On Rigorous Conditions for Automatically Generating Finite Element Meshes

Product Modeling for Computer-Aided Design and Manufacturing, Elsevier, pp.267-281, 1991

MESHING
RESEARCH
CORNER

SCOREC Report #32-1990
Scientific Computation Research Center

GE Corporate Research & Development Schenectady, New York 12301
Rensselaer Polytechnic Institute Troy, New York 12l50-359O

Abstract
Generating finite element meshes or computational grids from a geometric approximation is a key step in the engineering design process. Until now, exactly what constitutes a valid mesh has been informally stated. However, with the advent of automatic mesh generation systems, it is imperitive that a more formal definition is available.

In this paper we describe rigorous conditions for valid computational meshes. In particular,. we describe the conditions required for a mesh to be topologicaily and geometrically compatible with the original geometric representation. The paper presents definitions of topological and geometric compatibility, as well as necessary conditions for satisfying these properties. In addition, we present algorithms for detecting and resolving violations of these conditions.