An efficient nonlocal integral method based on the octree algorithm

IF 5.3 1区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers and Geotechnics Pub Date : 2024-10-05 DOI:10.1016/j.compgeo.2024.106796
Dechun Lu , Yaning Zhang , Xin Zhou , Fanping Meng , Cancan Su , Xiuli Du
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Abstract

The nonlocal integral method typically requires a very high computing cost to search neighborhood integration points for calculating the nonlocal variable, which limits its application in large-scale problems. This paper proposes an efficient nonlocal integral method based on the octree algorithm, in which the integration point information is stored in the tree data structure to accelerate the search task. Firstly, the fundamental principles and implementation details of using the octree algorithm to search neighborhood integration points are described in detail. Subsequently, a Mohr-Coulomb nonlocal damage plastic model is presented as the application object of the proposed method. The model is implemented further in the ABAQUS using the octree-based nonlocal method and the return mapping algorithm enhanced by a line search method. Finally, two typical boundary value problems are simulated to verify the effectiveness and to assess the computational efficiency of the proposed nonlocal method. For the given test environment, the octree algorithm can achieve up to 100 times speedup at the integration point level compared to the traversal algorithm, and the developed efficient nonlocal method can achieve up to 7.9 times speedup at the boundary value problem level compared to the original nonlocal method.
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基于八叉树算法的高效非局部积分法
非局部积分法通常需要很高的计算成本来搜索邻域积分点以计算非局部变量,这限制了它在大规模问题中的应用。本文提出了一种基于八叉树算法的高效非局部积分方法,将积分点信息存储在树形数据结构中,以加速搜索任务。首先,详细介绍了使用八叉树算法搜索邻域积分点的基本原理和实现细节。随后,介绍了一个 Mohr-Coulomb 非局部损伤塑性模型作为所提方法的应用对象。利用基于八叉树的非局部方法和通过线搜索方法增强的返回映射算法,在 ABAQUS 中进一步实现了该模型。最后,模拟了两个典型的边界值问题,以验证所提出的非局部方法的有效性并评估其计算效率。在给定的测试环境下,与遍历算法相比,八叉树算法在积分点层面的速度最多可提高 100 倍;与原始非局部方法相比,所开发的高效非局部方法在边界值问题层面的速度最多可提高 7.9 倍。
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来源期刊
Computers and Geotechnics
Computers and Geotechnics 地学-地球科学综合
CiteScore
9.10
自引率
15.10%
发文量
438
审稿时长
45 days
期刊介绍: The use of computers is firmly established in geotechnical engineering and continues to grow rapidly in both engineering practice and academe. The development of advanced numerical techniques and constitutive modeling, in conjunction with rapid developments in computer hardware, enables problems to be tackled that were unthinkable even a few years ago. Computers and Geotechnics provides an up-to-date reference for engineers and researchers engaged in computer aided analysis and research in geotechnical engineering. The journal is intended for an expeditious dissemination of advanced computer applications across a broad range of geotechnical topics. Contributions on advances in numerical algorithms, computer implementation of new constitutive models and probabilistic methods are especially encouraged.
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