应用NURBS-UTD方法分析受扰方向图

 本文研究基于任意曲面建模的UTD方法,引入NURBS曲面建模技术对电大尺寸目标建模,给出了NURBS-UTD方法中反射射线场以及表面绕射射线场的数值求解方法。与曲面有关的具体参数,根据微分几何的基本原理结合参数曲面定义使用各种数值方法进行处理,对线积分使用定义展开。针对实际当中任意几何造型的电大尺寸平台的电磁特性分析,本文方法不仅能够处理初等解析曲面,也能够处理任意弯曲的曲面模型,并且不需要消耗大量计算资源又提高了建模精度,文中给出实例进行说明。     

Fully Coupled Hybrid FEM-UTD Method Using NURBS for the Analysis of Radiation Problems

A novel hybrid finite element method (FEM) -uniform theory of diffraction (UTD) method for the analysis of radiating structures in the presence of electrically large objects is presented. The hybridization is done in a fully coupled way taking into account mutual interactions between the FEM and UTD regions. The UTD objects are modeled using non-uniform rational B-spline (NURBS) surfaces. Ray acceleration techniques and simple clustering strategies are used to speed up the computation time. Numerical results are presented showing the validity of the method.     

NURBS-UTD方法的反射射线寻迹算法研究

针对目前的UTD方法无法处理任意弯曲模型这一缺陷,该文将CAGD中广泛使用的NURBS曲面建模技术与计算电磁学中广泛使用的UTD方法相结合,讨论了NURBS-UTD方法的反射射线寻迹算法.该算法可应用于包括UTD方法中典型的柱、锥在内的任意曲面上,数值结果表明了算法的有效性及实用性.     

Preconditioned astigmatic beam tracing for urban propagation

In wireless communication network planning, deterministic and statistical propagation tools have been developed. Astigmatic Beam Tracing, a deterministic method based on ray tracing (GO/UTD), can be applied to urban propagation modeling. A numerical code has been applied to a model of urban scenario with increasing complexity. The results of a numerical analysis are discussed to evaluate the relevance of the test case size on the computational charge.     

Application of physical optics to the RCS computation of bodiesmodeled with NURBS surfaces

The paper presents a method for the computation of the monostatic radar cross section (RCS) of electrically large conducting objects modeled by nonuniform rational B-spline (NURBS) surfaces using the physical optic (PO) technique. The NURBS surfaces are expanded in terms of rational Bezier patches by applying the Cox-De Boor transform algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. The PO integral is evaluated over the parametric space of the Bezier surfaces using asymptotic integration. The scattering field contribution of each Bezier patch is expressed in terms of its geometric parameters. Excellent agreement with PO predictions is obtained. The method is quite efficient because it makes use of a small number of patches to model complex bodies, so it requires very little memory and computing time     

Combining the moment method with geometrical modelling by NURBSsurfaces and Bezier patches

Induced current distributions on conducting bodies of arbitrary shape modelled by NURBS (non uniform rational B-splines) surfaces are obtained by using a moment method approach to solve an electric field integral equation (EFIE). The NURBS surfaces are expanded in terms of Bezier patches by applying the Cox-de Boor transformation algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. New basis functions have been developed which extend over pairs of Bezier patches. These basis functions can be considered as a generalization of “rooftop” functions. The method is applied to obtain RCS values of several objects modelled with NURBS surfaces. Good agreement with results from other methods is observed. The method is efficient and versatile because it uses geometrical modelling tools that are quite powerful     

Combining the Higher Order Method of Moments With Geometric Modeling by NURBS Surfaces

This paper introduces the nonuniform rational B-spline (NURBS) surfaces to improve the geometric modeling of the higher order method of moments (MoM). The electric field integral equation (EFIE) is discretized by the hierarchical higher order basis functions and converted to a matrix equation. Then the elements of the impedance matrix are efficiently evaluated by a new set of formulas. The bistatic radar cross sections (RCS) obtained by this new technique are compared with those obtained by the commonly used higher order MoM. The example of a cylinder and a missile shows excellent accuracy of the NURBS surfaces and that of the resultant RCS. Moreover, this new technique can fully exploit the flexibility of the higher order basis functions when the surface is highly curved, whereas the commonly used higher order MoM can not.      

Efficient Analysis of Aperture Antennas on Generally Shaped Convex Multilayered Surfaces Using a Hybrid SD-UTD Method

A novel hybrid method is described for analyzing convex multilayered conformal array antennas. The hybrid method is based on the spectral domain approach in combination with the ray-based uniform theory of diffraction (UTD) method. The analysis is divided in two parts. First, the spectral domain approach is accelerated by using an asymptotic extraction technique where the extracted term of the Green's function is calculated using UTD. It is shown that this new approach results in significant acceleration of the existing spectral domain algorithm without losing accuracy. The modified spectral domain method is then used in the second part where generally shaped convex multilayered surfaces are analyzed by using sets of canonically shaped surfaces (spheres and/or circular cylinders). Their radii are obtained using the UTD formulation, which contains important information such as distance and curvature of the generally shaped surface along each geodesic. The results obtained using the new algorithm are compared to the available results (calculated and measured) for different conformal antennas, showing very good agreement.      

Surface-ray tracing on hybrid surfaces of revolution for UTD mutualcoupling analysis

An angle invariance property based on Hertz's principle of particle dynamics is employed to facilitate the surface-ray tracing on nondevelopable hybrid quadric surfaces of revolution (h-QUASOR's). This property, when used in conjunction with a geodesic constant method, yields analytical expressions for all the ray-parameters required in the UTD formulation. Differential geometrical considerations require that some of the ray-parameters (defined heuristically in the UTD for the canonical convex surfaces) be modified before the UTD can be applied to such hybrid surfaces. Mutual coupling results for finite-dimensional slots have been presented as an example on a satellite launch vehicle modeled by general paraboloid of revolution and right circular cylinder     

用射线跟踪法对室内电波传播进行预测

根据室内电波传播的特点，对室内电波的反射，透射和绕射等传播路径进行了分析，首次考虑了多层介质的反射，透射以及棱角边缘的绕射，建立了基于射线跟踪法的二维和三维传播预测模型，根据这些模型能够计算出室内各处电波传播的路径损耗。计算结果与测量结果符合很好。同时，将二维和三信跟踪预测结果作了比较，结果表明在有些情况下二维跟踪更经济实用。     

Computation of PO Integral on Parametric Surfaces

The paper presents a general method for computing the physical optics (PO) integral on the most of curved parametric surfaces. Today, most of radar cross section (RCS) codes use the parametric geometry code for modeling complex object geometry. The PO integral formulation is presented that fully utilize the geometry information available in parametric geometry codes. The formulation presented can be used with any of these geometry codes independent of the difference between versions. The PO integral is evaluated over the parametric space of the parametric surfaces using splitting extrapolation method. Therefore, the method is very general, allowing its use for the PO integral on the most of parametric surfaces. Moreover, it is efficient and accurate. The method is applied to calculate the RCS values of several objects modeled with non-uniformed rational B-spline (NURBS) surfaces at a millimeter-wave frequency, the results agree with geometric optics (GO) predictions.     

A dynamic model for predicting the motion of solder droplets during assembly

The dynamic motion of a solder droplet during assembly is a complex, unsteady, free surface problem involving surface tension and viscous effects. The motion of the droplet is coupled with the motion of the component or chip to be assembled and involves dynamic contact lines. A methodology based on a non-uniform rational b-spline (NURBS) discretization has been developed for the dynamic analysis of the droplet motion. A surface energy based formulation has been developed to incorporate the surface tension effects. The developed methodology leads to an updated Lagrangian scheme with a Galerkin in space and Least square in time formulation. The NURBS representation used for the spatial discretization enables the method to handle problems involving complex droplet geometries. The ability of the NURBS representation to provide both global and local control, along with the least square method used in this methodology, enables us to develop an unconditionally stable time integration scheme which can be optimized to achieve desired accuracy and numerical dissipation efficiently. A sample problem of droplet shape evolution has been solved to demonstrate the path prediction capability of the proposed methodology. In future, the method can be applied to solve various real world dynamic motion problems associated with droplets.     

基于三维的射线跟踪八叉树算法的城市微区电波传播预测算法模型

本文建立了一种有效的基于射线跟踪技术的三维城市微区电波传播预测的计算模型.该模型将计算机图形学中的八叉树分区技术扩展至射线跟踪技术,并由此提出了一种新的有效的射线跟踪算法,射线跟踪八叉树算法.并基于几何光学、一致性绕射(UTD)对场强进行计算,所得结果与实测值及FDTD的结果进行了比较.     

基于裁剪造型的等几何分析方法求解波导本征值问题

等几何分析方法使得几何模型和分析模型能够用NURBS统一表达,避免了模型转换过程,但由于其分析域是由张量积面片构成,很难处理截面形式复杂的多联通域问题。裁剪造型等几何分析方法通过背景曲面和裁剪曲线将复杂带孔结构作为一个被NURBS曲线裁剪后的参数区域直接映射而成,只需要一个参数空间就可以表示任意复杂的拓扑结构,该方法既保留了传统等几何分析方法的优点,又实现了对复杂多孔结构的处理。本文将裁剪造型的等几何分析方法扩展到TE波的波导本征值问题,对复杂多孔结构的截止波数进行有效求解,并通过相应的数值算例验证方法的有效性和高精度性。     

双三次B样条曲面片拟合技术在散射场计算中的应用

在复杂外形的电大尺寸目标的电磁散射特性计算中，由于一致性几何绕射理论的本身特点所局限，直接计算必然会带来很大的误差。     

任意形状电大散射体附近天线受扰方向图的快速分析

该文采用基于非均匀有理B样条曲面(NURBS)建模的物理光学方法结合矩量法(MoM-PO)分析任意形状电大散射体附近天线的受扰方向图。采用插值驻相点技术加快了方向图的计算速度。文章推导了基于有理贝齐尔曲面的物理光学散射场计算公式,采用驻相法(SPM)计算有理贝齐尔曲面上的物理光学感应电流积分从而得到物理光学散射场,并利用物理光学散射场迭代矩量法区域的电压矩阵。通过与传统平面片建模的物理光学方法的计算结果对比,说明该文方法的有效性和计算速度快的优点。