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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A comparison of different methods for calculating tangent-stiffness matrices in a massively parallel computational peridynamics code
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A comparison of different methods for calculating tangent-stiffness matrices in a massively parallel computational peridynamics code

机译：大规模并行计算周动力学代码中计算切线刚度矩阵的不同方法的比较

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摘要

In order to maintain the quadratic convergence properties of Newton's method in quasi-static nonlinear analysis of solid structures it is crucial to obtain accurate, algorithmically consistent tangent-stiffness matrices. A goal of the study described in this paper was to establish the suitability of an underexplored method for numerical computation of tangent-stiffness operators, referred to as "complex-step", and compare the method with other techniques for numerical derivative calculation: automatic differentiation, forward finite difference, and central finite difference. The complex-step method was implemented in a massively parallel computational peridynamics code for the purpose of this comparison. The methods were compared through profiling of the code for accuracy, speed, efficiency, and parallel scalability. This research provides data that can serve as practical guide for codedevelopers and analysts faced with choosing which method best suits the needs of their application code. Additionally, motivated by the reproducible research movement, all of the code, examples, and workflow to regenerate the data and figures in this paper are provided as open source.
机译：为了在实体结构的准静态非线性分析中保持牛顿方法的二次收敛性，获取精确的，算法上一致的切线刚度矩阵至关重要。本文所述研究的目的是要建立一种适用于正切刚度算子数值计算的未开发方法的适用性，称为“复杂步骤”，并将该方法与其他用于数值导数计算的技术进行比较：自动微分，正向有限差分和中心有限差分。为了进行比较，在大规模并行计算周动力学代码中实现了复杂步骤方法。通过对代码进行概要分析来比较这些方法的准确性，速度，效率和并行可伸缩性。这项研究提供的数据可以为代码开发人员和分析人员提供实用指南，以帮助他们选择最适合其应用程序代码需求的方法。此外，受可重现的研究运动的推动，本文中的所有代码，示例和工作流程（用于重新生成本文中的数据和图形）均以开放源代码形式提供。

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