2D structured grid generation method producing a mesh with prescribed properties near boundary

A variational method of generating a structured mesh on a two-dimensional domain is considered. To this end, a quasiconformal mapping of the parametric domain with a given Cartesian mesh onto the underlying physical domain is used. The functions implementing the mapping are sought by solving the Dirichlet problem for the system of elliptic second-order partial differential equations. An additional control for the cell shape is executed by introducing a local mapping which induces a control metric. In some particular cases, instead of an additional local mapping, a global mapping of the parametric domain onto the intermediate domain is used, where the curvilinear mesh is produced, and next this domain is mapped onto the underlying physical domain. The control metric allows to obtain a mesh with required properties: grid line orthogonality and prescribed mesh point clustering near the domain boundary. Examples of mesh in the annulus and near airfoil are presented.     

凸组合球面参数化

针对具有单边界的三角网格或与球面同胚的零亏格封闭网格，提出一种基于球面向量线性凸组合的三维网格球面参数化方法．把参数域从平面凸区域扩展到球面凸区域，并把具有凸性的重心坐标纳入到参数化框架中，使得参数化具有保形性质且变形小，同时证明了该参数化方法的存在性和惟一性．整个算法简单可靠．     

用于视频编码的小波域三角形网格构造方法

在深入研究视频图像冗余离散变换特征的基础上,提出一种用于视频编码运动补偿技术的小波域不规则三角形网格构造方法．基于孔径问题的原理,使用冗余离散变换小波的水平和垂直子带构造三角形网格节点的选择判据,把节点的特征匹配度集成到节点前向追踪过程的判据中;通过获得的节点运动矢量和网格映射实现运动补偿功能．实验证明,该方法获得了较好运动补偿的效果．     

Automatic Delaunay mesh generation method and physically-based mesh optimization method on two-dimensional regions

Delaunay mesh generation method is a common method for unstructured mesh (or unstructured grid) generation. Delaunay mesh generation method can conveniently add new points to the existing mesh without remeshing the whole domain. However, the quality of the generated mesh is not high enough if compared with some mesh generation methods. To obtain high-quality mesh, this paper developed an automatic Delaunay mesh generation method and a physically-based mesh optimization method on two-dimensional regions. For the Delaunay mesh generation method, boundary-conforming problem was ensured by create nodes at centroid of mesh elements. The definition of node bubbles and element bubbles was provided to control local mesh coarseness and fineness automatically. For the physically-based mesh optimization method, the positions of boundary node bubbles are predefined, the positions of interior node bubbles are adjusted according to interbubble forces. Size of interior node bubbles is further adjusted according to the size of adjacent node bubbles. Several examples show that high-quality meshes are obtained after mesh optimization.

     

非结构网格布点方法研究进展

用有限元方法求解偏微分方程初边值问题首先要离散求解区域,即网格生成,并且网格质量的好坏直接影响着有限元解的收敛性和精度,所以关于网格生成有很多学者从各自的领域出发做了大量的研究工作。论文关注于非结构网格点的布置方法,对已有的具有代表性的布点方法的研究进展进行了分类综述。     

Layered tetrahedral meshing of thin-walled solids for plastic injection molding FEM

This paper describes a method for creating a well-shaped, layered tetrahedral mesh of a thin-walled solid by adapting the surface triangle sizes to the estimated wall thickness. The primary target application of the method is the finite element analysis of plastic injection molding, in which a layered mesh improves the accuracy of the solution. The edge lengths of the surface triangles must be proportional to the thickness of the domain to create well-shaped tetrahedrons; when the edge lengths are too short or too long, the shape of the tetrahedron tends to become thin or flat. The proposed method creates such a layered tetrahedral mesh in three steps: (1) create a preliminary tetrahedral mesh of the target geometric domain and estimate thickness distribution over the domain; (2) create a non-uniform surface triangular mesh with edge length adapted to the estimated thickness, then create a single-layer tetrahedral mesh using the surface triangular mesh; and (3) subdivide tetrahedrons of the single-layer mesh into multiple layers by applying a subdivision template. The effectiveness of the layered tetrahedral mesh is verified by running some experimental finite element analyses of plastic injection molding.     

一种三角形网格模型数字水印算法

随着3D模型技术的发展,3D模型的版权保护问题越来越被重视.提出了一种基于三角域上V系统的3D网格模型数字水印算法.该算法首先将模型上的顶点到模型中心的距离进行三角域上的一次V变换,然后对变换后的系数进行量化来嵌入水印.由于该距离是一种全局几何特征,且算法将足够多的比特水印信息分布到模型各处,从而使得该水印方案具有一定的鲁棒性.实验结果表明该算法能够抵抗一般的平移、旋转等类型的攻击和随机噪声攻击.     

基于特定边界的组合保角球面参数化

针对亏格为零的流形三角网格模型,提出一种基于特定边界的组合保角球面参数化方法。该方法采用平均值坐标计算出原始三角网格模型各顶点间相关的权数,然后用这个权数去修正球面域上的顶点坐标得到新的具有保角性质的顶点坐标,再利用Möbius变换把新生成的球面域质心转化为球心,使其面积的变形程度降低,最后得到一个精度更高的初始球面域。实验结果表明该方法是有效的,且具有变形小、效率高的特点。     

解析二维非结构网格生成方法及其应用

提出弱区域指示函数描述流场形状并证明了其存在和不唯一性;利用该函数基于Delaunay方法依据流场尺度生成二维非结构网格。其中,边界引力有效解决了流场边界恢复和内嵌边界问题,弹簧振子和正三角形趋进技术有效改善网格质量。最后,弹簧振子随着弱区域指示函数的演变与监测函数的指导成功应用到自适应网格生成。     

边界简化与多目标优化相结合的高质量四边形网格生成

目的 高质量四边形网格生成是计算机辅助设计、等几何分析与图形学领域中一个富有挑战性的重要问题。针对这一问题,提出一种基于边界简化与多目标优化的高质量四边形网格生成新框架。方法 首先针对亏格非零的平面区域,提出一种将多连通区域转化为单连通区域的方法,可生成高质量的插入边界;其次,提出"可简化角度"和"可简化面积比率"两个阈值概念,从顶点夹角和顶点三角形面积入手,将给定的多边形边界简化为粗糙多边形;然后对边界简化得到的粗糙多边形进行子域分解,并确定每个子域内的网格顶点连接信息;最后提出四边形网格的均匀性和正交性度量目标函数,并通过多目标非线性优化技术确定网格内部顶点的几何位置。结果 在同样的离散边界下,本文方法与现有方法所生成的四边网格相比,所生成的四边网格顶点和单元总数目较少,网格单元质量基本类似,计算时间成本大致相同,但奇异点数目可减少70% 80%,衡量网格单元质量的比例雅克比值等相关指标均有所提高。结论 本文所提出的四边形网格生成方法能够有效减少网格中的奇异点数目,并可生成具有良好光滑性、均匀性和正交性的高质量四边形网格,非常适用于工程分析和动画仿真。     

A posteriori error analysis for a fractional differential equation

Numerical treatment for a fractional differential equation (FDE) is proposed and analysed. The solution of the FDE may be singular near certain domain boundaries, which leads to numerical difficulty. We apply the upwind finite difference method to the FDE. The stability properties and a posteriori error analysis for the discrete scheme are given. Then, a posteriori adapted mesh based on a posteriori error analysis is established by equidistributing arc-length monitor function. Numerical experiments illustrate that the upwind finite difference method on a posteriori adapted mesh is more accurate than the method on uniform mesh.     

车身冲压模型腔表面四边形网格的局部粗化

给定一车身冲压模型腔表面上结构化的四边形网格，通过单元合并对网格进行自动的粗化，其目的在于简化冲压仿真模型，提高仿真计算速度，首先，根据单元节点曲率半径的分布，搜寻出满足单元合并条件的初始四边形区域，接头，判断初始合交区域的边界过渡条件，最后，进行单合并，冲压成型仿真应用实例证明，文中算法既提高了仿真速度，又保持了仿真精度，该算法可以推广到任意曲面结构化四边形网格的局部粗化问题。     

A new approach to solid modeling with trivariate T-splines based on mesh optimization

We present a new method to construct a trivariate T-spline representation of complex genus-zero solids for the application of isogeometric analysis. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation.     

医学体数据中基于局部特征尺寸的Delaunay四面体化算法*

为了从医学体数据构建面向虚拟手术仿真系统的器官实体模型,提出一种基于局部特征尺寸的Delaunay四面体化算法。首先采用Marching Cubes算法和外存模型简化技术从体数据中得到器官等值面简化模型,提出重心射线法去除内部冗余网格,获得器官多面体表面;然后基于局部特征尺寸构建表面顶点保护球,结合Delaunay细分算法生成边界一致的初始四面体网格;最后提出基于随机扰动的空间分解法快速生成内部节点,并逐点插入到四面体网格中优化单元质量。该算法克服了Delaunay细分算法无法处理锐角输入的缺点,并从理论     

Moving mesh methods for solving parabolic partial differential equations

A new adaptive method is described for solving nonlinear parabolic partial differential equations with moving boundaries, using a moving mesh with continuous finite elements. The evolution of the mesh within the interior of the spatial domain is based upon conserving the distribution of a chosen monitor function across the domain throughout time, where the initial distribution is selected based upon the given initial data. The mesh movement at the boundary is governed by a second monitor function, which may or may not be the same as that used to drive the interior mesh movement. The method is described in detail and a selection of computational examples are presented using different monitor functions applied to the porous medium equation (PME) in one and two space dimensions.     

Parallel three-dimensional mesh generation on distributed memory MIMD computers

This paper discusses the development of an automatic mesh generation technique designed to operate effectively on multiple instruction multiple data (MIMD) parallel computers. The meshing approach is hierarchical, that is, model entities are meshed after their boundaries have been meshed. Focus is on the region meshing step. An octree is constructed to serve as a localization tool and for efficiency. The tree is also key to the efficient parallelization of the meshing process since it supports the distribution of load to processors. The parallel mesh generation procedure repartitions the domain to be meshed and applies on processor face removals until all face removals with local data have been performed. The portion of the domain to be meshed remaining is dynamically repartitioned at the octant level using an Inertial Recursive Bisection method and local face removals are reperformed. Migration of a terminal octant involves migration of the octant data and the octant's mesh faces and/or mesh regions. Results show relatively good speed-ups for parallel face removals on small numbers of processors. Once the three-dimensional mesh has been generated, mesh regions may be scattered across processors. Therefore, a final dynamic repartitioning step is applied at the region level to produce a partition ready for finite element analysis.     

Domain Decomposition Models for Parallel Monte Carlo Transport

We present a strategy for parallelizing computations that use the transport method. It combines spatial domain decomposition with domain replication to realize the scaling benefits of replication while allowing for problems whose computational mesh will not fit in a single processor's memory. The mesh is decomposed into a small number of spatial domains—typically fewer domains than there are processors—and heuristics are used to estimate the computational effort required to generate the solution in each subdomain using Monte Carlo. That work estimate determines the number of times a subdomain is replicated relative to the others. Timing of runs for two problems show that the new method scales better than traditional domain decomposition.     

A modified advancing layers mesh generation for thin three-dimensional objects with variable thickness

A method of generating modified advancing layers mesh is proposed. In this paper the mesh generation process of semi-unstructured prismatic/tetrahedral mesh is presented for relatively thin three-dimensional geometries with variable thickness, as in the case of injection molding analysis. Prismatic meshes are generated by offsetting initial surface triangular meshes. During the mesh generation process, mesh quality is efficiently improved with the use of a new node relocation method. Finally, tetrahedral meshes are automatically generated in the rest of the domain. The mesh generating capability of the proposed algorithm is demonstrated with the several practical test cases.     

Application of mortar elements to diffuse-interface methods

An adaptive 2D mesh refinement technique based on mortar spectral elements applied to diffuse-interface methods is presented. The refinement algorithm tracks the movement of the 2D diffuse-interface and subsequently refines the mesh locally at that interface, while coarsening the mesh in the rest of the computational domain, based on error estimators. Convergence of the method is validated using a Gaussian distribution problem and results are presented for a Cahn–Hilliard diffuse-interface model applied to capture the transient dynamics of polymer blends.