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301.
302.
A Monte Carlo study of size and angular properties of a three-dimensional Poisson-Delaunay cell 总被引:1,自引:0,他引:1
On the basis of simulation of 1.2×106 three-dimensional Poisson-Delaunay cells, the statistical properties of their size and angular parameters have been studied. The moments of the volume, face area, and edge length distributions are found to be equal to those obtained from the exact expressions of Miles and of Moller. The volume, surface area, and face area distributions can be described by the two-parameter gamma distribution. The normal distribution can be used to describe the distributions of the total edge length of a cell and the perimeter of a face. The edge length distribution has also been studied. The distribution of the angle in a face is found to be in accordance with its theoretical distribution. 相似文献
303.
In this note we present an algorithm for a construction of strongly regular families of triangulations for planar domains with a piecewise curved boundary. Some additional properties of the resulting triangulations are considered. 相似文献
304.
This paper discusses the problem of constructing a locally optimal mesh for the best approximation of a given function by discontinuous piecewise polynomials. In the one-dimensional case, it is shown that, under certain assumptions on the approximated function, Baines' algorithm [M.J. Baines, Math. Comp., 62 (1994), pp. 645-669] for piecewise linear or piecewise constant polynomials produces a mesh sequence which converges to an optimal mesh. The rate of convergence is investigated. A two-dimensional modification of this algorithm is proposed in which both the nodes and the connection between the nodes are self-adjusting. Numerical results in one and two dimensions are presented.
305.
Lutz Muche 《Journal of statistical physics》1996,84(1-2):147-167
This paper gives distributional properties of geometrical characteristics of the Delaunay tessellation generated by a stationary Poisson point process in 3. The considerations are based on a well-known formula given by Miles which describes the size and shape of the typical three-dimensional Poisson Delaunay cell. The results are the probability density functions for its volume, the area, and the perimeter of one of its faces, the angle spanned in a face by two of its edges, and the length of an edge. These probability density functions are given in integral form. Formulas for higher moments of these characteristics are given explicitly. 相似文献
306.
用于高速可压缩流体分析的带多维耗散格式的自适应Delaunay三角剖分 总被引:2,自引:1,他引:1
利用自适应Delaunay三角剖分并结合胞格中心迎风算法,分析非粘滞高速可压缩流体问题.推导了多维耗散格式,并采用非结构化三角网格的迎风算法,改善了激波的计算结果.解精度评价中引入误差估计,在网格重划分算法中,解梯度变化大的区域生成小单元格,解梯度变化小的区域使用大单元格.该格式能进一步推广到高阶时空的解精度分析中.通过稳态和不稳态的高速可压缩流体超音速激波和激波传播特性的分析,可以评估该算法的效率. 相似文献
307.
David Glickenstein 《Discrete and Computational Geometry》2007,38(4):651-664
Given a triangulation of points in the plane and a function on the points, one may consider the Dirichlet energy, which is
related to the Dirichlet energy of a smooth function. In fact, the Dirichlet energy can be derived from a finite element approximation.
S. Rippa showed that the Dirichlet energy (which he refers to as the “roughness”) is minimized by the Delaunay triangulation
by showing that each edge flip which makes an edge Delaunay decreases the energy. In this paper, we introduce a Dirichlet
energy on a weighted triangulation which is a generalization of the energy on unweighted triangulations and an analogue of
the smooth Dirichlet energy on a domain. We show that this Dirichlet energy has the property that each edge flip which makes
an edge weighted Delaunay decreases the energy. The proof is done by a direct calculation, and so gives an alternate proof
of Rippa’s result. 相似文献
308.
We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically independent and they tropically span a classical hexagon whose sides have slopes ∞, 0, 1. Using this classical hexagon, we determine a parameter space for transversal tropical triangles. The coordinates of the vertices of a transversal tropical triangle determine a tropically regular matrix. Triangulations of the tropical plane are obtained. 相似文献
309.
Gennaro Amendola 《Mathematische Nachrichten》2005,278(9):975-994
Refining the notion of an ideal triangulation of a compact three‐manifold, we provide in this paper a combinatorial presentation of the set of pairs (M,α), where M is a three‐manifold and α is a collection of properly embedded arcs. We also show that certain well‐understood combinatorial moves are sufficient to relate to each other any two refined triangulations representing the same (M,α). Our proof does not assume the Matveev–Piergallini calculus for ideal triangulations, and actually easily implies this calculus. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
310.