A geometric mesh smoothing algorithm related to damped oscillations

TL;DR

This paper presents a mesh smoothing algorithm based on a geometric transformation that models damped oscillations, offering a mathematically grounded and adaptive approach for improving mesh quality.

Contribution

It introduces a novel geometric transformation for mesh smoothing linked to a damped oscillation model, with adaptive parameters and demonstrated numerical effectiveness.

Findings

The transformation leads to a continuous damped oscillation model.

Adaptive parameters improve smoothing performance.

Numerical experiments show effective mesh quality enhancement.

Abstract

We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element transformation. In particular, the transformation gives rise directly to a continuous model given by a system of coupled damped oscillations. Derived from this physical model, adaptive parameters are introduced and their benefits presented. The second part discusses the mesh smoothing algorithm based on the element transformation and its numerical performance on example meshes.