Mesh adaptation algorithm

Goals

1. Mesh modifications in agreement to a size map
2. Generation of equilateral elements (possibly in a given metric)

Input data

A mesh and, eventually, nodal values prescribing the wanted edge sizes at each node (i.e. a size map).

Steps

1. Surface analysis
2. Rough surface mesh modifications for a good ‘samplig’ of the surface:
   • split too long edges (using patterns)
   • collapse too short edges
   • swap too bad elements
3. Size map construction:
   • intersection of the geometric (defined on boundaries) and user-prescribed (defined on the entire mesh) size maps
   • size map gradation with respect to the prescribed gradation parameter hgrad:
4. Fine surface mesh modifications with respect to the size map:
   • split (using patterns along the surface, and a Delaunay kernel inside the volume) or collape edges
   • swap edges belonging to too bad elements
   • vertex relocation to improve the quality