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Two techniques for the discretization of 3D domains described in terms of a boundary representation using the free-form model entities have been presented.

The first one is based on the advancing front technique and it is designated exclusively for the processing in a sequential environment. The main effort has been directed towards the robustness and performance of the designed and implemented algorithms. The octree data structure is used to control the mesh gradation and to efficiently perform the spatial localization. The mesh generation over surfaces and regions uses the element removal concept with a high quality runtime node placement strategy. The feedback to the parametric space of model entities is used to efficiently resolve some local problems. The validity of the final mesh is verified in terms of the topological compatibility and geometrical similarity with the underlying model. Meshes of a various density and mesh size gradation consisting of well-shaped elements are produced. The presented approach exhibits a favourable computational complexity, which makes it very competitive in practical applications. The performance of the algorithm is demonstrated in numerous examples.

The second technique utilizes a tree-based approach and is designed for the parallel processing on memory distributed computing platforms. The parallelization strategy is based on the domain decomposition concept. Two levels of the domain decomposition have been considered - the model level and the model entity parametric tree level. The discretization is accomplished by application of templates fitted into the cells of a generalized parametric tree data structure built over individual model entities. The actual parallel computing scheme is based on the master and slaves parallel paradigm. Since a dynamic load balancing mechanism is employed, an even distribution of the work load among the processors is ensured. A very favourable ratio between the computation and communication has been achieved and a considerable speedup has been evidenced. This has been illustrated on several examples. The algorithm has been successfully implemented on two massively parallel computing platforms - IBM SP2 and Transtech Paramid. A penalty is paid to outweigh the overall simplicity of the presented approach. The quality of the final mesh depends not only on the mesh size variation but also on the model parameterization. The computational performance of the algorithm depends also on the complexity of model parameterization. Moreover, the restriction on the model topology results in some reduction of modelling flexibility.


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Daniel Rypl