Bayesian calibration of GPU–based DEM meso-mechanics Part I: Parallelization of RVEs

Calibration of Discrete Element Method (DEM) parameters is essential for modeling geotechnical applications. This task can, however, be extremely tedious or sometimes even impossible to undertake. This is largely due to two issues namely: (1) a large sample size of DEM simulations and number of sampling iterations are necessary to accurately infer the probability distribution of a model over a large parameter space and (2) DEM is computationally intractable compared to other numerical methods. In the scope of reducing the number of sampling iterations, automatic calibration techniques are available to extract and make use of the hidden contact mesostructure correlations through adaptive sampling. Coincidentally, to improve computational speed, significant advances toward Graphics Processor Unit (GPU) based DEM algorithms have been achieved over the past years on particle parallelism. Nevertheless, the problem remains that DEM simulations are serialized during the calibration processes. While the companion paper addresses parameter calibration, this study presents a novel algorithm to parallelize independent simulations within a sample set. The selected system is the Representative Volume Element (RVE) which is widely used in geotechnics for solving soil response in the static regime. The algorithm includes the following key features: (1) simulation level parallelism of non-interacting RVEs through highly efficient hierarchical memory groups and access patterns (2) a low latency and memory-efficient implementation of deformable periodic boundary conditions (PBC) which uses lookup tables and bitmasks (3) modified Uniform Grid and Bounding Volume Hierarchy (BVH) contact detection algorithms which partitions the RVE index into the hashing keys. The drained DEM triaxial compression is used to validate the algorithm on dry graded quartz. Three performance degrading factors for the calibration processes are considered: (1) the number of particles per RVE (2) calibration sample size and (3) sequential launch time per calibration step. This algorithm shows a factor of about 9.8 times speedup when parallelizing 100 DEM RVEs in one batch.