The tolerance method for electromagnetic scattering

The original electromagnetic field will be disturbed when the parameter of a local region is changed. To find the distribution of the disturbed electromagnetic field a boundary value problem, which is different from the original one, must be solved. A method to find the disturbed electromagnetic field from the known original one with a minimum amount of computation would be very significant. In this paper, we present a method, tolerance method, which can save significant computer time in the computation of the disturbed electromagnetic field. This method can be used for many complicated boundary value problems as well as for optimum design in engineering. An example of the computation of an electromagnetic scattering problem is given in this paper     

The bymoment method for two-dimensional electromagnetic scattering

The bymoment method is presented for analyzing two-dimensional electromagnetic wave scattering in an unbounded region. The method introduces a conforming surface to geometrically decouple the interior region containing the scatterer from the exterior region extending to infinity. The solution in the interior is generated using the standard finite-element solution of an interior Dirichlet boundary-value problem. The interior solution is then coupled to the exterior using Green's theorem in the unbounded exterior region. The validity of the method and the associated computer program is demonstrated by comparing the results to those of other methods for scattering by various cylindrical geometries     

An improved quasi-static finite-difference scheme for induced field evaluation based on the biconjugate gradient method

This paper presents a biconjugate gradient (BiCG) method that can significantly improve the performance of the quasi-static finite-difference scheme, which has been widely used to model field induction phenomena in voxel phantoms. The proposed BiCG method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional iterative, successive overrelaxation algorithm. The scheme has been validated against other known solutions on a lossy, multilayered ellipsoid phantom excited by an ideal coil loop. The wide application capability and computational performance of the BiCG method is demonstrated by modeling the exposure of MRI healthcare workers to fields produced by pulsed field gradients. This is an important topic of research in light of the Physical Agents Directive 2004/40/EC because a variety of realistic operator postures near the bore entrance of an MRI system are modeled.     

The application of the conjugate gradient method for the solution of electromagnetic scattering from arbitrarily oriented wire antennas

The method of conjugate gradients is applied to the analysis of radiation from thin-wire antennas. With this iterative technique, it is possible to solve electrically large arbitrarily oriented wire structures without storing any matrices as is conventionally done in the method of moments. The basic difference between the proposed method and Galerkin's method, for the same expansion functions, is that for the iterative technique we are solving a least squares problem. Hence, as the order of the approximation is increased, the proposed technique guarantees a monotonic decrease of the least squared error (parallel AI - Yparallel^{2}), whereas Galerkin's method does not. Even though the method converges for any initial guess, a good one may significantly reduce the time of computation. Also, explicit error formulas are given for the rate of convergence of this method. Hence, any problem can be solved to a prespecified degree of accuracy. It is shown that the method has the advantage of a direct solution as the final solution is obtained in a finite number of steps. The method is also suitable for solving singular operator equations in which case the method monotonically converges to the least squares solution with minimum norm. Numerical results are presented for the thin-wire antennas and are compared with the solution obtained by the method of moments.     

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。     

Hierarchically spectral algebraic multigrid method for electromagnetic scattering

A novel spectral algebraic multigrid (SAMG) method is developed for solving electromagnetic scattering problems. Unlike traditional algebraic multigrid methods, the SAMG is an algebraic two-grid cycle built on a preconditioned iterative method that is used as the smoother, and the grid transfer operators are defined using the spectral information based on high-order hierarchical basis functions. Numerical results show that this method is very effective in electromagnetic scattering and can reduce overall simulation time significantly.     

介质体电磁散射的偶极子模型法研究

提出用偶极子模型法来分析介质体的电磁散射.该方法以矩量法和Schaubert-Wilton-Glisson(SWG)基函数为基础,把介质体剖分成一定数量的四面体元.在介质体内,把含有公共面的体元对等效成电偶极子;在介质体表面,把边界面及其对应的体元等效成电偶极子.当等效偶板子单元离观察点大于临界距离时,用偶极子模型法计算阻抗矩阵元素.偶极子模型法简单易操作,不仅能大幅度降低阻抗矩阵的计算时间,还简化了边界条件的处理.数值结果表明了该方法的高效性及与原方法几乎相同的计算精度.     

Boundary element method for electromagnetic scattering from cylinders

The computation of low frequency scattering of electromagnetic fields by solid/hollow dielectric or conducting cylinders using the boundary element method (BEM) is considered. A general computer program has been developed for both transverse electric and magnetic cases. Numerical examples are given for conducting circular cylinders, and solid and hollow dielectric cylinders. The computational accuracy is checked by comparing the results with the analytic solution or computing an error defined from the optical theorem. In addition some problems at an interior resonance of the scatterer are discussed. The method can be directly applied to more complicated geometries.     

A path integral time-domain method for electromagnetic scattering

A new full wave time-domain formulation for the electromagnetic field is obtained by means of a path integral. The path integral propagator is derived via a state variable approach starting with Maxwell's differential equations in tensor form. A numerical method for evaluating the path integral is presented and numerical dispersion and stability conditions are derived and numerical error is discussed. An absorbing boundary condition is demonstrated for the one-dimensional (1-D) case. It is shown that this time domain method is characterized by the unconditional stability of the path integral equations and by its ability to propagate an electromagnetic wave at the Nyquist limit, two numerical points per wavelength. As a consequence the calculated fields are not subject to numerical dispersion. Other advantages in comparison to presently popular time-domain techniques are that it avoids time interval interleaving and it does not require the methods of linear algebra such as basis function selection or matrix methods     

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.     

Calculation of electromagnetic scattering from a dielectric cylinder using the conjugate gradient method and FFT

The scattering problem of an axially uniform dielectric cylinder is formulated in terms of the electric field integral equation, where the cylinder is of general cross-sectional shape, inhomogeneity, and anisotropy, and the incident field is arbitrary. Using the pulse-function expansion and the point-matching technique, the integral equation is reduced to a system of simultaneous equations. Then, a published procedure for solving the system using the conjugate gradient method and the fast Fourier transform (FFT) is generalized to the case of oblique-incidence scattering.     

分段积分共形算法在电磁散射问题中的应用

提出一种分段积分共形时域有限差分算法(PI-CFDTD),用于计算电磁散射问题。首先采用邻近网格电场场量插值表示变形网格中沿线电场场量,再以分段积分代替传统电场沿线积分求解,减小了阶梯误差,提高了电场环路积分的计算精度。推导出两种不同类型变形网格的电场环路积分公式,并对PI-CFDTD算法的稳定性进行研究,归纳得到应用原则。以金属方形平板和金属圆形平板作为算例进行验证,通过与传统时域有限差分法(FDTD)、传统共形时域有限差分法(CFDTD)以及矩量法(MoM)进行比较,表明PI-CFDTD计算精度更高。     

FINITE DIFFERENCE METHOD FOR ELECTROMAGNETIC SCATTERING FROM PERFECTLY CONDUCTING CYLINDER

A numerical method of solving electromagnetic wave scattering problem is described.Radiation boundary condition(RBC)is applied to confine EM scattering problem in unboundedregion into problem in finite region.Combined with RBC and scatterer surface boundary condi-tion,Helmholtz equation in the finite region is solved numerically by the finite difference method.Thus the distribution of induced surface current on conducting cylinder and near field can beobtained.Computational results for both polarizations for circular,elliptic and square cylindersare presented.These results are in excellent agreement with those obtained by the eigenfunctionexpansion method or moment method and much better then the results of OSRC method.     

A fast convergent method in electromagnetic inverse scattering

The authors present a fast convergent technique of the Born iterative method for nonlinear two-dimensional lossless object profile inversion using time-domain data. The magnitudes of the scattered fields at different frequencies are weighted according to the properties of the object. It is shown that the technique can speed up the convergence of the Born iterative method     

复合网格法在电磁散射问题中的应用研究

复合网格方法采用区域分解算法的思想,将计算区域分为粗网格与细网格两个区域.在电磁散射问题中,细网格区域包含了微细结构的电磁散射信息.利用连接边界条件,将粗网格计算结果和细网格计算结果分步进行计算,从而得到包含有微细结构的电磁散射信息.该计算方法可以减少此类计算问题的计算量,所得结果与全部区域进行细网格划分的结果进行了比较,两种结果复合很好.     

电磁响应的时、频域同时外推法

将散射体在高斯脉冲平面波激励下感应电流的时域响应展开为连带Hermite级数的叠加，利用傅立叶变换和连带Hermite函数的自反性，得到与时域响应形式类似的感应电流的频域响应。根据时域解与频域解的对应关系，利用感应电流的早时响应和低频响应，可确定展开式的未知系数，从而同时获得了时域和频域和完全响应。     

Conjugate gradient method applied to inverse scattering problem

A new reconstruction algorithm for diffraction tomography is presented. The algorithm is based on the minimization of a functional which is defined as the norm of the discrepancy between the measured scattering amplitude and the calculated one for an estimated object function. By using the conjugate gradient method to minimize the functional, one can derive an iterative formula for getting the object function. Numerical results for some two-dimensional scatterers show that the algorithm is very effective in reconstructing refractive index distributions to which the first-order Born approximation can not be applied. In addition, the number of iterations is reduced by using a priori information about the outer boundary of the objects. Furthermore, the method is not so sensitive to the presence of noise in the scattered field data     

The field feedback formulation for electromagnetic scattering computations

A new procedure is described for the solution of electromagnetic scattering problems in unbounded regions. Using this technique a spatial region enclosing the scatterer is initially decoupled from the exterior region and the fields therein are considered as the solution of an interior Dirichlet boundary value problem. The interior region solution is then recoupled to the unbounded exterior region by use of the equivalence principle. Such a process can be symbolically represented as a simple feedback system. The formulation is demonstrated for the case of plane wave scattering by finite metallic circular cylinders. A finite element solution of the interior problem is utilized in this example in conjunction with a field representation using a special case of coupled azimuthal potentials.     

采用分部外推BCGS-FFT方法快速求解电磁散射问题

为了快速求解电磁散射问题中具有震荡性、奇异性、慢收敛性的索末菲积分,提出了一种利用分部外推算法加速索末菲尾部积分计算,并结合稳定双共轭快速傅里叶变换(stabilized biconjugate gradient fast Fourier transform,BCGS-FFT)算法求解电磁散射问题场分布情况的新方法. 首先给出电场积分方程(electric field integral equation, EFIE)的表达形式,且在求解过程的索末菲积分中应用一种便捷的椭圆积分路径来最小化索末菲积分的震荡性与奇异性,在索末菲尾部积分使用Levin分部外推法来提高积分收敛速度,以此来快速填充并矢格林函数矩阵. 然后对新方法进行了多种数值实验,验证算法的精确度,并对比了新方法与传统BCGS-FFT方法的计算效率,发现在保持相同计算精度的条件下,新方法可节省20%～37%的计算时间. 该方法能应用于复杂散射体嵌入多层空间的电磁散射计算,为快速求解目标区域的电磁散射场提供了一种新的方法.