Update to: Approaches to the automatic generation and control of finite element meshes

Appl Mech Rev, ASME, Vol 49, Num 10, pp.S5-S14, October 1996

MESHING
RESEARCH
CORNER

Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy NY 12180-3590

Abstract
This paper updates the status of efforts on the development of automatic mesh generation techniques for general three-dimensional domains. The technical areas reviewed include: (i) issues associated with automatic mesh generation of CAD geometric models, (ii) local mesh modification procedures for improving mesh quality, (iii) advances in tetrahedral mesh generators, (iv) generation of anisotropic meshes, (v) hexahedral mesh generators, and (vi) implementation of automatic mesh generators on parallel computers.

Introduction
The development of techniques to improve the level of automation and reliability of finite element methods has been central to its continued growth and use. A 1988 Applied Mechanics Reviews article [47] discussed the status of methods for the automatic generation and control of finite element meshes. The current article is an update to that article which focuses exclusively on the advances in the techniques for the automatic three-dimensional mesh generation.

The emphasis in the 1988 article on three-dimensional mesh generation was on the basic approaches for the automatic generation of simplex (tetrahedron) elements. Since that time, there have been a substantial number of additional papers devoted to this topic (Refs [1, 2, 19, 48, 52] are three special issues of journals, a proceedings, and a book on the topic). Although the same basic approaches dominate tetrahedral mesh generation, there are several areas of development which have been critical to the advancement of these techniques. The first area, considered in Section 2, is the ability to generate meshes of three-dimensional models defined in CAD systems. The other areas are procedures to improve the quality of the meshes created (Section 3), improvements to the meshing algorithms (Section 4). and the ability to create anisotropic mesh gradations (Section 5).

A substantial change since the 1988 paper is the emphasis on the development of automatic hexahedral mesh generation schemes. The more constrained nature of hexahedral mesh generation has forced consideration of new technologies to account for these constraints. Section 6 indicates the current approaches to the development of automatic hexahedral mesh generators.

A final area of development of automatic mesh generation is the development of automatic mesh generation pro-area are summarized in Section 7.