Non-convex CMC spheres

In this paper, we will construct examples of non-convex constant mean curvature spheres in R³${\mathbb{R}}^3$ with a local perturbation of the Euclidean metric. When the perturbation area becomes small and converges to the origin, the non-convex constant mean curvature sphere converges in the Hausdorff sense to the singular space of two tangent unit spheres.     

A simple quality triangulation algorithm for complex geometries

This paper presents a simple algorithm for quality triangulation in domains with complex geometries. Based on the fact that the equilateral triangles (regular meshes) are ideal for numerical computations in computational fluids dynamics (CFD) analysis, the proposed algorithm starts with an initial equilateral triangle mesh covering the whole domain. Nodes close to the boundary edges satisfy the so‐called non‐encroaching criterion, the distance from any inserted node to any boundary vertices and the midpoints of any boundary edge is greater than a given characteristic length. Both nearly uniform and non‐uniform triangle meshes can be generated using a mesh size reduction technique. Local refinement is achieved by using transition layers. More regular meshes can be generated in the interior of the domain and all angles of the triangle mesh produced by this algorithm are proven to be bounded in a reasonable range (19.5–141°). Copyright © 2010 John Wiley & Sons, Ltd.     

Grünbaum colorings of toroidal triangulations

We prove that if G is a triangulation of the torus and χ(G)≠5, then there is a 3‐coloring of the edges of G so that the edges bounding every face are assigned three different colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 68–81, 2010     

Dissections, Hom-complexes and the Cayley trick

We show that certain canonical realizations of the complexes Hom(G,H) and Hom₊(G,H) of (partial) graph homomorphisms studied by Babson and Kozlov are, in fact, instances of the polyhedral Cayley trick. For G a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of such projected Hom-complexes: the dissections of a convex polygon into k-gons, Postnikov's generalized permutohedra, staircase triangulations, the complex dual to the lower faces of a cyclic polytope, and the graph of weak compositions of an integer into a fixed number of summands.     

一种新的准结构网格生成方法

在有限元分析中,高质量的结构网格可以有效地提高有限元分析的精度,但结构网格的几何适应性差,针对复杂边界的二维计算模型,现有的方法很难自动生成高质量的结构网格;而非结构网格几何适应性很好,但存在计算效率低和精度差等问题。提出了一种新的准结构网格生成方法,能够实现复杂区域的网格自动生成并且具有高网格质量。该方法首先对计算区域运用Delaunay三角剖分技术生成粗背景网格;然后利用背景网格,使用优化的Voronoi图生成过渡的蜂巢网格;最后,通过中心圆方法对蜂巢网格单元进行结构网格剖分。分析NACA0012翼型数值模拟结果表明,提出的新准结构网格生成方法能够对边界复杂的模型自动生成高质量的网格,并且通过三种不同拓扑类型网格计算结果相互对比及与实验结果对比,证明准结构网格具有高计算精度。     

基于离散变分原理的耗散动力学模拟方法：模拟三维囊泡形状

将基于离散变分原理的耗散动力学模拟方法应用到三维囊泡体系,通过优化囊泡的弯曲能求解其平衡态形状. 该方法的优点之一是不需要预先假定对称性. 针对特定约化自发曲率的囊泡体系,该方法模拟获得了一系列轴对称形状,模拟结果与文献中预先假定轴对称条件的计算方法所报道的结果一致,这验证了该模拟方法的可靠性及精确性. 此外,使用该方法研究了两个差别巨大的平衡态形状之间的转变动力学,在转变过程中观察到了多个非轴对称的中间形状. 研究结果表明该方法不仅可以模拟囊泡的非轴对称结构,而且具备模拟囊泡在剧烈形变下演化过程的能力. 为研究更复杂的囊泡体系,特别是生物膜的形变提供了一个重要的理论模拟方法. 关键词： 生物膜 离散空间变分法 耗散动力学 三角网格划分     

二维非结构网格生成及自动加密技术

介绍一种可对任意二维区域进行非结构网格划分的方法,提出关于网格调整光滑的新思想,可对Laplace型滤波算子赋予新的意义。在此基础上再有目的选择松弛因子的大小,可达到同样的光滑效果而迭代次数显著减少。利用文献[3]提供的自动加点算法,对该方法稍加改进,就能完成自适应过程。利用该方法编制的程序,只需提供边界点座标,就能快速地得到满意的网格。     

A Kind of Multivariate NURBS Surfaces

The purpose of this paper is to construct a kind of multivariate NURBS surfaces by using the bivariate B-splines in the space S1/2(Δmn^(2) and discuss some properties of this kind of NURBS surfaces with multiple knots on the type-2 triangulation.     

自然单元法研究进展

自然单元法是一种基于Voronoi图和Delaunay三角化几何结构,以自然邻点插值为试函数的一种新型数值方法.其既具有无网格方法和经典有限元方法的优点,又克服了两者的一些缺陷,是一种发展前景广阔的求解微分方程的数值方法.自然单元法的形函数满足插值性质,可以像有限元法一样直接施加本质边界条件,不存在基于移动最小二乘拟合的无网格方法不能直接施加本质边界条件的难题.由于自然单元法是无网格方法,可以方便处理有限元方法较难处理的一些问题,例如移动边界和大变形等问题.自然单元法与其他数值方法的最根本区别于其插值格式的不同.将自然邻点插值用于Galerkin过程,就得到基于Voronoi结构的自然单元Galerkin法.自然邻点插值有自然邻点Sibson插值和Laplace插值(非Sibson插值)两种.Laplace插值比Sibson插值在计算上要简单的多,并且不论对凸的或非凸的区域都能精确施加本质边界条件.以Laplace插值为试函数的自然单元法在数值实施上比以Sibson插值为试函数的自然单元法简单.本文对基于Voronoi结构的自然邻点插值和自然单元法的基本思想作了介绍,综述了国内外关于自然单元法的研究成果,总结了自然单元法的优点和尚需解决的问题.      

A CHARACTERISTIC-LIKE METHOD FOR THERMALLY EXPANDABLE FLOW ON UNSTRUCTURED TRIANGULAR GRIDS

Finite-difference-like discretizations are developed for the time-dependent Navier–Stokes equations and the thermal energy equation on Delaunay triangulations of the flow domain. The flow is assumed to be thermally expandable; that is, the density varies only with temperature. A characteristic- like (CL) method is used to discretize the temporal and convective terms. The dual variable method reduces the size of the discrete system by a factor of five.