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Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

A 3D surface mesh generation scheme is suggested for the triangulation of general bi‐variate surfaces. The target surface to be meshed is represented as a union of bi‐variate sub‐surfaces and hence a wide range of surfaces can be modelled. Different useful features such as repeated curves, crack lines and surface branches are included in the geometrical and topological models to increase the flexibility of the mesh generation scheme. The surface metric tensor specification is employed to define and control the element characteristics in the mesh generation procedure. A robust metric triangulation kernel is used for parametric space mesh generation. The shape qualities of the sub‐surface meshes generated are then improved by using some ad hoc mesh quality enhancement schemes before they are combined together to form the final mesh. Numerical examples indicate that high quality surface meshes with rapid varying element size and stretching characteristics can be generated within a reasonable time limit in a few mesh adaptive iterations.

The purpose of this paper is to present an automatic approach for mesh sizing field generation of complicated  computer-aided design (CAD) models.

In this paper, the authors present an automatic approach for mesh sizing field generation. First, a source point extraction algorithm is applied to capture curvature and proximity features of CAD models. Second, according to the distribution of feature source points, an octree background mesh is constructed for storing element size value. Third, mesh size value on each node of background mesh is calculated by interpolating the local feature size of the nearby source points, and then, an initial mesh sizing field is obtained. Finally, a theoretically guaranteed smoothing algorithm is developed to restrict the gradient of the mesh sizing field.

To achieve high performance, the proposed approach has been implemented in multithreaded parallel using OpenMP. Numerical results demonstrate that the proposed approach is remarkably efficient to construct reasonable mesh sizing field for complicated CAD models and applicable for generating geometrically adaptive triangle/tetrahedral meshes. Moreover, since the mesh sizing field is defined on an octree background mesh, high-efficiency query of local size value could be achieved in the following mesh generation procedure.

How to determine a reasonable mesh size for complicated CAD models is often a bottleneck of mesh generation. For the complicated models with thousands or even ten thousands of geometric entities, it is time-consuming to construct an appropriate mesh sizing field for generating high-quality mesh. A parallel algorithm of mesh sizing field generation with low computational complexity is presented in this paper, and its usability and efficiency have been verified.

A new mesh generation procedure is suggested for the generation of 2D adaptive finite element meshes with strong element gradation and stretching effects. Metric tensors are employed to define and control the element characteristics during the mesh generation process. By using the metric tensor specification and a new, robust and refined advancing front triangulation kernel, triangles with nearly unit edge length with respect to the normalized space are generated. Highly graded and stretched elements can be generated without much difficulty and the operation complexity of the mesh generation process is exactly the same as the usual 2D advancing front mesh generator. A set of mesh quality enhancement procedures has also been suggested for the further improvement of the quality of the finite element meshes. A simple and effective mesh conversion scheme is used to convert the output triangular mesh to a pure quadrilateral mesh while all the essential element characteristics are preserved. Mesh generation examples show that high quality finite element meshes with element characteristics compatible with the specified metric tensors are generated within a reasonable time limit in a common small computing environment.

This article describes a method for mesh generation, suitable for applications of the finite‐element method, which proceeds fully automatically from a geometric model of the object provided by a CAD‐system. It first generates a coarse mesh which is then adapted to fit the finite‐element problem. A resulting system of equations can be solved by a Gaussian‐type matrix method with as few computations as are necessary for a well‐banded matrix, but without the need for node or element numbering.

This paper presents an algorithm for automatic generation of graded initial quadrilateral meshes targeted for the finite element analysis of metal‐forming processes. Meshing the domain geometry deals with a universe of shapes, and the procedure therefore takes into account the initial geometry of the billet. A grid‐based approach is utilised for generating an initial coarse mesh with well‐shaped (internal) elements, and in cases where non‐rectangular shapes are to be discretized, linking with the boundary is performed on the basis of constrained Delaunay triangulation. By analysing the contact situation between dies and mesh, an attempt is made to identify regions where plastic deformation is likely to be concentrated during the early stages of processing, and accordingly refinement of the mesh is performed locally by elemental subdivision. Simulation examples for closed‐die forging, forward rod and backward can extrusion substantiate the feasibility of this approach in terms of lowering the overall calculation error and limiting the interference between mesh and die.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Sizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating the procedure of creating a sizing function is a prerequisite to set up a fully automatic mesh generation pipeline. In this paper, an automatic algorithm is proposed to create a high-quality sizing function for an unstructured surface and volume mesh generation by using a triangular mesh as the background mesh.

A practically efficient and effective solution is developed by using local operators carefully to re-mesh the tessellation of the input Computer Aided Design (CAD) models. A nonlinear programming (NLP) problem has been formulated to limit the gradient of the sizing function, while in this study, the object function of this NLP is replaced by an analytical equation that predicts the number of elements. For the query of the sizing value, an improved algorithm is developed by using the axis-aligned bounding box (AABB) tree structure.

The local operations of re-meshing could effectively and efficiently resolve the banding issue caused by using the default tessellation of the model to define a sizing function. Experiments show that the solution of the revised NLP, in most cases, could provide a better solution at the lower cost of computational time. With the help of the AABB tree, the sizing function defined at a surface background mesh can be also used as the input of volume mesh generation.

Theoretical analysis reveals that the construction of the initial sizing function could be reduced to the solution of an optimization problem. The definitions of the banding elements and surface proximity are also given. Under the guidance of this theoretical analysis, re-meshing and ray-casting technologies are well-designed to initial the sizing function. Smoothing with the revised NLP and querying by the AABB tree, the paper provides an automatic method to get a high-quality sizing function for both surface and volume mesh generation.

Arbitrary constraints might be included into the problem domain in many engineering applications, which represent specific features such as multi-domain interfaces, cracks with small yield stresses, stiffeners attached on the plate for reinforcement and so on. To imprint these constraints into the final mesh, additional techniques need to be developed to treat these constraints properly.

This paper proposes an automatic approach to generate quadrilateral meshes for the geometric models with complex feature constraints. Firstly, the region is decomposed into sub-regions by the constraints, and then the quadrilateral mesh is generated in each sub-region that satisfies the constraints. A method that deals with constraint lines and points is presented. A distribution function is proposed to represent the distribution of mesh size over the region by using the Laplace equation. The density lines and points can be specified inside the region and reasonable mesh size distribution can be obtained by solving the Laplace equation.

An automatic method to define sub-regions is presented, and the user interaction can be avoided. An algorithm for constructing loops from constraint lines is proposed, which can deal with the randomly distributed constraint lines in a general way. A method is developed to deal with constraint points and quality elements can be generated around constraint points. A function defining the distribution of mesh size is put forward. The examples of constrained quadrilateral mesh generation in actual engineering analysis are presented to show the performance of the approach.

An automatic approach to constrained quadrilateral mesh generation is presented in this paper. It can generate required quality meshes for special applications with complex internal feature constraints.

Modern CAD systems facilitate the creation of any surface geometry imaginable, and complex surfaces for free-form grid shells are often represented by a set of Non-Uniform Rational B-Splines surface patches. But it remains an intractable issue how to generate high-quality grids on complex surfaces efficiently. To solve this issue, an automatic triangular mesh generation method is presented, based on bubble dynamics simulation and a modified Delaunay method.

A moderate amount of points are first distributed on a given surface. Next, by regarding the points as elastic bubbles with the same size and introducing the forces acting on bubbles, the motion control equations of bubbles are established. The equilibrium state of the bubble system is found by Verlet algorithm. Then, the Voronoi diagram on the surface is obtained by calculating the intersection between the surface and the three-dimensional (3D) Voronoi diagram of the centers of bubbles. Finally, a triangular mesh, Delaunay triangulation on the surface, is determined based on the dual change of the Voronoi diagram.

This method generates meshes on the surface directly, unlike mapping-based methods, avoiding the mapping distortion. Examples are given to demonstrate the successful execution of this method. The result also illustrates that this method is applicable to various surfaces in high automation level and resultant meshes are highly uniform and well-shaped.

Thus, this method provides the convenience for the geometry design of complex free-form grid structure.