A method for computing curved meshes via the linear elasticity analogy,application to fluid dynamics problems

We propose and analyze an algorithm for the robust construction of curved meshes in two and three dimensions. The meshes are made of curved simplexes. The algorithm starts from a mesh made of straight simplexes, and using a linear elasticity analogy applied on well‐chosen data, one can generate a curved mesh. Note that if the initial mesh has a boundary layer, this method allows to conserve it on the final mesh. This algorithm is used on several airfoils in two and three dimensions, including a turbulent M6 wing. Copyright © 2014 John Wiley & Sons, Ltd.     

Hitting times for random walks on subdivision and triangulation graphs

Let G be a connected graph. The subdivision graph of G, denoted by S(G), is the graph obtained from G by inserting a new vertex into every edge of G. The triangulation graph of G, denoted by R(G), is the graph obtained from G by adding, for each edge uv, a new vertex whose neighbours are u and v. In this paper, we first provide complete information for the eigenvalues and eigenvectors of the probability transition matrix of a random walk on S(G) (res. R(G)) in terms of those of G. Then we give an explicit formula for the expected hitting time between any two vertices of S(G) (res. R(G)) in terms of those of G. Finally, as applications, we show that, the relations between the resistance distances, the number of spanning trees and the multiplicative degree-Kirchhoff index of S(G) (res. R(G)) and G can all be deduced from our results directly.     

Proposal of FEM implemented with particle discretization for analysis of failure phenomena

A new method for numerical simulation of failure behavior, namely, FEM-β, is proposed. For a continuum model of a deformable body, FEM-β solves a boundary value problem by applying particle discretization to a displacement field; the domain is decomposed into a set of Voronoi blocks and the non-overlapping characteristic functions for the Voronoi blocks are used to discretize the displacement function. By computing average strain and average strain energy, FEM-β obtains a numerical solution of the variational problem that is transformed from the boundary value problem. In a rigorous form, FEM-β is formulated for a variational problem of displacement and stress with different particle discretization, i.e., the non-overlapping characteristic function of the Voronoi blocks and the conjugate Delaunay tessellations, respectively, are used to discretize the displacement and stress functions. While a displacement field is discretized with non-smooth functions, it is shown that a solution of FEM-β has the same accuracy as that of ordinary FEM with triangular elements. The key point of FEM-β is the ease of expressing failure as separation of two adjacent Voronoi blocks owing to the particle discretization that uses non-overlapping characteristic functions. This paper explains these features of FEM-β with results of numerical simulation of several example problems.     

带有临界点的解析函数的圆模式逼近

一个圆模式是指复平面C上具有特定交角的一种圆格局.给定有界单连通区域ΩC内一个具有有限多个临界点的解析函数F,首先利用有分枝圆模式枝术构造了F的离散近似解,然后证明了这个近似解序列在Ω的紧子集上一致收敛于该解析函数F.这为带有临界点的解析函数的数值计算提供一种新的方法.     

提高激光打标检测系统质量的理论分析

随着激光打标工艺的日趋成熟,对打标在线检测的需求日益增加.本文采用激光三角法应用于激光打标系统的在线检测,分析了各种可能影响测量系统精度的因素,以激光散斑的影响最为严重.本文针对不同的因素提出了相应的解决方案.     

Spanners of additively weighted point sets

We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p,r) where p is a point in the plane and r is a real number. The distance between two points (pi,ri) and (pj,rj) is defined as |pipj|−ri−rj. We show that in the case where all ri are positive numbers and |pipj|?ri+rj for all i, j (in which case the points can be seen as non-intersecting disks in the plane), a variant of the Yao graph is a (1+?)-spanner that has a linear number of edges. We also show that the Additively Weighted Delaunay graph (the face-dual of the Additively Weighted Voronoi diagram) has a spanning ratio bounded by a constant. The straight-line embedding of the Additively Weighted Delaunay graph may not be a plane graph. Given the Additively Weighted Delaunay graph, we show how to compute a plane straight-line embedding that also has a spanning ratio bounded by a constant in time.     

Rapid and flexible laser marking and engraving of tilted and curved surfaces

We present a novel method for rapid and flexible laser marking and engraving of tilted, curved and freeform work-piece surfaces. The method is based on integrating a three-dimensional (3D) laser measurement system into a 3D laser marking system. We use the same laser source and optics for measurement and processing with a minimum of additional hardware components. A low power CW laser regime is used to measure the 3D shape of a work-piece surface while a high-peak power-pulsed laser regime is used for processing. The acquired 3D surface data are used to determine the 3D trajectory of the processing beam focus. Neither the 3D shape of the work-piece nor its orientation needs to be known in advance as long as the processed surface lies within the working range of the 3D laser processing system. This eliminates the need for exact work-piece positioning before processing and substantially improves processing flexibility (allowing, e.g. variations in work-piece shape or/and orientation from mark to mark). This paper discusses key issues concerning an implementation of the method and presents typical examples of markings and engravings, which demonstrate the advantages of the method with respect to the existing industrial 2D and 3D laser marking and engraving methods. The method can also be applied to flexible laser structuring and microprocessing of curved surfaces.