Efficient data structures for model-free data-driven computational mechanics

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 model. From a computational effort point of view, the most challenging task is projection admissible states at points onto their closest set. In this study, we compare develop several possible structures for solving nearest-neighbor problem. We show that approximate (ANN) algorithms can accelerate searches orders magnitude relative exact searching algorithms. approximations are suggested by--and adapted to--the structure iterative solver result no significant loss solution accuracy. assess performance ANN algorithm with respect set size aid 3D elasticity test case. on single processor up one billion feasible within few seconds execution time speedup more than 106 k-d trees.