The FEM is currently the most widely used method for the structure analysis. As the power of today's computers steadily increases the engineering applications of FEM cease to be limited to ``simple'' problems. The investigation of more and more complex 3D models is becoming state of the art of the engineering practice. Therefore tools for an automated and efficient mesh generation, including the discretization of 3D surfaces, are of high importance. Typical fields of the use of surface meshes are not only shell analysis or BEM, for example, but also the generation of unstructured tetrahedral grids of 3D domains based on the discretization of boundary surfaces at first. However, there are some requirements for a practical surface meshing. Firstly, the algorithm should be able to deal with a wide collection of surfaces of different complexity without user intervention. Secondly, generation of well shaped triangles accurately representing the surface geometry is desirable. And finally, the algorithm must exhibit a favourable computational complexity, ideally the linear one.

Generally, the surface discretization algorithms may be classified as direct or indirect. The direct methods [1,2] work directly on the surface in the physical space. The main disadvantage of these methods consists in complexity associated with the mathematical description of the surface and in the necessity to deal with 3D objects. However, their application to a certain class of surfaces make them very competitive. The indirect methods [3,4,5,6], which are currently the most common ones, utilize the bijective mapping between the surface and a planar parametric space. The parametric space is triangulated using a suitable planar mesh generator and the generated grid is then mapped back onto the original surface. However, taking the advantage of generating the mesh in 2D, which can be done quite efficiently, some other problems are to be faced. Only certain class of surfaces can be considered because of the prerequisite existence of the mapping. The mapping is generally not affine. This implies presence of element distortion and stretching when elements are being mapped between the real and the parametric spaces and requires a special treatment to deal with singular cases [7] introduced by degenerated or badly parameterized surfaces.

In the presented approach the direct meshing algorithm using the parametric space to enhance the efficiency is applied.

*Daniel Rypl
2005-12-03*