Global numerical boundary condition based PDE solution techniquesfor open-region electromagnetic field problems

The underlying concept and algorithm for global numerical boundary condition (GNBC) based PDE solution techniques for open-region EMF problems are presented. This numerical procedure has been applied with success for various boundary-value problems in scattering, waveguide, and radiation analysis showing distinct advantages in generality, flexibility, and simplicity. All the GNBCs treated are of the first kind, i.e. eigenfunction-based GNBCs     

Numerically derived absorbing boundary condition for the solutionof open region scattering problems

An absorbing boundary condition is developed by means of a numerical approximation of the analytical behavior of the exact boundary condition. The boundary operator is more accurate than other analytically derived differential operators having the same order, and it can be applied to arbitrarily shaped scatterer geometries that can be handled most efficiently through the use of outer boundaries that conform to the body of the scatterer. Examples demonstrate the improvement in accuracy and efficiency achieved by the numerical boundary condition. The enhancement in accuracy is attributable to the inclusion of the evanescent harmonics behavior in the model     

Three-dimensional biorthogonal multiresolution time-domain method and its application to electromagnetic scattering problems

A three-dimensional (3-D) multiresolution time-domain (MRTD) analysis is presented based on a biorthogonal-wavelet expansion, with application to electromagnetic-scattering problems. We employ the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet basis, characterized by the maximum number of vanishing moments for a given support. We utilize wavelets and scaling functions of compact support, yielding update equations involving a small number of proximate field components. A detailed analysis is presented on algorithm implementation, with example numerical results compared to data computed via the conventional finite-difference time-domain (FDTD) method. It is demonstrated that for 3-D scattering problems the CDF-based MRTD often provides significant computational savings (in computer memory and run time) relative to FDTD, while retaining numerical accuracy.     

预条件共轭梯度法在辐射和散射问题中的应用

用矩量法求解一些辐射和散射问题 ,如线天线辐射和线状体散射等问题时 ,可以产生一个 Toeplitz线性方程组 ,采用预条件共轭梯度法 (PCG)与快速富里叶变换 (FFT)的结合方法 (PCGFFT)来求解该方程组 ,其中预条件器采用 T.Chan的优化循环预条件器。使用 PCGFFT算法 ,可有效地节省内存 ,提高了计算速度。为说明其有效性 ,将 PCGFFT算法与 CGFFT算法以及 Levinson递推算法进行了对比。     

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. Past approaches involved applying a radiation condition at some distance from the scatterer in order to achieve a nearly reflection-free truncation of a finite-difference time-domain lattice. However, it is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic (TM) case, the integrand is known explicitly. For the transverse electric (TE) case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples areka = 5andka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger thanka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC. These will be the subject of a forthcoming paper.     

Matrix interpretation of the spectral iteration technique[electromagnetic scattering]

A matrix interpretation of the spectral iteration technique is presented to illustrate improvements in accuracy and convergence for both transverse magnetic and transverse electric waves incident on two-dimensional homogeneous scatterers producing solutions identical to a method of moments scheme. In this scheme, it is possible to improve the convergence rate of the technique by the use of nonphysical Green's function terms in the extended matrix. These terms result in the generation of a nonphysical field outside the scatterer, while still maintaining the correct solution of the current. Although the problem of nonconvergence has not been entirely overcome, a particular taper method used in the examples provided shows an improvement over their nontapered counterparts     

Convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems

An iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems, in an attempt to characterize the typical rate of convergence of that method. It is found that this rate depends on the cell density per wavelength used in the discretization, the presence of symmetries in the solution, and the degree to which mixed cell sizes are used in the models. Assuming cell densities used in the discretization are in the range of ten per linear wavelength, the iterative algorithm typically requiresN/4toN/2steps to converge to necessary accuracy, whereNis the order of the matrix under consideration.     

Numerical solution of electromagnetic problems

Modern high-speed digital computers have made possible the solution, by theoretical-numerical techniques, of many problems in electromagnetics that have traditionally been solvable only by experimental methods. Formulated in terms of integral equations, the techniques described yield answers, with an accuracy and completeness unobtainable by experimental methods, in a small fraction of the time and at much less cost than by the experimental approach. Computer programs utilizing these techniques have been developed in the areas of radiation and scattering from arbitrary wire-antenna structures, bodies of revolution, and cylindrical bodies of arbitrary cross section.     

Highly storage-efficient hybrid finite element/boundary element method for electromagnetic scattering

By properly choosing boundary surfaces and meshes of the hybrid finite element/boundary element method, one can reduce storage requirements of the boundary element matrices to the order of M for M boundary nodes.<>     

Application of Haar-wavelet-based multiresolution time-domainschemes to electromagnetic scattering problems

The multiresolution time-domain (MRTD) algorithm is applied to the problem of general two-dimensional electromagnetic scattering. A Haar wavelet expansion is utilized. A parallel between Haar MRTD and the classic Yee finite-difference time-domain (FDTD) algorithm is discussed, and results of simulations on canonical targets are shown for comparison. We focus on the incident-field implementation, which, in our case, consists of a pulsed plane wave. Also, we consider scattering in a half-space environment, with application to subsurface sensing. The results illustrate the advantage of the Haar MRTD method as compared with the classic FDTD, which consists of reduced memory and execution time requirements, without sacrificing accuracy     

Use of the pattern equation method for solution of problems of scattering of electromagnetic waves by bodies covered with a dielectric

The pattern equation method is generalized to problems of scattering of electromagnetic waves by 3D perfectly conducting bodies covered with a dielectric. The method is implemented in an algorithm for bodies of a rather arbitrary shape. In the case of a sphere, explicit analytic expressions for the coefficients involved in the scattering pattern are obtained from the general system of equations for these coefficients. The expressions obtained coincide with the corresponding formulas in the theory of Mie series. Scattering patterns are calculated for various bodies of revolution. The calculation results for bodies with a coating are compared to similar characteristics obtained via simulation of a dielectric coating with the suitable impedance.     

Another method of extending the boundary condition for the problem of scattering by dielectric cylinders

Another method of extending the boundary condition resembling the extended boundary condition first developed by Waterman for the problem of scattering by homogeneous isotropic dielectric obstacles is presented. Differences between both methods are discussed from theoretical and numerical viewpoints.     

Numerical second-kind-integral-equation solutions of electromagnetic scattering problems

A new, highly accurate numerical method based on second-kind integral equations has been developed to solve electromagnetic scattering problems for closed conducting bodies in two dimensions. The method is approximately fourth-order convergent, owing to the use of accurate new quadrature formulas.<>     

A hybrid method for combining quasi-static and full-wave techniquesfor electromagnetic scattering problems

Electromagnetic scattering problems containing subregions which are electrically small but geometrically complex are examined. By utilizing quasi-static methods for the small regions, full-wave methods in the remaining region, and determining necessary coupling relations between the small regions and the overall geometry, a considerable improvement in numerical efficiency is realized. The particular method developed here is valid for quasi-static regions in which magnetic induction can be ignored. Results using the proposed method have been obtained for a pair of closely spaced collinear wires. A comparison of these results with the wire antenna code, MININEC, showed excellent agreement     

Reciprocity, discretization, and the numerical solution of directand inverse electromagnetic radiation and scattering problems

The author gives a formulation, based on Lorentz reciprocity, that unifies the finite element method (FEM) and the integral equation models. Wave propagation and scattering problems in electromagnetics have to be addressed with the aid of numerical techniques. Many of these methods can be envisaged as being discretized versions of appropriate weak formulations of the pertinent operator (differential or integral) equations. For the relevant problems as formulated in the time Laplace-transform domain it is shown that the Lorentz reciprocity theorem encompasses all known weak formulations, while its discretization leads to the discretized forms of the corresponding operator equations, in particular to their finite-element and integral-equation modeling schemes. Both direct (forward) and inverse problems are discussed     

Application of the unimoment method to electromagnetic scattering of dielectric cylinders

The unimoment method is applied to calculate the scattered fields of dielectric cylinders of arbitrary cross section or of inhomogeneous material. The basic technique of the method is the use of the finite element methods inside a mathematical circle, which encloses the inhomogeneous body. The fields outside are expanded in the usual cylindrical harmonics. The interior and exterior problems are then coupled at the circle. The versatility is increased greatly by introducing the method of "inhomogeneous element." The advantage of the proposed method is the simplicity and efficiency in programming. The validity of the computer program has been verified by comparing results with calculations from other methods for i) an off-centered circular cylinder, ii) two circular cylinders, and iii) a circular cylindrical shell.     

A method of moments solution for electromagnetic scattering by inhomogeneous dielectric bodies of revolution

A method of calculating the electromagnetic scattering from and internal field distribution of inhomogeneous dielectric bodies of revolution (BOR) is presented. The method uses a typical mode-by-mode solution scheme. The electric flux density is chosen as the unknown quantity, which, together with the special construction of basis and testing functions, enables considerable reduction of the number of unknowns. A key element in this technique is expressing of the azimuthal field components of basis functions in terms of transverse components. A Galerkin testing procedure is used, with special attention put on the efficiency of calculating scalar potential term. Results of calculation for a few classes of dielectric bodies are given and compared with calculations done by other authors.     

Solution of electromagnetic scattering problems using time domaintechniques

New method are developed to calculate the electromagnetic diffraction or scattering characteristics of objects of arbitrary material and shape. The methods extend the efforts of previous researchers in the use of finite-difference and pulse response techniques. Examples are given of the scattering from infinite conducting and nonconducting cylinders, open channel, sphere, cone, cone sphere, coated disk, open boxes, and open and closed finite cylinders with axially incident waves     

A novel technique to the solution of transient electromagnetic scattering from thin wires

Previous approaches to the problem of transient scattering by conducting bodies have utilized the well-known marching-on-in-time solution procedures. However, these procedures are very dependent on discretization techniques and in many cases lead to instabilities as time progresses. Moreover, the accuracy of the solution procedure cannot be verified easily and usually there is no error estimation. Recently an alternate approach to the solution of transient scattering by thin wires was presented based on the conjugate gradient (CG) method. In this procedure, space and time are discretized independently into subintervals and the error is minimized iteratively. Unfortunately, this procedure is very slow, not easily extendable to other geometries, and moreover, some of the advantages of marching-on-in-time are lost. In this paper, again the conjugate gradient method is applied to solve the above problem, but this time, reducing the error to a desired value at each time step. Since the error is reduced at each time step, marching-on-in-time can still be done without error accumulation as time progresses. Computationally, this procedure is as fast as conventional marching-on-in-time. Thus, this new method retains all the advantages of marching-on-in-time and yet does not introduce instabilities in the late time. It is also possible to apply this procedure to other geometries. Details of the solution procedure along with numerical results are also presented.     

Extended boundary condition method for scattering and emission from natural surfaces modeled by fractals

The extended boundary condition method with the Weierstrass-Mandelbrot fractal function (WM-EBCM) has been recently employed to model and solve the problem of electromagnetic scattering from natural surfaces. In this paper we first of all show, on the basis of theoretical considerations and of numerical examples, that this method can be used also for the evaluation of electromagnetic emission from natural surfaces. In addition, a small roughness approximation of the WM-EBCM solution is presented to highlight the connection between EBCM and SPM, and to avoid matrix ill-conditioning in scattering problems. Achieved results show that the zero-order scattered field is the (deterministic) field reflected by the mean plane, and that the first-order (random) scattered field is directly proportional to surface roughness. Validity limits of the approximated method are discussed and verified by studying the scattered field behavior at different surface roughness conditions.