多重网格法求解三维静电场分布

本文将一种高效率的数值计算方法——多重网格法引入三维静电场分布的计算,多重网格法利用限制和延拓可迅速求得满足精度要求的场分布.研究了求解各种静电透镜电子光学系统三维场分布的多重网格法程序,验算了静电同心球模型的三维场分布.通过与目前在场计算中常用的有限差分法进行比较,可以看出多重网格法的计算效率和计算精度优于有限差分法.本文表明利用多重网格法计算三维场大大提高了场分布的计算效率,缩短了计算时间,因此为后续计算打下了良好的基础.     

计算轴对称静电场的多重网格法的研究

本文研究的多重网格法,可用于区域形状任意和有“内电极”的实际电子光学系统轴对称电场的电位计算。其计算精度和效率均优于传统的有限差分法,故可广泛应用于分析设计静电聚焦像管的电子光学系统及摄像管电子枪的发射系统等。     

多重网格法对复杂边界电子光学系统三维场的计算

尝试多重网格法引入三维电子光学系统场的计算,用三维场计算程序（多重网格法）对第二代激光像增强器XX1380的电子光学系统进行了计算,结果表明多重网格法是电子光学系统CAD中计算三维场分布的一种高效、实用的数值方法。     

基于Matlab的非均匀介质静电特性分析

针对传统的静电场分析主要局限于同种介质,在介绍有限差分法求电位分布原理的基础上,导出了非均匀介质有限差分法的计算公式,并运用Matlab编程分析了所设定的非均匀介质区域静电特性。仿真结果与静电场理论符合较好,有助于加深对电介质静电特性的理解。     

基于MATLAB对二维混合边界静电场域的分析

本文分析了有限差分法的原理与概念,讨论了电磁场问题涉及3种类型的边界条件,采用有限差分数值计算分析边界问题,对二维混合型边界静电场进行分析,用MATLAB编程计算差分方程,并将超松弛迭代法引入到差分方程的计算,并与简单迭代方法进行比较,同样的计算精度下采用超松弛法不仅节省存储空间,而且加快了收敛速度。通过计算可以看出MATLAB在解决实际的工程和数学问题中,具有使用更为简便、语句功能更强的特点,能直观地演示二维混合边界静电场的电势分布图和场强立体分布图。     

静电场中电子轨迹的三维计算机模拟

本文讨论了静电场中电子轨迹的三维计算机模拟．给出了相应的计算公式．文中还对几种轨迹存在解析解的三维静电结构进行了计算．结果表明，本文所述方法精度较高，能满足电子光学ＣＡＤ的实际需要，是数值求解非轴对称静电结构下电子轨迹的有效方法．     

基于复合网格方法的低频近场通信天线等效电路参数分析

为解决计算区域的大尺度与天线尺寸的小尺度问题, 将复合网格法应用于近场通信(Near-Field Communication, NFC)天线等效电路参数的提取与计算, 该方法可以在计算效率和计算精度之间达到很好的平衡.为避免麦克斯韦方程的“低频崩溃”问题, 低频位移电流很小时, 采用静态场方法分析低频NFC天线的近场参数.其中对线圈天线分布电容的计算不同于以往的实验测量、理论估算和数值计算等研究方法, 而是基于其定义计算线圈相对于接地点的电容, 该方法可以得到与参考文献一致的计算结果, 同时具有能够分析周围环境对分布电容影响的优点.通过有限元分析, 将复合网格法与均匀网格法的计算结果对比, 证明了复合网格法在三维电磁场应用的可能性以及准确性.     

静电场中电子轨这的三维计算机模拟

本文讨论了静电场中电子轨这的三维计算机模拟，给出了其相应的计算公式，文中还对几各轨迹存在解析解的三维解电结构进行了计算，结果表明，本文所述方法精度较高，能满足电子光学ＣＡＤ的实际需要，是数值求解非轴对称静电结构下电子轨迹的有效方法。     

MPI下三维FDTD并行运算的分析与实现

基于Message-Passing Interface(MPI)的编程环境,以PML(Perfectly Matched Layer)为吸收边界条件,讨论了时域有限差分法FDTD的三维并行运算情况。通过一定的数值计算,定量地给出了MPI下FDTD并行算法中的网格数、进程数、分割方式三者之间的关系以及对计算效率的影响。     

IPO-FDTD混合法计算三维复杂腔体的RCS

运用IPO-FDTD混合法计算三维复杂腔体的电磁散射特性。该方法用物理光学迭代法计算腔体前端的缓变部分,用时域有限差分法计算含有复杂结构的腔体终端。在IPO和FDTD之间场耦合中,通过提取“本底噪声”来提高数值精度。数值结果表明该方法是准确有效的。     

Ellipsoidal refinement of the regularized inverse: performance in an anatomically realistic EEG model

Functional brain imaging and source localization based on the scalp's potential field requires a solution to the inverse electrostatic problem. This is an underdetermined problem with many solutions. Minimum norm and regularization methods involving the norm are often used, but generally give solutions in which current is widely distributed. One method for reducing the spatial distribution of a solution is to apply it iteratively within the bounds of a shrinking ellipsoid. This paper compares the performance of this approach with an exhaustive search at various noise levels using a numeric simulation of the electroencephalogram in a realistic conductor model. The results show that inverting a single dipolar source with a location accuracy comparable to an exhaustive search requires in the range of 5 to 10 dB higher signal-to-noise ratio.     

Efficient nearly-optimal motion and structure from images via analysis of dimensional reduction: application to safety checking system

In computing 3D motion and structure from image correspondences, often called the structure from motion (SFM) problem, dimensions of the used variable set are very large because it contains both motion and structure parameters. As a result, to solve the problem incurs much computational burden. However, in on-line applications of the SFM problem, computational efficiency needs to be stressed as some accuracy of the solutions is sacrificed. In this respect, various dimensional reduction methods are often introduced to improve computational efficiency and this usually leads to various reduced-form SFM problems. The so-obtained reduced-form SFM problems depend on fewer unknowns than the original SFM problem, thus allowing, in principle, for a less computationally intensive estimation, albeit potentially sacrificing accuracy of the results. It is thus interesting to study how much accuracy is lost. This is done by analytically proving results on equivalence or proximity of solutions for some example cases of the so-obtained reduced-form SFM problems. And then, based on the analysis, the author also proposes how to reduce the loss of accuracy in the reduced-form SFM problems (in the meaning of adjusting those reduced-form SFM problems to better approximate the original optimal SFM problem; that is, an optimal SFM problem that does not use any dimensional reduction methods). Experimental results are given to show the effect in practice. Finally, as an example application, a safety checking system using vision is considered.     

ESD field penetration through slots into shielded enclosures: atime domain approach

This paper presents a time domain approach for the analysis of the coupling between an electrostatic discharge (ESD) current and the internal region of a shielded enclosure with a slot. The application of the equivalence principle allows us to obtain an integro-differential equation for the unknown distribution of the aperture electric field. The numerical solution is obtained by an iterative procedure developed by the method of moments (MoM) in the time domain. The approach is also applied at the case of a transient incident field of a plane wave impinging on the enclosure. The use of proper impulse responses for the space and cavity regions make the model efficient from a computational point of view, without loss in accuracy. Theoretical results are validated by measurements     

An efficient forward solver in electrical impedance tomography by spectral element method

In electrical impedance tomography (EIT), a forward solver capable of predicting the voltages on electrodes for a given conductivity distribution is essential for reconstruction. The EIT forward solver is normally based on the conventional finite element method (FEM). One of the major problems of three-dimensional (3-D) EIT is its high demand in computing power and memory since high precision is required for obtaining a small secondary field which is typical for a small anomaly. This accuracy requirement is also set by the level of noise in the real data; although currently the noise level is still an issue, future EIT systems should significantly reduce the noise level to be capable of detecting very small anomalies. To accurately simulate the forward solution with the FEM, a mesh with large number of nodes and elements is usually needed. To overcome this problem, we proposed the spectral element method (SEM) for EIT forward problem. With the introduction of SEM, a smaller number of nodes and hence less computational time and memory are needed to achieve the same or better accuracy in the forward solution than the FEM. Numerical results demonstrate the efficiency of the SEM in 3-D EIT simulation.     

Efficient moment method analysis of a rectilinear edge-slot radiator in rectangular waveguide

A moment method (MoM) model of a rectilinear edge slot in rectangular waveguide is developed using entire domain trigonometric basis functions. This model has been found to provide an optimum trade-off between computational efficiency and accuracy. The intention behind the analysis is to provide an accurate, computationally fast model for the inclined edge slot radiator for incorporation into an array synthesis program. The basis functions for the ‘three-dimensional’ slot geometries involved in the analysis are generated using a simple transmission line representation of the slot field distribution to identify the resonant ‘slot modes’. The results obtained are compared with alternative modelling approaches to this problem, based on finite element method and finite difference time domain techniques, and also with measurement.     

Viable Three-Dimensional Medical Microwave Tomography: Theory and Numerical Experiments

Three-dimensional microwave tomography represents a potentially very important advance over 2D techniques because it eliminates associated approximations which may lead to more accurate images. However, with the significant increase in problem size, computational efficiency is critical to making 3D microwave imaging viable in practice. In this paper, we present two 3D image reconstruction methods utilizing 3D scalar and vector field modeling strategies, respectively. Finite element (FE) and finite-difference time-domain (FDTD) algorithms are used to model the electromagnetic field interactions in human tissue in 3D. Image reconstruction techniques previously developed for the 2D problem, such as the dual-mesh scheme, iterative block solver, and adjoint Jacobian method are extended directly to 3D reconstructions. Speed improvements achieved by setting an initial field distribution and utilizing an alternating-direction implicit (ADI) FDTD are explored for 3D vector field modeling. The proposed algorithms are tested with simulated data and correctly recovered the position, size and electrical properties of the target. The adjoint formulation and the FDTD method utilizing initial field estimates are found to be significantly more effective in reducing the computation time. Finally, these results also demonstrate that cross-plane measurements are critical for reconstructing 3D profiles of the target.      

Electron ray tracing by means of resistor network and digital computer

The problem of calculating electron trajectories in an electrostatic field is solved in two steps. First, the potential distribution for a given electrode configuration is found by means of a high precision resistor network. The second step requires a series of numerical calculations using the above potential values to determine the electron trajectories. All mathematical operations have been programmed for an IBM 709 digital computer. Three different mathematical methods are presented and compared. To check their accuracy test problems involving simple electrode configurations, for which the trajectories can be calculated analytically, were used. The error of a trajectory is defined bydelta/l, where δ is the maximum transverse deviation of a trajectory from its correct position andlis the length of the trajectory. Using the most accurate of the three methods for an electron in a homogeneous electric field between parallel planes the average error was1.3 times 10^{-4}. With the electric field between concentric spheres the average error was4 times 10^{-3}. The method of ray tracing described can be used for two-dimensional(x, y)and axially symmetric(r, z)fields. Space charge and magnetic fields can be taken into account. The time for calculating one trajectory over the whole length of the resistor network (50 units) is approximately 25 s.     

A multilevel formulation of the finite-element method forelectromagnetic scattering

Multigrid techniques for three-dimensional (3-D) electromagnetic scattering problems are presented. The numerical representation of the physical problem is accomplished via a finite-element discretization, with nodal basis functions. A total magnetic field formulation with a vector absorbing boundary condition (ABC) is used. The principal features of the multilevel technique are outlined. The basic multigrid algorithms are described and estimations of their computational requirements are derived. The multilevel code is tested with several scattering problems for which analytical solutions exist. The obtained results clearly indicate the stability, accuracy, and efficiency of the multigrid method