
Implementation in ALBERTA of an Automatic Tetrahedral Mesh Generator
Montenegro, R., J.M. Cascon, J.M. Escobar, E. Rodriguez and G. Montero
Proceedings, 15th International Meshing Roundtable, SpringerVerlag, pp.325338, September 1720 2006

IMR PROCEEDINGS

15th International Meshing Roundtable
Birmingham, Alabama, U.S.A.
September 1720, 2006
R. Montenegro, J.M. Escobar, E. Rodriguez and G. Montero
Institute for Intelligent Systems and Numerical Applications in Engineering,
University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, Las Palmas de G.C., Spain
rafa@dma.ulpgc.es, jescobar@dsc.ulpgc.es, barrera@dma.ulpgc.es, gustavo@dma.ulpgc.es
J.M. Cascon
Department of Mathematics, Faculty of Sciences, University of Salamanca, Spain
casbar@usal.es
Abstract
This paper introduces a new automatic tetrahedral mesh generator on the
adaptive finite element ALBERTA code. The procedure can be applied to 3
D domains with boundary surfaces which are projectable on faces of a cube.
The generalization of the mesh generator for complex domains which can be
split into cubes or hexahedra is straightforward. The domain surfaces must
be given as analytical or discrete functions. Although we have worked with
orthogonal and radial projections, any other onetoone projection may be
considered. The mesh generator starts from a coarse tetrahedral mesh which
is automatically obtained by the subdivision of each cube into six tetrahedra.
The main idea is to construct a sequence of nested meshes by refining only
the tetrahedra which have a face on the cube projection faces. The virtual
projection of external faces defines a triangulation on the domain boundary.
The 3D local refinement is carried out such that the approximation of domain
boundary surfaces verifies a given precision. Once this objective is achieved
reached, those nodes placed on the cube faces are projected on their corresponding true boundary surfaces, and inner nodes are relocated using a linear mapping. As the mesh topology is kept during node movement, poor quality
or even inverted elements could appear in the resulting mesh. For this reason, a mesh optimization procedure must be applied. Finally, the efficiency of the proposed technique is shown with several applications.
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