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Efficient data structures for model-free data-driven computational mechanics
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-05-06 , DOI: 10.1016/j.cma.2021.113855
Robert Eggersmann , Laurent Stainier , Michael Ortiz , Stefanie Reese

The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data set. In this study, we compare and develop several possible data structures for solving the nearest-neighbor problem. We show that approximate nearest-neighbor (ANN) algorithms can accelerate material data searches by several orders of magnitude relative to exact searching algorithms. The approximations are suggested by—and adapted to—the structure of the data-driven iterative solver and result in no significant loss of solution accuracy. We assess the performance of the ANN algorithm with respect to material data set size with the aid of a 3D elasticity test case. We show that computations on a single processor with up to one billion material data points are feasible within a few seconds execution time with a speed up of more than 106 with respect to exact k-d trees.



中文翻译:

高效的数据结构,适用于无模型的数据驱动计算机制

Kirchdoerfer&Ortiz(2016)最初引入的数据驱动计算范例使实体力学中的有限元计算可以直接从材料数据集中执行,而无需使用明确的材料模型。从计算工作的角度来看,最具挑战性的任务是将材料点上的可允许状态投影到材料数据集中最接近的状态。在这项研究中,我们比较并开发了几种可能的数据结构来解决最近邻问题。我们表明,相对于精确搜索算法,近似最近邻(ANN)算法可以将材料数据搜索加速几个数量级。这些近似值是由数据驱动的迭代求解器的结构建议的,并且适合于该结构,并且不会导致求解精度的重大损失。我们借助3D弹性测试用例,针对材料数据集大小评估了ANN算法的性能。我们证明了在具有多达十亿个材料数据点的单个处理器上进行的计算在几秒钟的执行时间内是可行的,并且速度可超过1个06 关于确切 ķ-d树。

更新日期:2021-05-06
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