination of the modes, requires these two sets of eigenvectors. For matrix equations, the eigenvectors of the adjoint equation correspond to the left eigenvectors of the original equation.

The method of hypersingular integral equations in the problem of electromagnetic wave diffraction by a dielectric body with a partial perfectly conducting coating

AbstractA problem of scattering of a monochromatic electromagnetic wave by a homogeneous dielectric body is considered. A part of the boundary of the body is a perfectly conducting thin surface. The problem is reduced to a system of the boundary integral equations containing integrals with strong singularity, the integrals are understood in terms of Hadamard final part. A numerical solution scheme is constructed on the base of approximate solution of these equations using the methods of piecewise-constant approximations and collocation. The constructed numerical scheme is tested on a model example.

TESTING OF NUMERICAL SOLUTION OF THE PROBLEM OF DETERMINING SOURCES OF MAGNETOSTATIC FIELD IN MAGNETIZED MEDIUM

Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use analytical solutions for problems of calculation of external electrostatic field effect on piecewise homogeneous dielectric bodies for testing integral equations of magnetostatics and algorithms for their numerical solutions. Practical value. The described method of testing integral equations of magnetostatics and their numerical solutions can be used for calculation of magnetic fields of spacecraft control system electromagnets.

The electromagnetic-thermal dosimetry for the homogeneous human brain model

The electromagnetic-thermal dosimetry model of the human brain exposed to electromagnetic (EM) radiation is developed. The EM model based on the surface integral equation (SIE) formulation is derived using the equivalence theorem for the case of a lossy homogeneous dielectric body. The thermal dosimetry model of the brain is based on the form of Pennes׳ equation for heat transfer in biological tissue. The numerical solution of the EM model is carried out using the Method of Moments (MoM) while the bioheat equation is solved using the finite element method (FEM). Developed EM-thermal model has been applied for the internal dosimetry of the human brain to assess the absorbed EM energy and the consequent temperature rise due to the exposure of 900MHz plane wave. Due to the variability of various parameters, the sensitivity of the maximum, minimum and the average steady-state temperature, on the various thermal parameters have been examined, as well as the influence of the parameters variation on the temperature distribution in case of EM exposure. The proposed model may be found useful in the rapid assessment of the temperature distribution in the human brain, prior to having to deal with a tedious development of a more complex models.

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.

Efficient propagation-inside-layer expansion algorithm for solving the scattering from three-dimensional nested homogeneous dielectric bodies with arbitrary shape.

This paper deals with the evaluation of electromagnetic scattering from a three-dimensional structure consisting of two nested homogeneous dielectric bodies with arbitrary shape. The scattering problem is formulated in terms of a set of Poggio-Miller-Chang-Harrington-Wu integral equations that are afterwards converted into a system of linear equations (impedance matrix equation) by applying the Galerkin method of moments (MoM) with Rao-Wilton-Glisson basis functions. The MoM matrix equation is then solved by deploying the iterative propagation-inside-layer expansion (PILE) method in order to obtain the unknown surface current densities, which are thereafter used to handle the radar cross-section (RCS) patterns. Some numerical results for various structures including canonical geometries are presented and compared with those of the FEKO software in order to validate the PILE-based approach as well as to show its efficiency to analyze the full-polarized RCS patterns.

An Efficient Single-Source Integral Equation Solution to EM Scattering From a Coated Conductor

The single-source integral equation (SSIE) technique is presented to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional conducting object coated by a homogeneous dielectric body. The external and interior surface equivalence principles combined with the continuity of the tangential components of the total electric and magnetic fields on the surface of the dielectric and zero tangential component of the total electric field on the surface of the conductor are used to formulate the single-source electric and magnetic field integral equations. With a localization procedure, the Calderon preconditioned single-source electric field integral equation (SSEFIE) is constructed and combined with single-source magnetic field integral equation (SSMFIE) to produce a single-source combined field integral equation (SSCFIE), which is free from spurious resonance and dense-mesh breakdown. Numerical results validate the good performance of the proposed algorithm.

Generation of Excitation-Independent Characteristic Basis Functions for Three-Dimensional Homogeneous Dielectric Bodies

The aim of this paper is the development of characteristic basis functions (CBFs) for homogeneous dielectric bodies that are modeled with the surface equivalence principle. This approach contributes to generalize the characteristic basis function method (CBFM) for any kind of material. The foundations for the generation of these new basis functions are widely revised and the CBFM is adapted for this purpose. The validity of the method is illustrated with the systematic analysis of canonical geometries as well as with the computation of the specific absorption rate inside a head-like geometry. In all the cases, the error in the current distribution as well as in the near- and far-field is considered. In addition, a detailed comparison of the generation of the CBFs using plane waves and spherical waves is also carried out.

Generalized method of moments: a framework for analyzing scattering from homogeneous dielectric bodies

In this paper, we present a novel framework for discretizing integral equations--specifically, those used for analyzing scattering from dielectric bodies. The candidate integral equations chosen for the analysis are the well-known Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and the Müller equations. Discrete solutions to these equations are typically obtained by representing the spatial variation of the currents using the Rao-Wilton-Glisson (RWG) basis functions or their higher order equivalents. In this paper, we propose a framework for defining basis functions that departs significantly from those of RWG functions in that approximation functions can be chosen independent of continuity constraints. We will show that using this framework together with a quasi-Helmholtz type representation has a number of benefits. Namely, (i) it shows excellent convergence, (ii) it permits inclusion of different orders of polynomials or different functions as basis functions without imposition of additional constraints, (iii) the method can easily handle nonconformal meshes, and (iv) the method is well conditioned at all frequencies. These features will be demonstrated via a number of numerical experiments.

Fast Inhomogeneous Plane Wave Algorithm for Homogeneous Dielectric Body of Revolution

To solve the electromagnetic scattering problem for homogeneous dielectric bodies of revolution (BOR), a fast inhomogeneous plane wave algorithm is developed. By using the Weyl identity and designing a proper integration path, the aggregation and disaggregation factors can be derived analytically. Compared with the traditional method of moments (MoM), both thememory and CPU time requirements are reduced for large-scale homogeneous dielectric BOR problems. Numerical results are given to demonstrate the validity and the efficiency of the proposed method. AMS subject classifications: 35Q61, 74F15, 74J20, 83C50

An Analysis of Scattering Caused by Dielectric Bodies Using Semi-Analytic Methods

A novel set of integrodifferential equations is formulated for the analysis of electromagnetic scattering and radiation by three-dimensional homogeneous dielectric bodies. The use of the Stratton-Chu integrals, the Atkinson-Wilcox and multipole representations of electromagnetic fields underlies the considered approaches. The equations are reduced to the infinite algebraic systems solved in a truncated representation. The results obtained by the numerical solution of these systems have been mutually compared and they have been shown to be in agreement. The investigation of convergence and time efficiency of the algorithms have been performed by the solution of the scattering problem for a cube and sphere excited by plane waves. Resonant regimes of dielectric cubes and spheres excited by probes have also been studied and the numerical results have been compared against the results predicted by the approximate theory of dielectric resonators. The convergence criterion for the Atkinson-Wilcox expansion has been formulated.

Indoor field strength prediction based on FMM

In this article, the fast multipole method (FMM) is applied to analyze the field strength of an ultra-wideband (UWB) signal. Small coverage of UWB communication systems and high efficiency of the algorithm make it possible to calculate the amplitude of electric field accurately. A homogeneous dielectric body and a multilayered dielectric object are studied. The computational results obtained by applying the FMM agree well with those obtained by applying the method of moments (MoM).

Numerical solution of the CFIE using vector bases and dual interlocking meshes

A numerical solution of the combined-field integral equation for wave scattering from homogeneous dielectric bodies is proposed. The approach uses a simultaneous representation of the equivalent surface current densities in both curl-conforming and divergence-conforming bases, defined on a dual interlocking mesh representing the scatterer surface. The dual-mesh based approach is stable at internal resonances and allows the use of the optimum type of basis function for each integral operator within the combined field equation. The procedure can also be used to obtain a radiation boundary condition for differential equation formulations.

Analysis of Scattering From Arbitrarily Shaped 3-D Conducting/Dielectric Composite Objects Using a Combined Field Integral Equation

In this paper, we present a new formulation for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) perfectly conducting and piecewise homogeneous dielectric composite body. The formulation treated here is the combined field integral equation (CFIE). The conducting/dielectric structure is approximated by planar triangular patches, which have the ability to conform to any geometrical surface. The surface covering the conducting body is replaced by an equivalent surface electric current and the surface of the dielectric by equivalent electric and magnetic currents. The all surface currents are approximated in terms of RWG (Rao, Wilton, Glisson) functions. The objective of this paper is to illustrate that the CFIE is a valid methodology in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results are presented and compared for composite scatterers with solutions obtained using other formulations.

Solution of time domain electric field integral equation for arbitrarily shaped dielectric bodies using an unconditionally stable methodology

In this work, we present a new and efficient numerical method to obtain an unconditionally stable solution for the time domain electric field integral equation (TD‐EFIE) for arbitrary homogeneous dielectric bodies, derived utilizing the surface equivalence principle. This novel method does not utilize the customary marching‐on in time solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives in the TD‐EFIE formulation can be handled analytically. Since these weighted Laguerre polynomials converge to zero as time progresses, the induced electric and magnetic currents when expanded in a series of weighted Laguerre polynomials also converge to zero. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the temporal testing procedure, the marching‐on in time procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the currents, the spatial and the temporal variables can be separated. For convenience, we use the Hertz vector as the unknown variable instead of the equivalent electric current density. However, we use the equivalent magnetic current density as it is. To verify our method, we apply the proposed method to various dielectric scatterers and compare the results of an inverse Fourier transform of a frequency domain EFIE.

Analysis of finite-microstrip structures using surface equivalence principle and multiple network theory (SEMN)

Two techniques are developed for the analysis of finite microstrip structures. They are based on electric and magnetic field integral equation (EFIE and MFIE) formulations of the surface equivalent principle and multiple network theory (SEMN) method. Using pulse surface basis functions, the surface of each homogeneous dielectric body is modeled by small flat segments of arbitrary geometry and constant electromagnetic field. Using the surface equivalence principle and the Green's functions of the homogeneous space, the admittance and impedance matrices are computed. Then, the boundary conditions and multiple network theory are applied to determine the overall characteristic of the entire space. Several radiation and scattering examples are numerically analyzed and their calculated near and far fields are presented. The numerical results of the two formulations are then compared with measurement and those of HFSS and ENSEMBLE.

A Survey of Various Frequency Domain Integral Equations for the Analysis of Scattering from Three-dimensional Dielectric Objects

In this paper, we present four dierent formulations for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) homogeneous dielectric body in the frequency domain. The four integral equations treated here are the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the PMCHW (Poggio, Miller, Chang, Harrington, and Wu) formulation. For the CFIE case, we propose eight separate formulations with dierent combinations of expansion and testing functions that result in sixteen dierent formulations of CFIE. One of the objectives of this paper is to illustrate that not all CFIE are valid methodologies in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results involving the equivalent electric and magnetic currents, far scattered fields, and radar cross section (RCS) are presented for three canonical dielectric scatterers, viz. a sphere, a cube, and a finite circular cylinder, to illustrate which formulation works and which does not.

A Survey of Various Frequency Domain Integral Equations for the Analysis of Scattering From Three-Dimensional Dielectric Objects - Abstract

In this paper, we present four different formulations for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) homogeneous dielectric body in the frequency domain. The four integral equations treated here are the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the PMCHW (Poggio, Miller, Chang, Harrington, and Wu) formulation. For the CFIE case, we propose eight separate formulations with different combinations of expansion and testing functions that result in sixteen different formulations of CFIE. One of the objectives of this paper is to illustrate that not all CFIE are valid methodologies in removing defects, which occur at a frequency corresponding to an internal resonance of the structure. Numerical results involving the equivalent electric and magnetic currents, far scattered fields, and radar cross section (RCS) are presented for three canonical dielectric scatterers, viz. a sphere, a cube, and a finite circular cylinder, to illustrate which formulation works and which does not.