Structure-preserving parametric finite element methods for anisotropic surface diffusion flow with minimal deformation formulation

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-04-16 DOI:10.1016/j.cpc.2025.109620

Yihang Guo, Meng Li

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引用次数: 0

Abstract

High mesh quality plays a crucial role in maintaining the stability of solutions in geometric flow problems. Duan and Li (2024) [20] applied the minimal deformation (MD) formulation to propose an artificial tangential velocity determined by harmonic mapping to improve mesh quality. In this work, we extend the method to anisotropic surface diffusion flows, which, similar to isotropic curvature flow, also preserves excellent mesh quality. Furthermore, developing a numerical algorithm for the flow with MD formulation that guarantees volume conservation and energy stability remains a challenging task. We, in this paper, successfully construct several structure-preserving algorithms, including first-order and high-order temporal discretization methods. Extensive numerical experiments show that our methods effectively preserve mesh quality for anisotropic surface diffusion flows, ensuring high-order temporal accuracy, volume conservation or/and energy stability.

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具有最小变形公式的各向异性表面扩散流的保结构参数有限元方法

在几何流动问题中，高网格质量对保持解的稳定性起着至关重要的作用。Duan和Li(2024)[20]应用最小变形（MD）公式提出了由谐波映射确定的人工切向速度，以提高网格质量。在这项工作中，我们将该方法扩展到各向异性表面扩散流，它与各向同性曲率流相似，也保持了良好的网格质量。此外，开发一种保证体积守恒和能量稳定的MD公式流的数值算法仍然是一项具有挑战性的任务。本文成功地构造了几种结构保持算法，包括一阶和高阶时间离散化方法。大量的数值实验表明，我们的方法有效地保持了各向异性表面扩散流的网格质量，确保了高阶时间精度，体积守恒或/和能量稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.