Optimization-based smoothing algorithm for triangle meshes over arbitrarily shaped domains

TL;DR

This paper presents a nonlinear optimization-based node relocation algorithm that improves triangle mesh quality over complex domains, suitable for mesh rezoning and initial mesh improvement in computational simulations.

Contribution

It introduces a damped Newton's method for mesh smoothing that handles arbitrary domain shapes and high curvature, enhancing mesh quality in complex geometries.

Findings

Effective for convex and non-convex domains

Handles high curvature regions well

Suitable for large deformation problems

Abstract

This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The local optimization scheme is a damped Newton's method in which the gradient and Hessian of the objective function are evaluated exactly. The algorithm has been developed in order to continuously rezone the mesh in arbitrary Lagrangian-Eulerian (ALE) methods for large deformation penetration problems, but it is also suitable for initial mesh improvement. Numerical examples highlight the capabilities of the algorithm.