Construction of 4D Simplex Space-Time Meshes for Local Bisection Schemes
Abstract
Adaptive mesh refinement is a key component of efficient unstructured space-time 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 four-dimensional simplex space-time meshes can be handled with a relaxed precondition. Namely, we prove that if a tetrahedral mesh is 4-colorable, 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 4-colorable.
Keywords
Cite
@article{arxiv.2108.06258,
title = {Construction of 4D Simplex Space-Time Meshes for Local Bisection Schemes},
author = {David Lenz},
journal= {arXiv preprint arXiv:2108.06258},
year = {2021}
}
Comments
9 pages, 3 figures. Submitted to Proceedings of the 26th International Conference on Domain Decomposition