LUDWIG算法的改进与应用

Ludwig积分在雷达散射截面(RCS)计算中被广泛应用.传统的Ludwig积分针对基于三角形面元的模型剖分技术,因此主要用于平面片积分.三角形面片由于是平面片,因此无法对复杂模型准确建模.本文改进了Ludwig积分,并将其用于基于NURBS(非均匀有理B样条)技术的曲面积分.通过计算实例可以看出改进后的Ludwig积分形式适用于基于曲面建模技术的物理光学(PO)算法.     

基于NURBS曲面的雷达散射截面物理光学算法研究

本文实现了一种使用物理光学（PO）计算雷达散射截面的算法。目标模型用非均匀有理B样条（NURBS）曲面建立,并使用等参数等弦长方法剖分为N个四边形面元。在剖分面元上,使用Gordon方法将物理光学积分转化为闭合区域线积分。整个算法在在保持计算精度的前提下有较高的计算速度。     

NURBS在自适应hp有限元分析系统中的应用

在传统的有限元分析中,对于曲边区域或者曲边的分界面并没有很好的近似方法,通常使用大量的线性单元近似的描述曲边计算区域.这些新增加的单元不仅浪费了计算时间,而且往往并不是需要求解的部分.采用曲线单元可以避免对单元的强制细化,有效的提高计算的精度.曲边单元使用非均匀有理B样条（NURBS）曲线实现,可以有效的消除几何离散误差,保证整体的高阶连续性.详细讨论了基于NURBS曲线的自适应三角形网格剖分和四边形网格剖分,并结合自适应hp有限元算法解决实际问题.从计算自由度和计算时间的角度比较典型的工程算例结果,采用NURBS曲边单元的hp有限元算法能够很好的消除几何近似导致的误差,提高计算的效率.     

基于NURBS建模和渐近物理光学的RCS计算研究

阐述了对于非均匀有理B样条（NURBS）技术和渐近物理光学来计算电大尺寸目标单雷达散射截面（RCS）的方法，在RCS的计算中是将散体表面的物理光学积分通过参数变换为NURBS参数域上的二重积分，利用驻定相位法得出组合NURBS表面的散射场，并与其他的方法进行比较，具有很好的一致性。     

电磁散射与辐射问题中的混合基函数矩量法

三维散射与辐射问题通常采用电场积分方程(EFIE)结合矩量法(MoM)求解，而基函数是决定矩量法精度和效率的重要因素。本文针对采用三角形网格剖分会引起未知元过多而采用四边形网格剖分会因为网格质量变差而影响计算精度的问题，提出一种基于三角形与四边形混合网格的混合基函数，应用于散射体RCS和天线阻抗特性计算。结果表明，相比于三角形剖分，混合基函数能够在减少未知元个数的同时获得较高的精度；另外也解决了基于单纯四边形网格的基函数在网格质量较差的情况下不能准确模拟表面电荷的问题。     

飞机尾流RCS计算中的网格剖分技术

飞机尾流雷达散射截面(RCS)通常可通过求解尾流的被动保守量和介电常数分布,对尾流区域的电场积分得到。实现尾流区域离散化处理,现有方法一般采用满足被动保守量求解精度要求的非均匀网格剖分技术。由于该剖分存在大量尺度与电磁波长相当甚至更大的网格,因此,不能直接用于计算尾流RCS。针对该问题,提出了一种线性插值处理方法,把被动保守量从被动保守量计算的非均匀网格上映射到满足RCS计算要求的均匀细网格上。该方法在保证较高的电磁计算精度的情况下,避免了使用电磁计算细网格求解被动保守量导致的计算量急剧增加。通过数值实验验证了本处理方法的高效性。     

一种基于解析积分的TDPO算法及其在散射问题中的应用

基于时域物理光学(Time-domain Physical Optics, TDPO)方法, 给出了三角面元剖分下散射场解析计算的求解思路.对三角面元进行二重积分求得散射场计算的最终表达式.与传统的TDPO方法相比, 在同等计算模型下, 解析方法具有更高的计算精度.在处理高频复杂问题时, 解析方法可以用更少的面元数量参与计算, 从而节省大量的计算时间与计算机内存.     

图形电磁计算方法的改进

为了克服传统方法存在的无法对所有棱边进行精确识别的弊端,采用了一种图形电磁计算与模型分析相结合的计算目标RCS的新方法,从而改善了RCS计算的精度.采用了一种增强图形电磁计算通用性的方法,克服了传统的图形电磁计算中要根据实际目标的尺寸不断调整可视空间的尺寸的弊端,从而实现在视口中完全显示物体和对物体完成尽可能细密剖分的目的,大大增强了软件的通用性.     

基于三角面元剖分的全波信号完整性建模方法

推导了一种采用三角面元剖分和RWG(Rao-Wilton-Glisson)基函数的部分元等效电路(PEEC)方法,在此方法中采用了离散复镜像(DCIM)来计算格林函数。对于有拐角的印刷电路板(PCB)走线,同传统PEEC的四边形剖分方法相比,采用RWG基函数定义的三角形剖分方法有更高的计算精度和计算效率;不同于一般的使用准静格林函数的PEEC方法,在高频条件下,采用离散复镜像的PEEC方法的计算结果依然准确,并可以兼容HSPICE仿真信号完整性(SI)问题。给出了联合使用PEEC和HSPICE仿真得到信号眼图的结果,将实际PCB板走线S参数的仿真结果和测量结果进行了对比。实验结果表明:RWG-DCIM-PEEC是一种有效的SI仿真与分析方法。     

目标的NURBS曲面建模及其RCS计算研究

为了提高计算的精度和效率，将NURBS参数曲面应用到电大尺寸目标的RCS预估中。使用CAD软件建立模型，通过对模型IGES文件中数据结构的分析，并以IGES文件为接口，从CAD软件模型中提取出NURBS曲面信息，然后用Cox-De Boor算法把NURBS曲面转换为Bezier曲面，结合物理光学法和渐进积分展开法精确、高效的求解出任意理想导体目标曲面的RCS。     

Computation of RCS of targets modelled with trimmed NURBS surfaces

A novel technique for the monostatic radar cross-section (RCS) computation of complex targets modelled with trimmed nonuniform rational B-spline (NURBS) surfaces is proposed using physical optics (PO). The stationary phase method (SPM) is demonstrated to be invalid in evaluation of the PO integral over trimmed surfaces. Thus a new method, which combines SPM with the Gordon method (namely SPM-Gordon) is presented as a substitute and good candidate. Examples show that excellent accuracy is obtained.     

Shape Reconstruction of Three-Dimensional Conducting Curved Plates Using Physical Optics, NURBS Modeling, and Genetic Algorithm

A microwave inverse scattering problem including a method for shape reconstruction of three-dimensional electrically large conducting patches with simple geometries using genetic algorithm is presented. Unknown shape reconstruction algorithm starts from the knowledge of the simulated radar cross-section (RCS) data through back-scattering far-field computation using physical optics approximation. The forward problem involves the computation of the multiple-frequency and multiple-direction RCS of three-dimensional large conducting patches modeled by nonuniform rational B-spline (NURBS) surfaces. The control points of NURBS are the geometrical parameters, which are optimized for the shape reconstruction procedure. The extended stationary phase method and critical cases, which occur in physical optics computations in the forward problem, are also discussed. Noise effect and the influence of increment in the number of control points of a NURBS over the inversion algorithm are investigated as well. Numerical results are presented to verify the operation of the proposed algorithm.     

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     

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.     

雷达散射截面预估的可视化技术

ＲＣＳ计算的可视化技术是高频ＲＣＳ预估方法与计算机图形学相结合的方法，以非均匀有理Ｂ样条函数的构造自由曲面，以计算机硬件自动处理目标遮挡面，并自动提取计算所需的几何信息。本文给出ＰＯ方法和可视化方法结合的一些结果。     

Analysis of Antenna Around NURBS Surface With Hybrid MoM-PO Technique

The hybrid method of moments and physical-optics (MoM-PO) approach is used to calculate the radiation pattern of antenna around arbitrarily shaped structure. The structure is modeled with Non-uniform rational B-spline (NURBS) surfaces. The hybrid MoM-PO approach is implemented by modifying the impedance matrix of the MoM region with PO. Formula for the scattered PO field is deduced for cases of antenna located around NURBS surface. The stationary phase method (SPM) is applied for the integral of the induced current in the PO region. Results obtained from this method and from MoM-PO approach based on triangle facet model agree well while the former is more efficient in execution time     

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.      

NURBS曲面建模的电大目标的宽带RCS快速计算

该文采用物理光学方法(PO),快速计算了非均匀有理B样条 (NURBS) 曲面建模的电大目标的时域瞬态散射和宽带雷达截面(RCS)。通过对频域物理光学散射场表达式进行逆傅里叶变换推导出卷积形式的瞬态散射表达式;对频域物理光学积分进行逆傅里叶变换得到时域物理光学积分的表达式。为了避免数值积分的使用,将NURBS曲面等参数离散为一组三角面片,运用Radon变换得到了时域和频域物理光学积分的精确闭式表达式。遮挡消隐时使用改进的z-buffer方法进行了加速。对时域瞬态散射场快速傅里叶变换得到目标的宽带RCS。文中计算了高斯脉冲平面波入射下模型的瞬态散射响应和宽带RCS,数值结果表明该文方法具有很高的计算精度,且计算速度快于传统时域物理光学法(TDPO)。