A Weak Compatibility Condition for Newest Vertex Bisection in any dimension

TL;DR

This paper introduces a weak compatibility condition for the Newest Vertex Bisection algorithm applicable in any dimension, ensuring algorithm termination and providing an efficient renumbering method to meet this condition.

Contribution

It defines a new weak compatibility condition for simplex grids, proves its effectiveness for algorithm termination, and offers an O(n) renumbering algorithm to achieve it.

Findings

The weak compatibility condition guarantees successful termination of the bisection algorithm.

The O(n) renumbering algorithm efficiently transforms grids to meet the condition.

Experiments show the geometric quality of meshes and their proximity to standard compatibility.

Abstract

We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n) algorithm that renumbers any simplex grid to fulfil this condition. Furthermore we conduct experiments to estimate the distance to the standard compatibility and also the geometric quality of the produced meshes.