An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

Kang Zhao,Xin Yin,Yufei Guo,You Wang,Yabang Ma

doi:10.4236/jamp.2020.811186

Abstract

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

Highlights

Mesh quality is import for the finite element method
In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper
Mesh quality improvement methods are often used in the mesh generation [3] [4]

Summary

Introduction

Mesh quality is import for the finite element method. Mesh with high quality can reduce the time to solution, and increase the solution accuracy [1] [2]. Geometrical optimization is called smoothing, since it improves the mesh by relocating mesh vertices, while preserving mesh topology. Optimization-based smoothing can avoid bad elements and obtain a higher quality mesh. With the increasing of the mesh nodes, the Hessian-based methods are more unsuitable for global smoothing. The gradient-based methods appear to be dominant in the global optimization-based smoothing. The conjugate gradient method requires more storage of intermediate results and more computational cost in a single iteration than the steepest descent method. Improving performance of the steepest descent method will facilitate the global optimization-based smoothing. We presented a method which works better than the steepest descent method, but with same storage and almost negligible added computational cost.

Steepest Descent Method and Its Drawbacks

Enhanced Steepest Descent Method

Numerical Experiments

Triangular Mesh Experiments

Tetrahedral Mesh Experiments

Conclusions