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).     

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.     

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.     

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。     

As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

This paper presents an efficient and stable as-rigid-as-possible mesh deformation algorithm for planar shape deformation and hexahedral mesh generation. The deformation algorithm aims to preserve two local geometric properties: scale-invariant intrinsic variables and elastic deformation energy, which are together represented in a quadric energy function. To preserve these properties, the position of each vertex is further adjusted by iteratively minimizing this quadric energy function to meet the position constraint of the controlling points. Experimental results show that the deformation algorithm is efficient, and can obtain physically plausible results, which have the same topology structure with the original mesh. Such a mesh deformation method is useful to project the source surface mesh onto the target surfaces in hexahedral mesh generation based on sweep method, and application results show that the proposed method is feasible to mesh projection not only between similar surface contours but also dissimilar surface contours.     

Automatic mesh generation and modification techniques for mixed quadrilateral and hexahedral element meshes of non-manifold models

A typical geometric model usually consists of both solid sections and thin-walled sections. Through using a suitable dimensional reduction algorithm, the model can be reduced to a non-manifold model consisting of solid portions and two-dimensional portions which represent the mid-surfaces of the thin-walled sections. It is desirable to mesh the solid entities using three-dimensional elements and the surface entities using two-dimensional elements. This paper proposes a robust scheme to automatically generate such a mesh of mixed two-dimensional and three-dimensional elements. It also ensures that the mesh is conforming at the interface of the non-manifold geometries. Different classes of problems are identified and their corresponding solutions are presented.     

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.     

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.     

Genetic algorithms in mesh optimization for visualization and finite element models

This paper investigates the use of a genetic algorithm (GA) to perform the large-scale triangular mesh optimization process. This optimization process consists of a combination of mesh reduction and mesh smoothing that will not only improve the speed for the computation of a 3D graphical or finite element model, but also improve the quality of its mesh. The GA is developed and implemented to replace the original mesh with a re-triangulation process. The GA features optimized initial population, constrained crossover operator, constrained mutation operator and multi-objective fitness evaluation function. While retaining features is important to both visualization models and finite element models, this algorithm also optimizes the shape of the triangular elements, improves the smoothness of the mesh and performs mesh reduction based on the needs of the user.     

Octree-based automatic mesh generation for non-manifold domains

Automatic mesh generation within the context of non-manifold geometric models is far from a commercial reality. While manifold objects are the most commonly encountered domains in many applications, other applications such as those requiring multiple material models and mixedmodel representations (combination of 1-D, 2-D and 3-D domains) fall beyond the realm of the existing automatic meshing procedures as they require a non-conventional modeling enviroment, namely the non-manifold topology (NMT) based environment. This paper focuses on automatic mesh generation issues in the context of two such applications: (i) finite element modeling for multiple material models and (ii) geometric abstractions requiring a mixed-model representation. Specifically, the paper describes a geometry utility system, built around an NMT data structure and geometry-based meshing algorithms that ensure the validity of the mesh for non-manifold domains.GE Consulting Services.     

The geometric element transformation method for mixed mesh smoothing

The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.     

Intelligent finite element mesh generation

A knowledge-based and automatic finite element mesh generator (INTELMESH) for two-dimensional linear elasticity problems is presented. Unlike other approaches, the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a priori finite element mesh which is more refined around the critical regions of the problem domain. INTELMESH uses a blackboard architecture expert system and the new concept of substracting to locate the critical regions in the domain and to assign priority and mesh size to them. This involves the decomposition of the original structure into substructures (or primitives) for which an initial and approximate analysis can be performed by using analytical solutions and heuristics. It then uses the concept of wave propagation to generate graded nodes in the whole domain with proper density distribution. INTELMESH is fully automatic and allows the user to define the problem domain with minimum amount of input such as object geometry and boundary and loading conditions. Once nodes have been generated for the entire domain, they are automatically connected to form well-shaped triangular elements ensuring the Delaunay property. Several examples are presented and discussed. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near optimal initial meshes, will be more accurate and efficient.     

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.     

Skeleton-based computational method for the generation of a 3D finite element mesh sizing function

This paper focuses on the generation of a three-dimensional (3D) mesh sizing function for geometry-adaptive finite element (FE) meshing. The mesh size at a point in the domain of a solid depends on the geometric complexity of the solid. This paper proposes a set of tools that are sufficient to measure the geometric complexity of a solid. Discrete skeletons of the input solid and its surfaces are generated, which are used as tools to measure the proximity between geometric entities and feature size. The discrete skeleton and other tools, which are used to measure the geometric complexity, generate source points that determine the size and local sizing function at certain points in the domain of the solid. An octree lattice is used to store the sizing function as it reduces the meshing time. The size at every lattice-node is calculated by interpolating the size of the source points. The algorithm has been tested on many industrial models, and it can be extended to consider other non-geometric factors that influence the mesh size, such as physics, boundary conditions, etc.Sandia National Laboratory is a multiprogram laboratory operated by the Sandia Corporation, a Lockheed Martin Company, for the US Department of Energy under contract DE-AC04-94AL85000.     

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvement of meshes in a broad range of applications.     

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.     

Hexahedral mesh development of free-formed geometry: The human femur exemplified

The objective of the present research is to develop a standard hexahedral Finite Element (FE) model of the human femur accounting for the material characteristics of cortical bone, cancellous bone and bone marrow. The anatomical data were acquired from the Visible Human Project. A detailed outline of the steps necessary in developing hexahedral FE meshes from computed tomography (CT) data is provided, along with a section on modelling strategies providing comprehensive suggestions on how to overcome meshing difficulties due to geometrical non-linearities. The stress and deformation results are discussed.     

An algorithm for automatic 2D quadrilateral mesh generation with line constraints

Finite element method (FEM) is a fundamental numerical analysis technique widely used in engineering applications. Although state-of-the-art hardware has reduced the solving time, which accounts for a small portion of the overall FEM analysis time, the relative time needed to build mesh models has been increasing. In particular, mesh models that must model stiffeners, those features that are attached to the plate in a ship structure, are imposed with line constraints and other constraints such as holes. To automatically generate a 2D quadrilateral mesh with the line constraints, an extended algorithm to handle line constraints is proposed based on the constrained Delaunay triangulation and Q-Morph algorithm. The performance of the proposed algorithm is evaluated, and numerical results of our proposed algorithm are presented.     

Algorithm,software, and hardware optimizations for Delaunay mesh generation on simultaneous multithreaded architectures

This article focuses on the optimization of PCDM, a parallel, two-dimensional (2D) Delaunay mesh generation application, and its interaction with parallel architectures based on simultaneous multithreading (SMT) processors. We first present the step-by-step effect of a series of optimizations on performance. These optimizations improve the performance of PCDM by up to a factor of six. They target issues that very often limit the performance of scientific computing codes. We then evaluate the interaction of PCDM with a real SMT-based SMP system, using both high-level metrics, such as execution time, and low-level information from hardware performance counters.