8.2 Outlook

Although important research questions have been answered (cf. Section 8.1), additional research is required to further optimize the utilization of symmetries and similarities for mesh generation processes. Some potential research suggestions are given in the following.

The theory presented in Appendix A is a solid background for this work. However, the sets used for mesh elements and geometries are restricted to linear sets due to the IPC property (cf. Definition A.28), which is required by the boundary patch partition. Some mesh elements used in the literature, e.g., hexahedrons, might not be linear which will exclude them from the templated approaches in this work. Therefore, further research should investigate, how the geometry space $\mathfrak{L}^n$ can be abstracted to include more general sets.

This work primarily focuses on the theory and the generation of templated meshes. However, there are a lot of mesh adaptation algorithms which have only been briefly discussed. A more-in-depth investigation of these algorithms would enable an increase of the mesh adaptation possibilities for templated meshes. Additionally, special cases of these algorithms for symmetric objects would decrease instance interface issues or issues with irregular instance graphs.

A combined pipeline of automatic symmetry and similarity detection and mesh generation of symmetric objects has briefly been covered in previous work [48]. A more in-depth study of a combined approach would increase the usability of templated meshes and their generation. Furthermore, future research should investigate automatic decomposition of geometries with similarities or symmetries for templated mesh generation.

As of yet, investigations on parallelization of the algorithms involved in templated mesh generation have been conducted. In the light of stagnating single-core performance and ever-growing core-counts of modern multi-core processors, future research should cover this research gap to further improve runtime performance and to make efficient use of modern computing platforms.