Automatic mesh generation using a modified Delaunay tessellation

Springer tracts in mechanical engineering, 2018

The quality of a mesh is crucially important if FEM solutions are to be deemed acceptable. Too coarse a mesh will lead to inaccurate FEM solutions. The finer the mesh, the better the convergence of the numerical solution. However, finer meshes tend to be expensive in terms of computing resources. The experienced user of FEM would have, over time, developed the skills required for creating just the right mesh for a given problem. Becoming proficient users of FEA, with the ability to create representative meshes of the idealized physical problem will serve as a motivation for this chapter. This chapter presents fundamentals of finite element meshes by defining nodes and elements, and the different types of elements. The chapter also describes the principle behind meshing algorithms in commercial FEM solvers. This chapter concludes by presenting reflections on quality of meshes and the type of meshes needed for different type of practical problems. It is expected that at the end of this chapter, readers should have developed a holistic understanding of the effects of meshes to the FEM process.

Computer Methods in Applied Mechanics and Engineering, 2010

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.

1994

The research reported in this dissertation was undertaken to investigate efficient computational methods of automatically generating three dimensional unstructured tetrahedral meshes. The work on two dimensional triangular unstructured grid generation by Lewis and Robinson [LeR76] is first examined, in which a recursive bisection technique of computational order nlog(n) was implemented. This technique is then extended to incorporate new methods of geometry input and the automatic handling of multiconnected regions. The method of two dimensional recursive mesh bisection is then further modified to incorporate an improved strategy for the selection of bisections. This enables an automatic nodal placement technique to be implemented in conjunction with the grid generator. The dissertation then investigates methods of generating triangular grids over parametric surfaces. This includes a new definition of surface Delaunay triangulation with the extension of grid improvement techniques to...

Encyclopedia of Computational Mechanics, 2004

In this chapter we are concerned with mesh generation methods and mesh adaptivity issues. Nowadays, many techniques are available to complete meshes of arbitrary domains for computational purposes. Planar, surface and volume meshing have been automated to a large extent. Over the last few years, meshing activities have focused on adaptive schemes where the features of a solution field must be accurately captured. To this end, meshing techniques must be revisited in order to be capable of completing high quality meshes conforming to these features. Error estimates are therefore used to analyze the solution field at a given stage and, based on the results and the information they yield, adapted meshes are created before computing the next stage of the solution field. A number of novel meshing issues must be addressed including how to construct a mesh adapted to what the error estimate prescribes, how to validate and construct high-order meshes, how to handle large size meshes, how to consider moving boundary problems, etc.

Citeseer

Computers & Mathematics with Applications, 1979

A method for automatic generation of triangnlar finite element meshes for starshaped domains is introduced. The mesh is simply obtained by inputting, besides the data defining the boundary of the domain, a positive integer parameter p for specification of the wished degree of refinement. It is proved that, for a very wide class of starshaped two dimensional domains, the following necessary condition for convergence of the finite element method is satisfied: There exists a strictly positive constant c, independent of p. such that: minm>c T m(T) vp, p=l,Z,... p(T) and h(T) being respectively the dieter of the inscribed circle and the largest edge of a generated triangle T.

We present a preliminary method to generate polyhedral meshes of general non-manifold domains. The method is based on computing the dual of a general tetrahedral mesh. The resulting mesh respects the topology of the domain to the same extent as the input mesh. If the input tetrahedral mesh is Delaunay and well-centered, the resulting mesh is a Voronoi mesh with planar faces. For general tetrahedral meshes, the resulting mesh is a polyhedral mesh with straight edges but possibly curved faces. The initial mesh generation phase is followed by a mesh untangling and quality improvement technique. We demonstrate the technique on some simple to moderately complex domains.

Journal of Computational Physics

We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute crosses. Instead, we compute a high order accurate guiding field using a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element method to solve a Laplace equation for each of the field variables using the open source code Nektar++. The spectral method provides spectral convergence and sub-element resolution of the fields. The DG approximation allows meshing of corners that are not multiples of π/2 in a discretization consistent manner, when needed. The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order separatrix integration method to avoid features like limit cycles. The result is a mesh with naturally curved quadrilateral elements that do not need to be curved a posteriori to eliminate invalid elements. The mesh generation procedure is implemented in the open source mesh generation program NekMesh.

Communications in Numerical Methods in Engineering, 1994

The paper demonstrates an approach to generate three-dimensional boundary-fitted computational meshes efficiently. One basic idea underlying the present study is that often similar geometries have to be meshed, and therefore an efficient mesh-adaption method, which allows adaptation of the topological mesh to the specific geometry, would be more efficient than generating all new meshes. On the other hand the mesh generation for Cartesian topologies has been shown to be a very simple task. It can be executed by connecting and removing brick elements to a basic cube. In connection with a so-called 'Macro Command Language', a high degree of automation can be reached when adapting topologically defined meshes to a surface. Furthermore, a high mesh quality has proved to be the key to good simulation results. During the mesh generation it is important to provide the possibility of modifying the mesh quality and also the mesh density at any time of the meshing process. Using this generation method the meshing time is reduced-e.g. a computational mesh for a two-valve cylinder head can be generated within a few hours.

Finite Elements in Analysis and Design, 2004