Work

Construction of 4D Simplex Space-Time Meshes for Local Bisection Schemes

Year: 2021

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2108.06258

Author: Lenz, David

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, Office of Science, National Nuclear Security Administration, Advanced Scientific Computing Research

Awards: G1193633358, G1796307089, G2287611682, G262962599, G3318903820, G3886122786, G498139845, G5398989114, G5692331544, G6848031779, G6918803902, G878601127, G969889393, G993149817

OpenAlex ID: W4324392579

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