Tet Meshing: Construction, Optimization, And Adaptation

Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.133-141, October 1999

MESHING
RESEARCH
CORNER

Abstract
The Finite Element Method (among others) is a popular way for the numerical solution of a large variety of physical problems(PDE's problems) in various engineering applications. The crucial requisite of this modeling method is the construction of a suitable mesh which further serves as a spatial support for the governing equations of the problem to be solved.

Depending on the complexity of the geometry to be modeled and on the space dimension, there exist various mesh generation methods. Apart from some specific geometries, unstructured mesh generation methods proved to be a solution capable to handle arbitrarily shaped domains. In general, such methods produce triangles (in two dimensions) and tetrahedra (in three dimensions). Most techniques currently in use for this purpose fit into one of the three main types: octree based, advancing-front based or Delaunay like techniques

In this paper we briefly describe the two first types of methods and we focus on the third one. Hence, Delaunay triangulation issues are recalled and the way in which the corresponding procedures apply for mesh construction purposes is discussed. Various aspects are included in the discussion, some coming from the Computational Geometry, some more clearly related to a Finite Element context, some regarding the numerical troubles that necessarily arise in the computer implementation of any mesh generation procedure.

In addition to the discussion about tet mesh generation, ideas are given about mesh optimization and mesh adaptation in this context.

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