# Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction

## TL;DR

This paper presents a comprehensive framework for tetrahedral mesh improvement by integrating moving mesh smoothing, lazy flips, and RBF surface reconstruction, leading to enhanced mesh quality especially on curved surfaces.

## Contribution

It introduces a novel combination of smoothing, flipping, and surface reconstruction techniques for improved tetrahedral mesh quality.

## Key findings

- Achieves mesh quality improvements comparable or superior to previous methods.
- Effectively handles curved boundary surfaces with RBF reconstruction.
- Numerical tests validate the effectiveness of the combined approach.

## Abstract

Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones.