The data-driven computing paradigm initially introduced by Kirchdoerfer and 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 speedup of more than 106 with respect to exact k-d trees.
翻译:Kirchdoerfer和Ortiz(2016年)最初采用的由Kirchdoerfer和Ortiz(Ortiz)(数据驱动的计算模式)最初采用的数据驱动计算模式使固体机械中的有限要素能够直接从材料数据集中进行,而没有明确的材料模型。从计算努力的角度来看,最具挑战性的任务是在材料数据集中将材料点的可允许状态投射到最接近的状态。在本研究中,我们比较并开发了几种可能的数据结构,以解决最近的邻居问题。我们显示,近似邻居(ANN)算法可以比精确的搜索算法以几个数量级的速度加速材料数据搜索。近似值由数据驱动的迭代求解器结构提出,并经过调整后不会导致显著的解决方案准确性损失。我们用3D弹性测试案例的辅助,评估了非NN值算法在材料数据组大小方面的性能。我们显示,在短短短短短短几秒的执行时间内计算出最多10亿个材料数据点的单一处理器是可行的,在精确的K型树上速度超过106个。