Which algorithms for conventional meshes also work for templated meshes? Which modifications are required for these algorithms?

Two general mesh generation algorithms for templated meshes have been developed and presented in Section 5.1:

(i)

An algorithm which generates volumetric meshes for each template independently and then adapts the instance interfaces to ensure conformity (cf. Algorithms 5.1 to 5.4).

(ii)

An algorithm which at first generates a conforming surface mesh for all templates and then uses these surface mesh to generate volumetric mesh templates (cf. Algorithms 5.5 to 5.7).

Both algorithms utilize conventional mesh generation algorithms for surface and volumetric mesh generation. Thus, existing implementations of mesh generation algorithms can be re-used for templated mesh generation algorithms. Although the second algorithm requires the boundary patch partition and thus is more complicated, it is numerically more stable and generates meshes of higher quality.

Issues and modifications for mesh adaptation algorithms have been discussed and presented in Section 5.2. Mesh adaptation algorithms do not require any modification as long as they work on interior elements of a mesh template. If an algorithm alters the surface of a mesh template, the conformity of the structure instance has to be preserved (cf. Lemma 4.2). Thus, mesh adaptation algorithms have less freedom in modifying elements on the surface of mesh templates. In some cases, certain modifications are even forbidden.