任意三维物体FDTD共形网格生成算法

时域有限差分法(FDTD)是计算电磁学广泛使用的方法之一.作为一种数值方法,首先要对目标模型进行网格离散.它直接影响到计算的精确性与复杂性.为了避免采用Yee氏单元对复杂模型建模所产生的阶梯误差,实现了一种任意复杂形状三维物体FDTD共形网格自动生成算法.对于由AutoCAD等建模软件生成的目标模型(三角形和四边形构成),应用计算机图形学方法求出网格线与模型的交点,在三个网格面分别生成共肜网格.数值结果证实了共形网格生成方法的正确性和在提高FDTD方法计算精度方面的有效性.     

基于关键点路径的快速测试用例自动生成方法

测试数据的自动生成,是提高软件测试效率的重要手段.从软件测试工程实践的角度提出快速生成测试数据的完整模型,更有利于提高测试数据生成效率.为此:(1)提出关键点路径表示法,以得出待测程序的理论路径数,并快速确定已覆盖路径的邻近路径;(2)用随机生成的数据运行简化后的插装程序,得到部分测试数据;(3)将理论路径分成易覆盖路径、难覆盖路径和不可行路径;(4)根据已覆盖路径及其测试数据提供的信息,使用遗传算法生成难覆盖路径的测试数据.仿真实验结果表明了所提方法的有效性.     

基于Visual C+ +6.0实现有限元分析系统的前置处理

在利用ActiveX通信控件实现数字化仪和计算机的串口通信的基础上 ,建立有限元分析系统的物理边界模型 .本文综合TheAdvancingFront与DelaunayTriangulation两种算法的优点提出一种新的 2D网格的自动生成算法。由此建立一个完整的基于VisualC + +的有限元分析系统前置处理模块。     

基于矢量场的二维区域全自动四边网格生成

为了实现任意二维几何模型的高质量分块结构四边形网格自动生成,提出一种基于矢量场的二维区域全自动分解方法.首先利用边界元法求解拉普拉斯型控制方程,获取一个反映模型边界几何特征、覆盖整个问题域的矢量场;然后结合矢量与标架的映射关系,将计算得到的矢量场转化为标架场;最后通过分析标架场的奇异结构将问题域分解成多个四边子区域,并在每个子区域利用映射法生成高质量的结构四边形网格.通过复杂区域的网格生成实例,验证了该方法的有效性和可靠性.     

基于ICD的接口通讯程序代码自动生成技术

为快速开发嵌入式应用中的接口通讯程序,提高其效率和可靠性,本文提出了一种基于ICD的代码自动生成技术.首先确定了目标代码的形式,通过设计系统结构、建立驱动模型和代码生成单元结构,最终实现了代码生成器.本文设计的代码生成器,能够根据ICD数据库自动生成符合ANSI C标准的接口通讯程序,并在某航天工程的集成仿真测试系统中得到应用验证.     

一种基于IMM方法的气囊折叠参数化设计的应用

为提高驾驶员侧环向折叠气囊模型的生成效率，开发了基于IMM算法的参考网格模型和映射网格模型自动生成程序。程序在VC＋＋环境中开发，对模型实现了基于气袋直径、折叠次数、折叠环间距和网格密度等参数的参数化设计，并通过算例对建模过程和映射算法进行了验证。结果表明此程序能够快速、准确地生成参考网格模型和映射网格模型。极大地缩短模型生成时间，同时保证有限元网格的均匀性和参考网格与映射网格的对应。     

测量造型技术在汽车覆盖件成形数值模拟中的应用

汽车覆盖件冲压成形数值模拟需要有精确的曲面CAD模型来划分有限元网格。利用测量造型技术从覆盖件产品的原模型获得CAD模型,并在此基础上建立成形数值模拟所需有限元模型的全过程,讨论了其中的关键技术和难点。     

平面及空间区域渐变无结构网格的自动生成

１．前 言 网格生成是许多数值计算首先要解决的问题．规则区域上的均匀网格,比较容易生成．但许多工程实际问题,求解区域边界形状极不规则,且由于物理参数的剧烈变化及解的性态复杂,对求解区域的网格疏密变化有某些特殊的要求．如何在非规则区域上自动生成符合使用者特殊要求的网格,是科学计算过程中人们所关心的问题． 本文基于 Ｄｅｌａｕｎａｙ三角划分原理,在二维（三维）区域给出一种自动生成渐变无结构三角形（四面体）网格的方法．对事先给定的指定结点集合和对应的间隔值集合,算法将首先自动生成全部边界结点和内部结点,然…     

弹性网格变形方法及其应用

1.引言 网格生成是数值计算中的基础问题.在微分方程数值方法的实现过程中,一个合适的计算网格可以提高计算精度,大大降低计算复杂性.近年来,人们所关注的数值求解微分方程自适应方法也包含了网格自动生成的研究.目前,国内外在这方面的研究工作很多.以网格类型而言,有结     

基于球填充法的STL模型曲面自适应网格生成方法

为满足有限元分析的需要,针对STL模型提出一种基于球填充法的自适应网格生成方法.首先识别STL模型的线曲率、面曲率和区域形状特征;其次采用八叉树做背景网格来建立尺寸场信息;最后,利用球填充算法在STL曲面生成自适应网格.文中方法不需要点面投影、前沿判交等复杂计算,能高效地生成STL曲面自适应网格.数值实验结果表明,该方法比NetGen速度更快,产生的自适应网格质量更优.     

A mesh generation method based on set theory

A method is proposed to study automatic generation of input data to finite element programs by the computer with minimal human involvement. Based on a set of objective criteria, a consistent procedure is developed to scan through the geometric idealization of a boundary to form regions for mesh generation. This procedure is supported by a rigorously built mathematical model. A cyclic set is defined according to the ordering of segments on a boundary. Corresponding to this is a quadrilateral set whose elements represent the partitioning of the geometry into regions for mesh generation. Theorems are proven establishing the uniqueness and completeness of this procedure. By means of this mathematical model, a computer program is written for automatic mesh generation together with evaluation of results by a given set of objective criteria.Examples are presented with simply connected and with multiply connected geometry.     

用局部阻尼波形法的自连贯网格生成法

介绍将生成或已有的有限元规则六面体单元改变成形状复杂且光滑的六面体单元的一种新技术——波形法．简单建立了波形法的数学模型并编程进行了网格生成．实验结果表明,只要把复杂外部形状按波的形式传输给指定的规则六面体单元模型,就可以得到具有复杂外部形状的六面体单元网格模型,且网格生成速度快、不出现单元或节点漏洞、欠缺等问题,同时不受单元类型的限制。     

VCMM: A visual tool for continuum molecular modeling

This paper describes the design and function of a visualization tool, VCMM, for visualizing and analyzing data, and interfacing solvers for generic continuum molecular modeling. In particular, an emphasis of the program is to treat the data set based on unstructured mesh as used in finite/boundary element simulations, which largely enhances the capabilities of current visualization tools in this area that only support structured mesh. VCMM is segmented into molecular, meshing and numerical modules. The capabilities of molecular module include molecular visualization and force field assignment. Meshing module contains mesh generation, analysis and visualization tools. Numerical module currently provides a few finite/boundary element solvers of continuum molecular modeling, and contains several common visualization tools for the numerical result such as line and plane interpolations, surface probing, volume rendering and stream rendering. Three modules can exchange data with each other and carry out a complete process of modeling. Interfaces are also designed in order to facilitate usage of other mesh generation tools and numerical solvers. We develop a technique to accelerate data retrieval and have combined many graphical techniques in visualization. VCMM is highly extensible, and users can obtain more powerful functions by introducing relevant plug-ins. VCMM can also be useful in other fields such as computational quantum chemistry, image processing, and material science.     

Guaranteed-quality anisotropic mesh generation for domains with curved boundaries

Anisotropic mesh generation is important for interpolation and numerical modeling. Recently, Labelle and Shewchuk proposed a two-dimensional guaranteed-quality anisotropic mesh generation algorithm called a Voronoi refinement algorithm. This algorithm treats only domains with straight lines as inputs. In many applications, however, input domains have many curves and the exact representation of curves is required for efficient numerical modeling. In this paper, we extend the Voronoi refinement algorithm and propose it as a guaranteed-quality anisotropic mesh generation algorithm for domains with curved boundaries. Some experimental results are also shown.     

以数学建模为载体的学生实践能力培养探索与实践

讨论了以数学建模为载体,如何提高学生的实践能力和创新意识。并从数学模型课的课堂教学、数学建模竞赛、基于数学模型的项目团队建设等多个层面进行了详细剖析。探讨了案例式教学、模块化教学以及以数学建模为内容的项目培育等多种手段的综合利用对提高学生分析问题能力、程序设计能力以及综合实践能力的重要作用。     

Numerical study of singularly perturbed differential-difference equation arising in the modeling of neuronal variability

The objective of this paper is to present a numerical study of a class of boundary value problems of singularly perturbed differential difference equations (SPDDE) which arise in computational neuroscience in particular in the modeling of neuronal variability. The mathematical modeling of the determination of the expected time for the generation of action potential in the nerve cells by random synaptic inputs in dendrites includes a general boundary-value problem for singularly perturbed differential difference equation with shifts. The problem considered in this paper exhibit turning point behavior which add to the complexity in the construction of numerical approximation to the solution of the problem as well as in obtaining theoretical estimates on the solution. Exponentially fitted finite difference scheme based on Il’in-Allen-Southwell fitting is used on a specially designed mesh. Some numerical examples are given to validate convergence and computational efficiency of the proposed numerical scheme. Effect of the shifts on the layer structure is illuminated for the considered examples.     

Octree-based automatic mesh generation for non-manifold domains

Automatic mesh generation within the context of non-manifold geometric models is far from a commercial reality. While manifold objects are the most commonly encountered domains in many applications, other applications such as those requiring multiple material models and mixedmodel representations (combination of 1-D, 2-D and 3-D domains) fall beyond the realm of the existing automatic meshing procedures as they require a non-conventional modeling enviroment, namely the non-manifold topology (NMT) based environment. This paper focuses on automatic mesh generation issues in the context of two such applications: (i) finite element modeling for multiple material models and (ii) geometric abstractions requiring a mixed-model representation. Specifically, the paper describes a geometry utility system, built around an NMT data structure and geometry-based meshing algorithms that ensure the validity of the mesh for non-manifold domains.GE Consulting Services.     

多介质拉氏自适应流体动力学软件LAD2D研制及其应用

拉氏方法是内爆动力学过程数值模拟的主要方法.针对高温、高压、多介质和大变形等内爆问题,采用非结构任意多边形网格底层管理、计算过程中网格邻域可变技术,以及拉氏自适应网格加密方法和层次化、模块化程序设计思想,自主研发非结构拉氏自适应网格流体动力学软件LAD2D.从物理模型、计算方法、程序设计、程序验证与确认、大变形问题数值模拟等方面系统地介绍LAD2D.LAD2D对多介质爆轰弹塑性流体大变形问题有很强的适应能力.     

Manifold splines with a single extraordinary point

This paper develops a novel computational technique to define and construct manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The central idea and new computational paradigm of manifold splines are to systematically extend the algorithmic pipeline of spline surface construction from any planar domain to an arbitrary topology. As a result, manifold splines can unify planar spline representations as their special cases. Despite its earlier success, the existing manifold spline framework is plagued by the topology-dependent, large number of singular points (i.e., |2g−2| for any genus-g surface), where the analysis of surface behaviors such as continuity remains extremely difficult. The unique theoretical contribution of this paper is that we devise new mathematical tools so that manifold splines can now be constructed with only one singular point, reaching their theoretic lower bound of singularity for real-world applications. Our new algorithm is founded upon the concept of discrete Ricci flow and associated techniques. First, Ricci flow is employed to compute a special metric of any manifold domain (serving as a parametric domain for manifold splines), such that the metric becomes flat everywhere except at one point. Then, the metric naturally induces an affine atlas covering the entire manifold except this singular point. Finally, manifold splines are defined over this affine atlas. The Ricci flow method is theoretically sound, and practically simple and efficient. We conduct various shape experiments and our new theoretical and algorithmic results alleviate the modeling difficulty of manifold splines, and hence, promote the widespread use of manifold splines in surface and solid modeling, geometric design, and reverse engineering.     

A continuous DC programming approach for resource allocation in OFDMA/TDD wireless networks

The next generation broadband wireless networks deploys OFDM/OFDMA as the enabling technologies for broadband data transmission with QoS capabilities. Many optimization problems have arisen in the conception of such a network. This article studies an optimization problem in resource allocation. By using mathematical modeling technique we formulate the considered problem as a pure integer linear program. This problem is reformulated as a DC (Difference of Convex functions) program via an exact penalty technique. We then propose a continuous approach for its resolution. Our approach is based on DC programming and DCA (DC Algorithm). It works in a continuous domain, but provides integer solutions. To check globality of computed solutions, a global method combining DCA with a well adapted Branch-and-Bound (B&B) algorithm is investigated. Preliminary numerical results are reported to show the efficiency of the proposed method with respect to the standard Branch-and-Bound algorithm.