Efficient data structures for model-free data-driven computational mechanics
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.
© 2021 Published by Elsevier B.V. Received 30 November 2020, Revised 27 March 2021, Accepted 7 April 2021, Available online 6 May 2021. MO gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG), Germany through the Sonderforschungsbereich 1060 "The mathematics of emergent effects" and the Mercator fellowhip within the collaborative research centre SFB/TRR87. SR and RE gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG), Germany through the project RE 1057/40-2 "Model order reduction in space and parameter dimension — towards damage-based modeling of polymorphic uncertainty in the context of robustness and reliability" within the priority program SPP 1886 "Polymorphic uncertainty modelling for the numerical design of structures". Finally, all authors acknowledge the financial support of the DFG, Germany and French Agence Nationale de la Recherche (ANR) through the project "Direct Data-Driven Computational Mechanics for Anelastic Material Behaviours" (project numbers: ANR-19-CE46-0012-01, RE 1057/47-1) within the French-German Collaboration for Joint Projects in Natural, Life and Engineering (NLE) Sciences. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Submitted - 2012.00357.pdf