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The finite element method is currently the most widely used method for the structural analysis. As the power of the computing systems is steadily increasing the engineering applications of FEM cease to be limited to ``simple'' problems. The investigation of more and more complex 3D problems is becoming state of the art of the engineering practice. Therefore tools for automated and effective surface and volume discretization are of high importance. The algorithms for automatic mesh generation have been investigated for last two decades and significant progress in the area of their performance, reliability and versatility has been achieved. Nevertheless, some issues, as generation of all-hexahedral meshes for general 3D geometries, are still unresolved and subjected to further research. A lot of research is also focused on parallelization of existing and development of new parallel algorithms for mesh generation. This effort is driven not only by the need to reduce the computational time required for mesh generation but also by the need to overcome problems with limited resources (memory, disk space) of computing systems.

A lot of research so far has been concentrated on different triangulation schemes advantage of which lies in the fact that simplex elements (triangles and tetrahedras) are most suitable to discretize domains of arbitrary complexity. The following approaches become the most widespread for generation of triangular and tetrahedral meshes -- tree based techniques, advancing front technique and Delaunay triangulation. The quadrilateral and hexahedral elements, on the other hand, are most popular among the analysts because of their favourable properties from the computational analysis point of view. However, generation of these types of elements is much more complicated and usually also computationally demanding. The most frequently used approaches for generation of quadrilateral and hexahedral meshes are tree based techniques, paving and plastering, medial axes based subdivision and mapping.

In the following, two discretization techniques will be presented. Firstly the advancing front technique for sequential generation of high quality triangular and tetrahedral meshes will be described and its computational complexity will be discussed. And secondly, tree based approach for parallel discretization will be outlined and the parallel performance presented.

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Daniel Rypl