An automatic strategy for adaptive tetrahedral mesh generation

Abstract

This paper introduces a new automatic strategy for adaptive tetrahedral mesh generation. A local refinement/derefinement algorithm for nested triangulations and a simultaneous untangling and smoothing procedure are the main involved techniques. The mesh generator is applied to 3-D complex domains whose boundaries are projectable on external faces of a meccano approximation composed of cuboids. The domain surfaces must be given by a mapping between meccano surfaces and object boundary. This mapping can be defined by analytical or discrete functions. At present, we have fixed mappings with orthogonal, cylindrical and radial projections, but any other one-to-one projection may be considered. The mesh generator starts from a coarse and valid hexahedral mesh that is obtained by an admissible subdivision of the meccano cuboids. The automatic subdivision of each hexahedron into six tetrahedra produces an initial tetrahedral mesh of the meccano approximation. The main idea is to construct a sequence of nested meshes by refining only those tetrahedra with a face on the meccano boundary. The virtual projection of meccano external faces defines a valid triangulation on the domain boundary. Then a 3-D local refinement/derefinement is carried out so that the approximation of domain surfaces verifies a given precision. Once this objective is reached, those nodes placed on the meccano boundary are really projected on their corresponding true boundary, and inner nodes are relocated using a suitable mapping. As the mesh topology is kept during node movement, poor quality or even inverted elements could appear in the resulting mesh; therefore, we finally apply a mesh optimization procedure. The efficiency of the proposed technique is shown with several applications to complex objects.