Overview

Mesh generation techniques are widely employed in various engineering fields including those related to physical models described by partial differential equations (PDE). Numerical simulations of such models are intensively used for design, dimensioning and validation purposes. One of the most frequently used methods, among many others, is the finite element method (FEM). In this method, a continuous problem (the initial PDE model) is replaced by a discrete problem that can actually be computed thanks to the power of currently available computers. The solution to this discrete problem is an approximate solution to the initial problem whose accuracy is based on the various choices that were made in the numerical process.

The first step (in terms of actual computation) of such a simulation involves constructing a mesh of the computational domain (i.e., the domain where the physical phenomenon under interest occurs and evolves) so as to replace the continuous region by means of a finite union of (geometrically simple and bounded) elements such as triangles, quadrilaterals, tetrahedra, pentahedra, prisms, hexahedra, etc., based on the spatial dimension of the domain. For this reason, mesh construction is an essential pre-requisite for any numerical simulation of a PDE problem. Moreover, mesh construction could be seen as a bottleneck for a numerical process in the sense that a failure in this mesh construction step jeopardizes any subsequent numerical simulation.

Mesh construction in general and more precisely for numerical simulation purposes involves several different fields and domains. These include (classical) geometry, so-called computational geometry...