The following goals are considered for further improvements of the developed mesh generation algorithms:

- In order to make the mesh generators widely applicable, the development of an interface to geometric modelling systems, including consistency checks and fault corrections, is highly desirable. This will also require an extension of the family of free-form entities manageable by the mesh generator.
- The quality of the meshes, especially those produced by the parallel mesh generator, still needs to be improved. The use of ``smart'' smoothing algorithms and optimization-based techniques combined with topological transformations is a good way to achieve this objective.
- To provide a more flexible interface with finite element analysis packages, it is desirable to enlarge the set of elements available in the mesh generators. This can be accomplished by appropriate conversions, either to quadrilateral and hexahedral elements (the sequential mesh generator) or to triangular and tetrahedral elements (the parallel mesh generator). Note, however, that in the case of the parallel mesh generator, further communication between the processors might be required to ensure the compatibility of the converted mesh on the interprocessor boundaries.
- The strategy of the tree building adopted in the parallel mesh generator can be replaced by the tree-based approach described in [152,153] subjected to some modifications to take into account the parametric nature of the tree structure. This will significantly enlarge the proportion of the number of pure hexahedral elements with respect to the total number of elements.
- Although the currently employed concept of the domain decomposition in the parallel mesh generator ensures a very good load balancing, the size of the interface between the subdomains is not taken into account. This usually does not cause problems because a relatively small amount of data is communicated between the processors during the mesh generation. However, this is not true for application analysis, in which a much bigger amount of data is typically transfered. It is therefore beneficial to improve the domain decomposition by use of more sophisticated algorithms or, more likely, by repartitioning the final mesh (preferably in parallel) using the original domain decomposition as the initial partitioning.
- In order to make the parallel mesh generator portable also to heterogeneous computing platforms (computer clusters), the construction of the domain decomposition must take into account performance of individual processors. This will require to enhance the dynamic load balancing mechanism in an appropriate way.

*Daniel Rypl
2005-12-07*