Automatic Mesh Generation: Application to Finite Element Methods

, Wiley, pp.333, 1991

MESHING
RESEARCH
CORNER

Director of Research at INRIA, France

Abstract
The finite element method is used more and more for numerical simulation of a large variety of physical problems. The first step consists of constructing an appropriate mesh of the domain under consideration. This is an important part of this simulation (in particular w.r.t. time) and proves to be delicate when complex geometries are considered. Furthermore, the quality of the numerical results is strongly linked to the quality of the corresponding mesh.

This book intends to investigate these mesh generation problems and, in particular the following four aspects:

1. The definition of the set of information composing a mesh in order to apply the finite element method;
2. The development of a general methodology to conceive a mesh. In this respect a top-down analysis of the problem and associated bottom-up generation will be introduced;
3. The description of mesh generation algorithms for two-dimensional and three- dimensional geometries;
4. The presentation of usual transformation methods and their numerous applications.

Each section is illustrated by various examples and figures corresponding to the two-dimensional and three-dimensional cases. INRIA, in particular with regard to the finite element code Modulej, offers a number of software packages dedicated to mesh creation and manipulation; most of the examples given in this book are a result of these codes.