An efficient three-dimensional mesh quality optimization method based on gradient-enhanced probabilistic model

Abstract

As a cornerstone of numerical simulations, mesh generation establishes the initial discrete model required for simulations, and the quality of the mesh significantly impacts the accuracy of the analysis results. However, the initial mesh elements generated by automated mesh generators often do not meet the stringent requirements of numerical simulations due to their poor mesh quality. This paper proposes an efficient three-dimensional tetrahedral mesh quality optimization method based on gradient-enhanced probabilistic model. The proposed method includes a preprocessing step that first solves for the steepest descent direction and optimal step length of nodes, allowing for the rapid optimization of early node movement and placement, subsequently completing the initial relocation of nodes. By establishing a probabilistic model for determining the optimal node positions and creating a memoryless stochastic process, the method ensures good convergence speed and accuracy as the node positions approach their optimal solutions. Therefore, the proposed method not only accelerates the overall optimization efficiency but also enhances mesh quality, achieving a balanced improvement between smoothing efficiency and mesh quality. This paper validates the proposed method on both three-dimensional tetrahedral meshes and surface meshes, and develops a parallel version, demonstrating the method's broad applicability and strong optimization capability. Through ablation study and comparisons with classic methods, it is shown that the proposed method outperforms traditional methods in both optimization efficiency and mesh quality. The GitHub repository link is: https://github.com/suyi-92/EMeshOptimization.git. And the input files can be found at: https://drive.google.com/drive/folders/1ziiWzmorx82NiVJPxWI0yoBrPpk_Lzrg?usp=sharing