This approach is computationally expensive and introduces the complexities of mapping solution fields from one mesh to another. Such local operations can be performed efficiently and can effectively address the issues associated with the transfer of solution information. The local retriangulation tools improve the quality of the elements involved without the need to perform the same degree of over-refinement other procedures may require. This is important since the amount of over-refinement caused by procedures with implicit assurance of element quality maintenance can be very large. The retriangulation procedures are also critical for allowing the proper application of refinement of elements on curved domain boundaries.
Triangulations can also be over-refined when triangulation quality is degrading.
This is an important addition since the more straight-forward procedures, including all those with a priori control of element shapes, are limited to domains with planar faces. Since the local mesh modification procedures are invoked directly from within the analysis procedures, and the analysis procedures for large problems are carried out in parallel, it is critical that these procedures run in parallel and scale well. All aspects of this adaptation procedure have therefore been parallelized, and show good speed-ups on large meshes.