Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.     

表面散射光对激光三角法位移测量的影响

三角测量法是一种位移测量方法, 其测量精度不但受到传感器本身因素如光源、探测器、机械结构特性等因素的影响, 还受到被测表面特性如色泽、材料、粗糙度、倾斜度以及外界环境的影响。国内外的一些学者提出了许多提高传感器测量精度的方法, 但这些研究都是针对某一特性表面进行的, 没有涉及到对不同表面的测量时存在的问题。利用随机行走理论对物体表面的散射场进行了分析, 给出了不同粗糙度表面下弱散射光强与散射角及入射角的关系。由于设计制造的传感器量程范围内接收散射光的角度在15°至25°内变化, 因此取20°作为散射角角度, 理论计算模拟的三种不同粗糙面散射光强变化最大能达到300%左右。该结果对于优化激光三角传感器的设计和提高测量精度有一定的意义。     

水珠滴落的最小二乘粒子有限元方法模拟

提出了一种最小二乘粒子有限元方法,用其模拟了二维水珠滴落水面并飞溅散开的过程.该法基于拉格朗日描述,在每个时间步上使用扩展的Delaunay划分更新计算网格,并应用α形方法识别自由面形状;用最小二乘有限元方法离散流体运动的Navier-Stokes方程,并推导了一种自适应时间步长方案以提高计算效率和鲁棒性;引入网格拉伸技术修正减小流体质量误差.对水滴飞溅进行仿真,得到了与商用软件Flow-3d比较符合的结果,且具有更清晰锐利的自由面. 关键词： 滴落 网格划分 α形')" href="#">α形 最小二乘有限元     

基于同心圆光栅的远心三维测量系统

针对条纹投影术对简化系统模型、降低运算量并有效抑制误差扩散等要求,提出并构造了一种基于同心圆光栅的广义远心三维测量系统。该系统利用菲涅尔透镜与投影仪产生平行光线建立线性投影模型,降低运算复杂度,利用傅里叶变换得到经物体高度调制的初始相位信息,同时结合同心圆光栅标定技术的并行运算,通过逐点计算获取真实相位。全过程只需对一个系统参数进行标定,并且摆脱解相过程,有效抑制了误差扩散。对最大高度20 mm的物体进行形貌测量,最大误差0.23 mm,相对误差仅为1.15%。     

Polymorphism in Multisymmetric Close Packings of Equal Spheres on a Spherical Surface

Locally optimum, high-symmetry solutions are sought to the Tammes problem: to determine the maximum angular diameter of n equal circles, which can be packed on a sphere without overlapping. By using triangular surface lattices, in the range 1 n 500, those values of n are determined, for which the circles can be close packed in arrangements different from each other with tetrahedral, octahedral, and icosahedral symmetry. Tables are given of the results.     

生成Delaunay三角网的快速合成算法

合成算法结合了传统的递归分割法和逐点插入法的优点,兼顾空间和时间性能.然而,该算法不可避免地继承了两种传统算法的不足,在执行效率上受到限制.为了解决执行效率问题,提出了快速合成算法,对合成算法进行了改进和优化.该算法基于面积坐标的点定位算法和简化的高效空外接圆判断算法,从而大大提高算法的整体执行效率;同时充分考虑平面点集的任意性,适用于对任意平面点集构建Delaunay三角网.     

TWO NEW FORMULAS FOR TRIANGULATION NUMBER T

The present paper reports two [new formulas for calculating triangulation number T.They are T =L~2/l~2 and T = 1.45r~2/l~2, where L is the distance between pentons, l the distancebetween any two adjacent capsomeres, r the radius of viral nucleocapsid. The formulas havebeen verified and applied. It is worth noticing that the triangulation number, viral size anddistance between capsomeres are fully connected by the formula r/(Tl)~(1/2) = 0. 83, and the capsidparameters of all icosahedral viruses are unified in one constant, 0.83.     

C~2有限元与插值（I）

本文首先在ＣＴ细分三角形剖分上，建立起六次二阶光滑样条函数空间的维数结论。利用我们的构造性证明方法，给出了该空间中的一个Ｃ￣２有限元插值格式，并给出有限元的计算方法。     

THE DIMENSION OF A CLASS OF BIVARIATE SPLINE SPACES

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Stabbing Delaunay Tetrahedralizations

A Delaunay tetrahedralization of $n$ vertices is exhibited for which a straight line can pass through the interiors of $\Theta(n^2)$ tetrahedra. This solves an open problem of Amenta, who asked whether a line can stab more than $O(n)$ tetrahedra. The construction generalizes to higher dimensions: in $d$ dimensions, a line can stab the interiors of $\Theta(n^{\lceil d / 2 \rceil})$ Delaunay $d$-simplices. The relationship between a Delaunay triangulation and a convex polytope yields another result: a two-dimensional slice of a $d$-dimensional $n$-vertex polytope can have $\Theta(n^{\lfloor d / 2 \rfloor})$ facets. This last result was first demonstrated by Amenta and Ziegler, but the construction given here is simpler and more intuitive.