有限元网格生成方法发展综述

在参阅和分析大量有关文献的基础上，对现有的各种有限元网格生成方法进行了总结，特别是对当前广泛使用的Ｄｅｌａｕｎａｙ三角化，推进波前法和八叉树方法等，从理论到具体的算法程序实现等各个方面都作了详尽的剖析，分析了各种方法的优缺点。为深入研究开发全自动、自适应有限元网格生成软件提供了有益的参考。     

有限元网格自动生成典型方法及发展方向

在分析大量的有限元网格自动生成算法的基础上，阐述了有限元网格的一般描述和通用方法，总结了各类主要的网格生成方法的优缺点及数据特性，最后指出了自动网格生成的几个主要发展方向。     

复杂曲面上的四边形网格生成方法

提出了一种曲面上全四边形网格的生成方法。该方法从曲面的边界开始,向内逐个生成单元,利用曲面的局部形状特征控制单元的尺寸,这样可以适应复杂的边界形状,通用性较强。文中介绍了算法的基本思想,提出了多个曲面相邻情况下边界上节点的生成以及一个新的节点环冲突检测方法,最后给出了两个网格生成的实例。     

前沿法生成四边形网格的改进方法

针对传统前沿法生成四边形网格时算法不稳定,有残余三角形等缺点,该文提出泛前沿的概念。泛前沿是对目前前沿概念的更高层次上的抽象,不但避免了前沿拆分和合并带来的不稳定,而且使得前沿操作起来更简单有效。然后文章通过消除坏四边形单元,消除残余三角形单元等操作,最终得到了质量较好的全四边形网格。最后,给出了用此法划分的例子。     

基于STEP的三维表面有限元网格生成技术的研究*

研究了三维表面有限元网格自动生成的技术,利用映射法实现了模型表面的三角网格剖分。基于STEP文件格式的模型的导入和重建,将模型的每个表面映射至参数空间,利用推进波前法生成参数面网格,然后映射回三维表面。研制了一套网格剖分策略,运用该策略对多种类型表面进行了分析求解。     

基于黎曼度量的复杂参数曲面有限元网格生成方法

给出了三维空间的黎曼度量和曲面自身的黎曼度量相结合的三维复杂参数曲面自适应网格生成的改进波前推进算法.详细阐述了曲面参数域上任意一点的黎曼度量的计算和插值方法;采用可细化的栅格作为背景网格,在降低了程序实现的难度的同时提高了网格生成的速度;提出按层推进和按最短边推进相结合的方法,在保证边界网格质量的同时,提高曲面内部网格的质量.三维自适应黎曼度量的引入,提高了算法剖分复杂曲面的自适应性.算例表明,该算法对复杂曲面能够生成高质量的网格,而且整个算法具有很好的时间特性和可靠性.     

有限元网格自动生成系统MESHG

本文介绍了一个适用于微机的有限元网格自动生成系统 MESHG2.00的特点和功能,该系统利用映射法可生成膜、板、壳、实体及其组合结构的网格,输入的初始网格及生成网格均可通过图形诊断,生成网格信息数据输出形式可由使用者选择或根据实际需要方便地重新组织,实践证明该系统是个方便,有效、对硬件环境适应力强的有限元分析前处理系统。     

三维空间非结构网格生成方法研究

随着计算流体力学领域待解决问题复杂程度的不断提高,传统的统一贴体结构网格已不能很好地满足针对复杂外形的高精度网格生成需求,而非结构网格以其独特优势受到CFD工作者的普遍关注。带有附面层的非结构网格是非结构网格生成的难点。进行了非结构四面体网格的生成方法研究,同时结合Spider软件平台中结构网格参数化附面层推进的技术优势,进行了基于Spider软件平台中非结构网格生成模块“UGCS”的开发。通过分析大量网格生成实例中网格质量和数值计算结果,验证了算法的可靠性与鲁棒性。     

有限元网格自动生成典型方法及发展方向

在分析大量的有限元网格自动生成算法的基础上，阐述了有限元网格的一般描述和通用方法，总结了各类主要的网格生成方法的优缺点及数据特性，最后指出了自动网格生成的几个主要发展方向。     

平面有限元网格生成的自适应技术

在Ｗａｔｓｏ逐点插入算法的基础上发展了边界自适应和约束结点距离自适应技术。与汉往的方法相比,该方法不但提高了网格生成的自动化程度,而且使生成的单元微量有所减少,实例表明,该算法对于具有任意边界和任意约束结点的平面区域,能在最少的人工干预下获得满意的网格划分结果。     

A Geometrical Based Method for Highly Complex Structured Textures Generation

Conventional 2D or 3D texturing methods do not permit an efficient simulation of highly complex structured textures like fire, fur, cotton, etc. More recent techniques, using specific kinds of 3D textures, such as hypertextures or texels based on volume rendering algorithms, are more interesting, for the simulation of such special types of textures. Unfortunately, these techniques remain still restricted because either they need a functional modelling of the object, as it is the case of hypertextures, or they are strictly limited to one specific kind of texture, as it is the case of texels. In this paper we present a new approach for applying a wide range of very different types of highly complex structured textures (fur, fire, water drops, cotton, fume, …) on every kind of objects. This method is particularly based on the geometrical information given by a geometrical model (as the polyhedral or CSG modelling). Like hypertextures or texels, our method uses the volume density rendering, but it isfree of the serious above mentioned restrictions of these methods. In addition, it allows an easy and very intuitive control of the global geometrical shape of generated textures. Its manipulation is simple evenfor a novice user.     

A Procedure for Tetrahedral Boundary Layer Mesh Generation

. We develop a methodology for introducing regions of high anisotropy in existing isotropic unstructured grids in complex, curved, three-dimensional domains. The new procedures are here applied to the capturing of solution features in the proximity of model boundaries (e.g. boundary layers). Suitable voids are created in an existing grid in the regions of localization using a mesh motion algorithm that solves a fictitious elasticity problem. The voids are then filled with stacks of prisms that are subsequently tetrahedronized to yield a simplicial mesh. The mesh motion algorithm allows us to deal in a simple and effective manner with the problem of self-intersection of elements in concave regions of the model boundaries, and in the case of closely spaced model faces, avoiding the need for cross-over checks and complex grid correction procedures. The capabilities and performance of the proposed methodology are illustrated with the help of practical examples.     

多孔平面的快速边界元划分

在 3D VL SI互连寄生电容的边界元素法计算中 ,多孔平面的边界元划分是十分困难的问题 .文中提出一种快速划分多孔平面边界元的方法 ,它可高效处理非正交几何边界形状 ,形成规则的梯形元 .与全局扫描线法相比 ,有较高的划分速度、计算速度与精度     

CGM: A Geometry Interface for Mesh Generation, Analysis and Other Applications

Geometry modeling has recently emerged as a commodity capability. Several geometry modeling engines are available which provide largely the same capability, ad most high-end CAD systems provide access to their geometry through APIs. However, subtle differences exist between these modelers, both at the syntax level and in the underlying topological models. A modeler-independent interface to geometry bridges these differences, allowing applications to be developed in a true modeler- independent manner. The Common Geometry Module, or CGM, provides such an interface to geometry. At the most basic level, CGM translates geometry function calls to access geometry in its native format. To smooth over topological differences between modelers, and to allow modeler-independent modification of topology, CGM maintains its own topology datastructure. CGM also provides functionality not found in most modelers, like support for non-manifold topology, and alternative representations, including facet-based and ‘virtual’ geometry. CGM is designed to be extensible, allowing applications to derive application-specific capabilities from topological entities defined in CGM. The CUBIT Mesh Generation Toolkit has been modified to work directly with CGM. CGM is also designed to simplify the implementation of other solid model-based or alternative representations of geometry. Ports to Solid Works and Pro/Engineer are underway. CGM is also being used as the foundation for parallel mesh generation and is being used for geometry support in several advanced finite element analysis codes.     

三维网格模型的边界性度量方法

在三维网格分割中,如何实现网格模型边界的自动准确分割是目前亟待解决的问题。为给自动分割提供理论依据,提出了一种新的三维网格模型表面边界性计算方法,将少量手工标注的边界点视为能量的放射源,根据能量流动原理,自动计算出其他点作为分割边界的可能性。实验表明,该方法是行之有效的,可以依据手工标注的少量边界点找到更多的真实边界点,进而为最终实现网格模型的自动分割提供可行的理论基础。     

复杂三角网格模型分治加工刀具轨迹生成

为了解决复杂三角网格模型数控加工效率与精度之间的矛盾,提出包括模型分割以及子区域轨迹规划的分治加工方法.针对分治加工的需求,提出一种基于加工区域特征表述的区域生长原则,用于模型的区域生长分割;为避免在子区域中生成过多的短刀具轨迹,对分割后的子区域进行区域优化合并与边界光顺处理,子区域轨迹规划时对不同的特征子区域采用不同的刀具轨迹生成策略.在等残留高度法刀具轨迹生成中,提出初始轨迹生成方法,并改进扩展了刀具轨迹的投影偏置扩展过程,以解决边界不规则子区域的刀具轨迹生成问题.实例结果表明,基于加工区域特征表述的区域生长原则能够有效地驱动加工模型的区域生长分割,不同特征子区域以适当的刀具轨迹生成策略生成了有效的刀具轨迹.     

一种快速的三维有限元网格生成方法

针对三维有限元网格的生成的速度较慢并且网格质量不高的问题,提出了一种基于约束波前法的三维有限元网格生成算法。算法的主要思想是用背景网格提高网格单元的可控性,避免网格单元生成时验证有效性的计算量,从而快速生成高质量的三维有限元网格。算法首先借助八叉树方法生成背景网格,其次利用背景网格的密度对模型表面进行三角剖分得到初始波前,然后依据背景网格的特征生成实体网格单元,最后对得到的结果进行优化。实验证明结合了八叉树和推进波前法的三维网格生成算法降低了波前法的时间复杂度,将其效率提高了20%,而且能得到更高质量的网格。     

一种基于多边形剖分的有限元网格生成方法

在两步网格化过程中,待分析区域首先被剖分为具有三条或四条边的简单子区域部分.然后将利用传递模板法或映射法对这些子区域进行网格生成.本文结合计算几何和有限元网格自动生成问题,给出了一种基于简单多边形剖分的全四边形有限元网格自动生成方法.该方法分两步实现有限元网格生成首先通过权函数的引导,对待分析的简单多边形区域先进行子域剖分,得到一组三角形和凸四边形子域(大单元)的集合;然后利用中点剖分方法,将三角形和凸四边形子域单元剖分为全四边形有限元网格.实践证明,本文提出的方法实现简单、使用灵活,结果网格的质量良好.     

Taylor Prediction for Mesh Geometry Compression

In this paper, we introduce a new formalism for mesh geometry prediction. We derive a class of smooth linear predictors from a simple approach based on the Taylor expansion of the mesh geometry function. We use this method as a generic way to compute weights for various linear predictors used for mesh compression and compare them with those of existing methods. We show that our scheme is actually equivalent to the Modified Butterfly subdivision scheme used for wavelet mesh compression. We also build new efficient predictors that can be used for connectivity‐driven compression in place of other schemes like Average/Dual Parallelogram Prediction and High Degree Polygon Prediction. The new predictors use the same neighbourhood, but do not make any assumption on mesh anisotropy. In the case of Average Parallelogram Prediction, our new weights improve compression rates from 3% to 18% on our test meshes. For Dual Parallelogram Prediction, our weights are equivalent to those of the previous Freelence approach, that outperforms traditional schemes by 16% on average. Our method effectively shows that these weights are optimal for the class of smooth meshes. Modifying existing schemes to make use of our method is free because only the prediction weights have to be modified in the code.     

A Shape Modulus for Fractal Geometry Generation

We present an efficient new method for computing Mandelbrot-like fractals (Julia sets) that approximate a user-defined shape. Our algorithm is orders of magnitude faster than previous methods, as it entirely sidesteps the need for a time-consuming numerical optimization. It is also more robust, succeeding on shapes where previous approaches failed. The key to our approach is a versor-modulus analysis of fractals that allows us to formulate a novel shape modulus function that directly controls the broad shape of a Julia set, while keeping fine-grained fractal details intact. Our formulation contains flexible artistic controls that allow users to seamlessly add fractal detail to desired spatial regions, while transitioning back to the original shape in others. No previous approach allows Mandelbrot-like details to be “painted” onto meshes.