Simultaneous surface and tetrahedron mesh adaptation using mesh-free techniques

• Published in: International journal for numerical methods in engineering Vol. 57; no. 3; pp. 371 - 389
• Main Authors: Rassineux, A., Breitkopf, P., Villon, P.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 21.05.2003; Wiley
• Subjects: Adaptation; Computer graphics; Criteria; diffuse approximation; Engineering Sciences; Finite element method; Interpolation; Mathematical models; mesh adaptation; mesh refinement; mesh-free methods; Meshless methods; tetrahedral meshes; Tetrahedrons; unstructured meshes; tetrahedral meshes; mesh refinement; mesh adaptation; mesh-free methods; diffuse approximation; unstructured meshes
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.681

We present a method to adapt a tetrahedron mesh together with a surface mesh with respect to a size criterion. The originality of our work lies in the fact that both surface and tetrahedron mesh adaptation are carried out simultaneously and that no CAD is required to adapt the surface mesh. The adaptation procedure consists of splitting or removing interior and surface edges which violate a given size criterion. The enrichment process is based on a bisection technique. In order to guarantee mesh conformity during the refinement process, all possible remeshing configurations of tetrahedra have been examined. Once the tetrahedron mesh has been adapted, surface nodes are projected on a geometrical model. The building of a surface model from discrete data has already been presented in this journal. The method is based on a mesh‐free technique called Hermite Diffuse Interpolation. Surface and volume mesh optimization procedures are carried out during the adaptation and at the end of the process to enhance the mesh. Copyright © 2003 John Wiley & Sons, Ltd.