FULLY-AUTOMATIC MESH GENERATION FOR 3-D DOMAINS BASED UPON VOXEL SETS

Fully automatic three-dimensional mesh generation is an essential and increasingly crucial requirement for finite element solution of partia l derivative equations. The results of numerical simulation, more prec isely the convergence and accuracy of numerical solutions, closely dep ends on the quality of the underlying mesh. This work introduces a ful ly automatic finite element mesh algorithm with simplexes (tetrahedra) , adapted to complex geometries described by discrete data. This paper is divided in four sections: (a) brief introduction to discrete geome try is given, as well as the basic definition of the domain of interes t; (b) description of the voxel approach to tetrahedronization. The te trahedronization process uses a divide-and-conquer method, which provi des small elements on the boundary of the domain of interest. Voxels o f the domain are subdivided according to an automatic procedure, which preserves the topology. Specific rules were introduced which allow re ducing the number of voxel configurations to be treated, and consequen tly the computation time; (c) presentation of results and performances of the mesh algorithms. The resulting algorithm demonstrates an n log n growth rate with respect to the number of elements; (d) optimizatio n of the mesh generation process at hand of a 'finite-octree' type of explicit controlling space.