Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes

TL;DR

This paper introduces a systematic mathematical framework for global optimization-based smoothing methods tailored for mixed-volume meshes, enhancing mesh quality and computational efficiency.

Contribution

It develops a formal framework and explicit algorithms for global optimization-based smoothing of mixed-volume meshes, advancing beyond heuristic approaches.

Findings

Identifies efficient smoothing algorithms for specific algebraic mesh quality measures.

Provides explicit constructions of potentially useful smoothing algorithms.

Enhances mesh quality and computational efficiency for mixed-volume meshes.

Abstract

Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a systematic approach to global optimization-based versions of such methods for mixed volume meshes. In particular, we identify efficient smoothing algorithms for certain algebraic mesh quality measures. We also provide explicit constructions of potentially useful smoothing algorithms.