New method for graded mesh generation of all hexahedral finite elements

Mapping method is widely applied by most of commercial mesh generators because of its efficiency, mesh quality. One of the obstacles to apply the mapping method and generate a graded all hexahedral mesh of high quality in an arbitrarily three-dimensional domain is the generation of hexahedral parent elements on a super-element that allows for gradations in three co-ordinate directions. This paper presents a pattern module’s method to generate the graded mesh of all hexahedral elements in a cube and thus improves the mapping method. The method requires few calculations.     

Node-based dynamic adaptive grid with quadrilateral and hexahedral elements

A node-based data structure is developed for use in either two-dimensional (2-D) or three-dimensional (3-D) finite element method (FEM) problems. This grid uses quadrilateral (2-D) or hexahedral (3-D) elements and is dynamically adaptive according to the 1-irregular requirement for refinement–derefinement. Implemented in C++, the grid consists of node objects linked with pointers to neighboring node objects. The algorithm used to traverse the grid starts at the first node of the grid and constructs each FEM element by following the links of the nodes. This algorithm uses a stack to maintain the correct order of elements during the grid traversals. Because the elements and their connectivity are not permanently stored, the computer storage requirements for the grid are reduced significantly in 3-D compared with an element-based approach. Although the node-based approach may increase the CPU-time and complexity to access an element, it reduces the complexity and time required to refine and derefine an element. This implementation is applicable to many FEM domains.     

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.     

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.     

An efficient generation method of embedded reinforcement in hexahedral elements for reinforced concrete simulations

In this paper, an automatic procedure for the generation of embedded steel reinforcement inside hexahedral finite elements is presented. The automatic mapping of the entire reinforcement network inside the concrete hexahedral finite elements is performed using the end-point coordinates of the rebar reinforcement macro-elements. By introducing a geometrical constraint, this procedure decreases significantly the computational effort for generating the input data of the embedded rebar elements in three-dimensional finite-element analysis, particularly when dealing with relatively large-scale reinforced concrete models. The computational robustness and efficiency of the proposed mesh generation method are demonstrated through numerical experiments.     

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.     

Automatic hexahedral mesh generation for multi-domain composite models using a hybrid projective grid-based method

This paper presents an algorithm to generate an all-hexahedral mesh of a multi-domain solid model using a hybrid grid-based approach. This is based on a projective concept during the boundary adaptation of the initial mesh. In general, the algorithm involves the generation of a grid structure, which is superimposed on the solid model. This grid structure forms an initial mesh consisting of hexahedral elements, which intersect fully or partially with the solid model. This initial mesh is then shrunk in an outside-in manner to the faces of the model through a node projection process using the closest position approach. To match the resulting mesh to the edges of the model, a minimal deformation angle method is used. Finally, to match the vertices with the nodes on the mesh, a minimal warp angle method is employed. To create the mesh of a multi-domain solid model, an outside-in and inside-in hybrid of the grid-based method is used. This hybrid method ensures that the meshes of the different domains are conforming at their common boundary. This paper also describes two methods for resolving cases of degenerate elements: a splitting technique and a wedge insertion technique.     

Molecular dynamics-based unstructured grid generation method for aerodynamic applications

A new approach to triangular mesh generation based on the molecular dynamics method is proposed. Mesh nodes are considered as interacting particles. After the node placement by molecular dynamics simulation, well-shaped triangles or tetrahedra can be created after connecting the nodes by Delaunay triangulation or tetrahedrization. Some examples are considered in order to illustrate the method’s ability to generate a mesh for an aircraft with a complicated boundary. Mesh adaptation technology for molecular dynamics simulation is presented.     

A multiblock multigrid grid generation method for complex simulations

This paper deals with the aim of coupling multigrid generation of boundary-fitted grids with an effective domain decomposition technique. We present multiblock grid generation algorithms for efficient solutions of domain discretization problems. We propose the generation of structured grids by multiblock transformation of the domains, the choice of specific elliptic systems and the application of multigrid cycling. We assume the Laplacians of the curvilinear coordinates to be equal to appropriate functions of the curvilinear coordinates in the physical domain and, by interchanging the independent and the dependent variable, we obtain the transformed systems in the multiblock transformed computational domain. We adopt standard central differencing for the approximation of the nonlinear generating 2D and 3D systems and full approximation storage algorithms to solve the resulting discrete equations. We use block matching with two-surface overlapping and block by block iterations along with multigrid cycling in each block. We present computed multiblock grids by Figures and evaluation results of method performance by Tables.     

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.     

一种新的六面体有限元网格算法

在有限元网格产生过程中，吸取弦须编织法中的STC概念，将六面体以节点剖分为基础的思想转变为以单元点为基础，建立了以单元生长为核心的剖分算法，以期解决节点拓扑结构在三维情况下的控制问题，对进一步实现稳定、全自动的六面体剖分具有很大的帮助。     

基于Gregory法的N边域非自交结构网格生成

提出了在N边域裁减参数曲面上生成非自交光顺结构网格的方法。利用Gregory法,首先在参数坐标平面上将N边域分成N个四边形区域,并生成每个四边形区域内的网格,然后通过映射获得三维空间上的网格坐标点。为消除映射过程中所产生的自交现象,根据非自交特性和光顺网格的特点,提出了优化目标函数,并采用共轭梯度数值解法获得了最优解。利用该方法可以获得N边域上非自交光顺的结构网格,拓展了N边域裁剪曲面的使用范围。     

A grid-based algorithm for the generation of hexahedral element meshes

An algorithm for the generation of hexahedralelement meshes is presented. The algorithm works in two steps: first the interior of the volume is filled with a regular grid; then the boundary region is meshed by using basically twodimensional operations.The algorithm was designed for use in the fem-simulation of metal forming processes where a remeshing must be done very often. In principle, it can be used for meshing any geometry with hexahedral elements and examples of meshes for geometries arising from various applications are given. The algorithm is checked against the criteria proposed by Sabin [1] (Advances in Engineering Software, 13, 220–225).     

A consistent octree hanging node elimination algorithm for hexahedral mesh generation

A new algorithm for hanging node elimination in octree structures is developed. The proposed algorithm utilizes hanging node elimination by refinement templates and a new mesh conditioning technique based on decoupling templates. Refinement templates insert transition elements to eliminate hanging nodes. Decoupling templates insert circular loops in the dual mesh without introducing or removing hanging nodes. Decoupling templates are introduced to avoid full refinement in the cases that do not match any of the available refinement templates. The proposed algorithm eliminates hanging nodes for concavely refined regions without excessive refinement. Another advantage of the proposed algorithm lies in eliminating narrow gaps of coarse meshes between refined regions. This step has a positive effect on the mesh quality as it avoids introducing non-regular templates with a limited penalty of uniform refinement. The presented algorithm produces good quality meshes and provides a consistent and complete method for producing conformally refined octree structures.     

A method for conservative remapping on hexahedral meshes

A method for conservative interpolation (remapping) of physical parameters from one structured hexahedral mesh to another is described. The conservative remapping is reduced to determining the volume of the overlapping between the old and new mesh cells. A hexahedral cell with ruled faces is replaced by two dodecahedra with planar triangular faces. As a result, the remapping is reduced to construction of the overlapping between two dodecahedra. An optimal algorithm is suggested for examining the old mesh cells that have a nonempty overlapping with the current cell of the new mesh. The interpolation error is estimated. Examples of remapping are presented.     

A constructive approach to constrained hexahedral mesh generation

Mitchell proved that a necessary and sufficient condition for the existence of a topological hexahedral mesh constrained to a quadrilateral mesh on the sphere is that the constraining quadrilateral mesh contains an even number of elements. Mitchell’s proof depends on Smale’s theorem on the regularity of curves on compact manifolds. Although the question of the existence of constrained hexahedral meshes has been solved, the known solution is not easily programmable; indeed, there are cases, such as Schneider’s Pyramid, that are not easily solved. Eppstein later utilized portions of Mitchell’s existence proof to demonstrate that hexahedral mesh generation has linear complexity. In this paper, we demonstrate a constructive proof to the existence theorem for the sphere, as well as assign an upper-bound to the constant of the linear term in the asymptotic complexity measure provided by Eppstein. Our construction generates 76 × n hexahedra elements within the solid where n is the number of quadrilaterals on the boundary. The construction presented is used to solve some problems posed by Schneiders and Eppstein. We will also use the results provided in this paper, in conjunction with Mitchell’s Geode-Template, to create an alternative way of creating a constrained hexahedral mesh. The construction utilizing the Geode-Template requires 130 × n hexahedra, but will have fewer topological irregularities in the final mesh.     

A strategy of automatic hexahedral mesh generation by using an improved whisker-weaving method with a surface mesh modification procedure

One of the demands for three dimensional (3D) finite element analyses is the development of an automatic hexahedral mesh generator. For this problem, several methods have been proposed by many researchers. However, reliable automatic hexahedral mesh generation has not been developed at present. In this paper, a new strategy of fully automatic hexahedral mesh generation is proposed. In this strategy, the prerequisite for generating a hexahedral mesh is a quadrilateral surface mesh. From the given surface mesh, combinatorial dual cycles (sheet loops for the whisker-weaving algorithm) are generated to produce a hexahedral mesh. Since generating a good quality hexahedral mesh does not depend only on the quality of quadrilaterals of the surface mesh but also on the quality of the sheet loops generated from it, a surface mesh modification method to remove self-intersections from sheet loops is developed. Next, an automatic hexahedral mesh generator by the improved whisker-weaving algorithm is developed in this paper. By creating elements and nodes on 3D real space during the weaving process, it becomes possible to generate a hexahedral mesh with fewer bad-quality elements. Several examples will be presented to show the validity of the proposed mesh generation strategy.     

网格计算中一种基于属性的访问控制方法*

为了迎合目前网格计算对动态、细粒度授权的需求,针对网格资源分层式的组织结构特点,在现有的基于属性的访问控制（ABAC）模型的基础上,提出了一种针对网格资源的ABAC模型Grid_ABAC,并设计了基于XACML的Grid_ABAC实现框架,应用在GT4平台上。最后对GT4中的应用作了测试,测试结果表明授权结果与预期结果相同,且时间开销随着规模的增长并没有增长很多,在可接受范围内。证明Grid_ABAC模型在网格平台上具有一定的实用性。