An efficient isogeometric topology optimization based on the adaptive damped geometric multigrid method

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software Pub Date : 2024-07-13 DOI:10.1016/j.advengsoft.2024.103712

Shijie Luo , Feng Yang , Yingjun Wang

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引用次数: 0

Abstract

The efficiency of solving sparse linear equations in isogeometric topology optimization (ITO) can be improved by the multigrid algorithm due to its excellent convergence rate. However, its convergence rate heavily relies on the smoother's parameters. To address this problem, a new h-refinement multigrid conjugate gradient method with adaptive damped Jacobi (ADJ-hMGCG) has been developed. By analyzing the eigenvalues of the stiffness matrix, the damping coefficient of the smoother that achieves the fastest convergence rate has been determined. Due to the significant computational resources required to compute eigenvalues in the stiffness matrix, this paper also presents a preconditioned power method based on ITO and geometric multigrid characteristics to improve the efficiency of adaptive damping solutions. The results of 2D and 3D numerical examples show that the ADJ-hMGCG method successfully improves the solution speed and robustness while meeting the accuracy requirements of topology optimization, and the total computational cost can be reduced by up to 59 % compared to traditional solvers for large-scale problems.

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基于自适应阻尼几何多网格法的高效等几何拓扑优化方法

多网格算法具有出色的收敛速度，可以提高等距拓扑优化（ITO）中稀疏线性方程的求解效率。然而，它的收敛速度在很大程度上依赖于平滑器的参数。为了解决这个问题，我们开发了一种新的具有自适应阻尼雅各比的 h- 精化多网格共轭梯度法（ADJ-hMGCG）。通过分析刚度矩阵的特征值，确定了实现最快收敛速度的平滑器阻尼系数。由于计算刚度矩阵中的特征值需要大量的计算资源，本文还提出了一种基于 ITO 和几何多网格特性的预条件幂方法，以提高自适应阻尼解的效率。二维和三维数值实例的结果表明，ADJ-hMGCG 方法在满足拓扑优化精度要求的同时，成功地提高了求解速度和鲁棒性，与大规模问题的传统求解器相比，总计算成本最多可降低 59%。

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

Advances in Engineering Software 工程技术-计算机：跨学科应用

CiteScore

7.70

自引率

4.20%

发文量

169

审稿时长

37 days

期刊介绍： The objective of this journal is to communicate recent and projected advances in computer-based engineering techniques. The fields covered include mechanical, aerospace, civil and environmental engineering, with an emphasis on research and development leading to practical problem-solving. The scope of the journal includes: • Innovative computational strategies and numerical algorithms for large-scale engineering problems • Analysis and simulation techniques and systems • Model and mesh generation • Control of the accuracy, stability and efficiency of computational process • Exploitation of new computing environments (eg distributed hetergeneous and collaborative computing) • Advanced visualization techniques, virtual environments and prototyping • Applications of AI, knowledge-based systems, computational intelligence, including fuzzy logic, neural networks and evolutionary computations • Application of object-oriented technology to engineering problems • Intelligent human computer interfaces • Design automation, multidisciplinary design and optimization • CAD, CAE and integrated process and product development systems • Quality and reliability.