Construction of 4D Simplex SpaceTime Meshes for Local Bisection Schemes
Abstract
Adaptive mesh refinement is a key component of efficient unstructured spacetime finite element methods. Underlying any adaptive mesh refinement scheme is, of course, a method for local refinement of simplices. However, simplex bisection algorithms in dimension greater than three have strict mesh preconditions which can be hard to satisfy. We prove that certain fourdimensional simplex spacetime meshes can be handled with a relaxed precondition. Namely, we prove that if a tetrahedral mesh is 4colorable, then we can produce a 4D simplex mesh which always satisfies the bisection precondition. We also briefly discuss strategies to handle tetrahedral meshes which are not 4colorable.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.06258
 Bibcode:
 2021arXiv210806258L
 Keywords:

 Mathematics  Numerical Analysis;
 65M50;
 65N50;
 65M60
 EPrint:
 9 pages, 3 figures. Submitted to Proceedings of the 26th International Conference on Domain Decomposition