Automatic generation of triangular finite element meshes

International Journal for Numerical Methods in Engineering, 1980

This paper describes a method for the automatic triangulation of arbitrary multilateral plane domains. In addition, the method can be used in connection with that suggested by Zienkiewicz and Phillips' for the subdivision of curved-boundary domains. The method can be described as general fully automatic and computer oriented. A Fortran computer program has been prepared by the author. Output can be of interactive, graphical or alphanumerical form. The program has been applied to a number of cases. The resulting triangulations are always satisfactory, even when vigorous changes of mesh sizes are encountered.

International Journal for Numerical Methods in Engineering, 2002

Guaranteed-quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert's Delaunay refinement algorithm to twodimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries. We provide implementation details for two-dimensional boundary patches such as lines, circular arcs, cubic parametric curves, and interpolated splines. We present guaranteed-quality triangular meshes generated with curved boundaries, and propose solutions to some problems associated with the use of curved boundaries.

International Journal of Machine Learning and Computing

Objective of this paper is to propose a new semi-automatic, adaptive and optimized triangular mesh generation technique for any domain (including free formed curves). This new technique is found by merging the generalised equations which were proposed in previous works with Delaunay triangulation method. The new technique is demonstrated for several domains with various boundaries. Initial meshes are generated for these domains, which are later optimized manually by addition, removal or replacement of sampling points. Finalized meshes consist of triangular elements with aspect ratio of less than 2 and minimum skewness of more than 45 degrees.

Computational Geometry, 2009

Mesh generation in regions in Euclidean space is a central task in computational science, and especially for commonly used numerical methods for the solution of partial differential equations, e.g., finite element and finite volume methods. We focus on the uniform Delaunay triangulation of planar regions and, in particular, on how one selects the positions of the vertices of the triangulation. We discuss a recently developed method, based on the centroidal Voronoi tessellation (CVT) concept, for effecting such triangulations and present two algorithms, including one new one, for CVT-based grid generation. We also compare several methods, including CVT-based methods, for triangulating planar domains. To this end, we define several quantitative measures of the quality of uniform grids. We then generate triangulations of several planar regions, including some having complexities that are representative of what one may encounter in practice. We subject the resulting grids to visual and quantitative comparisons and conclude that all the methods considered produce high-quality uniform grids and that the CVT-based grids are at least as good as any of the others.

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.

International Journal for Numerical Methods in Engineering, 1983

The development and implementation of a comprehensive interactive computer package for the generation of finite element meshes for two-dimensional problems is described. The package, AGTHOM, minimizes the user defined input and attempts to maximize the flexibility for the user with regard to modifying the mesh. An important feature of AGTHOM is its independence of expensive graphics hardware by using approximate terminal plots. Versions are available in both extended BASIC and FORTRAN.

Computer Aided Geometric Design, 1998

This paper describes a new computational method for fully automated triangulation of the trimmed parametric surfaces used in finite element analysis. The method takes as input the domain geometry and a node-spacing function, and then generates a mesh, or a set of connected triangles, that satisfies basic requirements such as (1) precise control over node spacing or triangle size, (2) node placement that is compatible with domain boundaries, (3) generation of well-shaped triangles, and (4) continuous remeshing and local remeshing capabilities. The approach consists of two stages: placing initial nodes using recursive spatial subdivision, and relaxing the mesh by assuming the presence of proximity-based, repulsive/attractive internode forces and then performing dynamic simulation for a force-balancing configuration of nodes. In both stages, algorithms are developed in accordance with the observation that a pattern of tightly packed spheres mimics Voronoi polygons, from which well-shaped Delaunay triangles can be created by connecting the centers of the spheres.

2014

This paper describes a scheme for finite element mesh generation of a convex, non-convex polygon and multiply connected linear polygon. We first decompose the arbitrary linear polygon into simple sub regions in the shape of polygons.These subregions may be simple convex polygons or cracked polygons.We can divide a nonconvex polygon into convex polygons and cracked polygons We then decompose these polygons into simple sub regions in the shape of triangles. These simple regions are then triangulated to generate a fine mesh of triangular elements. We propose then an automatic triangular to quadrilateral conversion scheme. Each isolated triangle is split into three quadrilaterals according to the usual scheme, adding three vertices in the middle of the edges and a vertex at the barrycentre of the element. To preserve the mesh conformity a similar procedure is also applied to every triangle o f the domain to fully discretize the given convex polygonal domain into all quadrilaterals, thus...

IOSR Journals , 2019

This article includes an automatic mesh generation scheme foran arbitrary convex domain constituted by straight lines or curves employing lower or higher-order quadrilateral finite elements.First, we develop the general algorithm for hand p-version meshes, which require the information of sides of the domain and the choice of the order as well as the type of elements.The method also allows one to form the desired fine mesh by providing the number of refinements. Secondly, we develop the MATLAB program based on the algorithm that provides all the valuable and needful outputs of the nodal coordinates, relation between local and global nodes of the elements, and displays the desired meshes. Finally, we substantiate the suitability and efficiency of the scheme through the demonstration of several test cases of mesh generation. We firmly believe that the automatic hand p-version mesh generation scheme employing the quadrilateral elements will find immense application in the FEM solution procedure.

Engineering With Computers, 2004

To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains these meshes are characterized by having large curved elements over smooth portions of the domain and geometri- cally graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents