Adaptive generation of hexahedral element mesh using an improved grid-based method

An improved grid-based algorithm for the adaptive generation of hexahedral finite element mesh is presented in this paper. It is named as the inside-out grid-based method and involves the following four steps. The first step is the generation of an initial grid structure which envelopes the analyzed solid model completely. And the elements size and density maps are constructed based on the surface curvature and local thickness of the solid model. Secondly, the core mesh is generated through removing all the undesired elements using even and odd parity rules. The third step is to magnify the core mesh in an inside-out manner through a surface node projection process using the closest position approach. To match the mesh to the characteristic boundary of the solid model, a minimal Scaled Jacobian criterion is employed. Finally, in order to handle the degenerated elements and improve the quality of the resulting mesh, two comprehensive techniques are employed: the insertion technique and collapsing technique. The present method was applied in the mesh construction of different engineering problems. Scaled Jacobian and Skew metrics are used to evaluate the hexahedral element mesh quality. The application results show that all-hexahedral element meshes which are well-shaped and capture all the geometric features of the original solid models can be generated using the inside-out grid-based method presented in this paper.     

一种基于逻辑栅格的网格自动生成算法

针对基于栅格法对表面变动较大的模型进行网格划分适应性差的问题,提出一种基于逻辑栅格的六面体网格自动生成算法。该算法对基于栅格法的思想进行改进,避开一次生成模型初始栅格,将模型离散为一系列截面,对相邻截面采用矢量求交方法形成一对截面的初始栅格,修正初始栅格形成两截面之间的一层网格,形成整体模型。采用改进的栅格法进行复杂地形拱坝坝肩块体网格自动生成,取得较好的效果,结果证明改进的栅格法对复杂地形适应性强,模型表面变动较大时能自动进行网格退化。     

Automatic hexahedral mesh generation using a new grid-based method with geometry and mesh transformation

A geometry and mesh transformation approach is proposed to overcome the traditional problem of poorly shaped elements at the boundary using the grid-based method of mesh generation. This is achieved by transforming the original geometric model to a topologically similar recognition model which conforms fully to the Cartesian directions. Such a recognition model is constructed by tessellating the original model and then employing a fuzzy logic method to determine the normal directions of the faces. A three-dimensional field morphing algorithm is used to position the features of the recognition model. Such a recognition model is then meshed with hexahedral elements without any degeneracy using the new grid-based algorithm. The mesh of the recognition model is mapped back to the original geometric model by employing a transformation based on the Laplacian-isoparametric equation.     

Grid-based hexahedral element meshing algorithms for solid models with concave curved boundary lines

This paper presented a grid-based hexahedral element mesh generation algorithm for solid models with concave curved boundary lines. A deep study was focused on the boundary matching and quality improvement techniques. Firstly, a method for computing the curvature values of the triangle facets and sub-surfaces was proposed. In order to improve the surface mesh quality, a layer of new elements was inserted on the surface of the jagged core mesh. Then, a relative position relationship method was used to match C-edges of the solid model. Eight different types of free quadrilateral facet configurations were established. In order to handle the concave curve-matching problem, this paper proposed a method to modify the matching properties of the degenerate quadrilateral facets fitted on the same concave curved boundary line by unifying their orientations to point to the same sub-surface. In addition, six mixed templates were newly proposed to improve the geometrical topology of the degenerate elements associated with concave curves and sharp features. The positions of the nodes were smoothed by the modified Laplacian method and objective function. Finally, the effectiveness and reliability of the algorithms proposed in this paper were demonstrated by a practical example.     

Adaptive hexahedral mesh generation and quality optimization for solid models with thin features using a grid-based method

This paper presented an automatic inside-out grid-based hexahedral element mesh generation algorithm for various types of solid models. For the thin features with small thickness of the geometric model, corresponding treatment methods were given for successfully implementing each meshing step, containing the techniques for adaptive refinement, boundary match, topological optimization and local refinement. In order to realize the reasonable identification of refinement regions and resolve the expansion problem of refinement information fields, a thin-feature criterion and a supplementary criterion were proposed aiming at thin features of the geometry. To implement accurate boundary match for thin features, ten basic types and five complementary types of facet configurations were established, and a priority-node identification method was proposed additionally. Three topological optimization modes were newly proposed to improve the topological connections of the boundary mesh in thin features. Local refinement techniques were also built to refine the thin features of solid models. Finally, several examples were provided to demonstrate the effectiveness and reliability of the proposed algorithms.     

Block Cartesian abstraction of a geometric model and its application in hexahedral mesh generation

In this work, a fuzzy logic approach is proposed to transform a geometric model of arbitrary shape to its block Cartesian abstraction. This abstraction is topologically similar to the original model and it contains geometric sub-entities which are all aligned in the Cartesian directions. This is achieved by calculating the modifications made to the face normal vectors as a result of the influences of the adjacent faces. A fuzzy logic inference engine is developed by combining heuristics to emulate the local changes in face normal vectors with respect to the changes in the global space. A three-dimensional field morphing algorithm is used to position the features of this block Cartesian abstraction so that a congruent geometric model can be reconstructed. Such a model is useful for the generation of structured quadrilateral boundary element meshes or structured hexahedral meshes based on grid-based meshing method, mesh mapping or sweeping. This approach is also able to overcome the traditional problem of having poorly shaped elements at the boundary using the grid-based method of mesh generation. As the topology of the block Cartesian abstraction is congruent to the original model, the mesh can be mapped back to the original model by employing an inverse operation of the transformation.     

Hybrid grid generation for two-dimensional high-Reynolds flows

An hybrid mesh generation algorithm for two-dimensional viscous flows at high-Reynolds number is presented. An advancing-front method is used close to solid surfaces and in the wake region(s). The boundary layer and wake grids possibly contain both highly stretched quadrilateral and triangular elements. The latter are inserted locally to improve the quality of the grid, thus circumventing some drawbacks of standard structured grid advancing-front methods. An advancing-front/Delaunay algorithm triangulates the remaining portion of the computational domain. An overview of both algorithms is given and results for viscous laminar and turbulent compressible flows around single and multi-element airfoils are shown to support the present approach.     

The receding front method applied to hexahedral mesh generation of exterior domains

Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.     

Subdomain generation using emergent ant colony optimization

Finite elements mesh decomposition is a well known optimization problem and is used to split a computationally expensive finite elements mesh into smaller subdomains for parallel finite elements analysis.The ant colony optimization is a type of algorithm that seeks to model the emergent behaviour observed in ant colonies and utilize this behaviour to solve combinatorial problems. This technique has been applied to several problems, most of which are graph related because the ant colony metaphor can be most easily applied to such types of problems. This paper examines the application of ant colony optimization algorithm to the partitioning of unstructured adaptive meshes for parallel explicit time-stepping finite elements analysis.The concept of ant colony optimization technique in addition to the notion of swarm intelligence for finding approximate solutions to combinatorial optimization problems is described. This algorithm combines the features of the classical ant colony optimization technique with swarm intelligence to form a model which is an artificial system designed to perform a certain task.The application of the ant colony optimization for partitioning finite elements meshes based on triangular elements using the swarm intelligence concept is described. A recursive greedy algorithm optimization method is also presented as a local optimization technique to improve the quality of the solutions given by the ant colony optimization algorithm. The partitioning is based on the recursive bisection approach.The mesh partitioning is carried out using normal and predictive modes for which the predictive mode uses a trained multi-layered feedforward neural network that estimates the number of triangular elements that will be generated after finite elements mesh generation is carried out.The performance of the proposed hybrid approach for the recursive bisection of finite elements meshes is examined by decomposing two mesh examples and comparing them with a well known finite elements domain decomposer.     

基于扩展和网格的多密度聚类算法

提出了网格密度可达的聚类概念和边界处理技术，并在此基础上提出一种基于扩展的多密度网格聚类算法。该算法使用网格技术提高聚类的速度，使用边界处理技术提高聚类的精度，每次聚类均从最高的密度单元开始逐步向周围扩展形成聚类．实验结果表明，该算法能有效地对多密度数据集和均匀密度数据集进行聚类，具有聚类精度高等优点．     

A template-based approach for parallel hexahedral two-refinement

We provide a template-based approach for generating locally refined all-hex meshes. We focus specifically on refinement of initially structured grids utilizing a 2-refinement approach where uniformly refined hexes are subdivided into eight child elements. The refinement algorithm consists of identifying marked nodes that are used as the basis for a set of four simple refinement templates. The target application for 2-refinement is a parallel grid-based all-hex meshing tool for high performance computing in a distributed environment. The result is a parallel consistent locally refined mesh requiring minimal communication and where minimum mesh quality is greater than scaled Jacobian 0.3 prior to smoothing.     

Improving Initial Flattening of Convex-Shaped Free-Form Mesh Surface Patches Using a Dynamic Virtual Boundary

This study proposes an efficient algorithm for improving flattening result of triangular mesh surface patches having a convex shape. The proposed approach, based on barycentric mapping technique, incorporates a dynamic virtual boundary, which considerably improves initial mapping result. The dynamic virtual boundary approach is utilized to reduce the distortions for the triangles near the boundary caused by the nature of convex combination technique. Mapping results of the proposed algorithm and the base technique are compared by area and shape accuracy metrics measured for several sample surfaces. The results prove the success of the proposed approach with respect to the base method.     

多域光网络中应用混合拓扑聚合的分段保护算法

研究了多域光网络中的路由保护问题;为了克服多域光网络中可扩展性约束,提出了一种混合拓扑聚合方法。该方法结合了全连通和生成树拓扑聚合的优点,在网络中需要存储和发布的链路状态信息与聚合信息反映实际物理拓扑的精确性之间进行了折中;然后在此混合拓扑聚合方法的基础上,提出了一种基于查询机制的多域分段保护算法。仿真表明,相比传统的多域保护算法,该算法阻塞率低,可扩展性好。     

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle-based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid-based advection in other regions of the flow. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C¹ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.     

滑动窗口内基于密度网格的数据流聚类算法

提出了一种基于密度网格的数据流聚类算法。通过引入“隶度”,对传统的基于网格密度的数据流聚类算法,以网格内数据点的个数作为网格密度的思想加以改进,解决了一个网格内属于两个类的数据点以及边界点的处理问题。从而既利用了基于网格算法的高效率,还较大程度地提高了聚类精度。     

An adaptive wavelet collocation method for solving optimal control of elliptic variational inequalities of the obstacle type

This paper presents a fast computational technique based on the wavelet collocation method for the numerical solution of an optimal control problem governed by elliptic variational inequalities of obstacle type. In this problem, the solution divides the domain into contact and noncontact sets. The boundary between the contact and noncontact sets is a free boundary, which is not known a priori and the solution is not smooth on it. Accordingly, a very fine grid is needed in order to obtain a solution with a reasonable accuracy. In this paper, our aim is to propose an adaptive scheme in order to generate an appropriate and economic irregular dyadic mesh for finding the optimal control and state functions. The irregular mesh will be generated such that its density around the free boundary is higher than in other places and high-resolution computations are focused on these zones. To this aim, we use an adaptive wavelet collocation method and take advantage of the fast wavelet transform of compact-supported interpolating wavelets to develop a multi-level algorithm, which generates an adaptive computational grid. Using this adaptive grid takes less CPU time than using a full regular mesh. At each step of the algorithm, the active set method is used for solving the optimality system of the obstacle problem on the adapted mesh. Finally, the numerical examples are presented to show the validity and efficiency of the technique.     

Parallelization of structured,hierarchical adaptive mesh refinement algorithms

We describe an approach to parallelization of structured adaptive mesh refinement algorithms. This type of adaptive methodology is based on the use of local grids superimposed on a coarse grid to achieve sufficient resolution in the solution. The key elements of the approach to parallelization are a dynamic load-balancing technique to distribute work to processors and a software methodology for managing data distribution and communications. The methodology is based on a message-passing model that exploits the coarse-grained parallelism inherent in the algorithms. The approach is illustrated for an adaptive algorithm for hyperbolic systems of conservation laws in three space dimensions. A numerical example computing the interaction of a shock with a helium bubble is presented. We give timings to illustrate the performance of the method. Received: 28 April 1999 / Accepted: 25 November 1999     

TUM.GeoFrame: automated high-order hexahedral mesh generation for shell-like structures

This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order all-hexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.     

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。