3D mesh adaptation. Optimization of tetrahedral meshes by advancing front technique

Abstract

The objective of the paper is to present an automatic mesh generator which builds a mesh which respects the element densities prescribed as a result of an error sensitivity analysis. The desired new mesh is fully characterized by the distribution of the refinement levels on the initial mesh. Therefore, the most important criterion in the choice of a mesh generator comes from the ability to produce a mesh with imposed density while meeting ‘acceptable’ shape quality requirements. In this spirit, a new method for tetrahedron mesh generation and optimization with respect to both a shape and a size criterion is presented. The advancing front technique is used to mesh the whole volume. Then, optimization procedures make astute local use of the algorithm used to mesh the complete model. The process is iterative. The corresponding method involves extracting sub-volumes or shells from the tetrahedron mesh volume, which are then remeshed by an advancing front technique to improve their quality. The sub-volumes are constructed by determining the set of tetrahedra which touch the same node, edge or face. Local transformations are extended to non-convex sub-regions which gives a higher quality mesh. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method.