Verlet buffer for broad phase interaction detection in Discrete Element Method

The Extended Discrete Element Method (XDEM) is a novel and innovative numerical simulation technique that extends the dynamics of granular materials or particles as described through the classical discrete element method (DEM) by additional properties such as the thermodynamic state, stress/strain for each particle. Such DEM simulations used by industries to set up their experimental processes are complexes and heavy in computation time. Therefore, simulations have to be precise, efficient and fast in order to be able to process hundreds of millions of particles. To tackle this issue, such DEM simulations are usually parallelized with MPI. One of the most expensive computation parts of a DEM simulation is the collision detection of particles. It is classically divided into two steps: the broad phase and the narrow phase. The broad phase uses simplified bounding volumes to perform an approximated but fast collision detection. It returns a list of particle pairs that could interact. The narrow phase is applied to the result of the broad phase and returns the exact list of colliding particles. The goal of this research is to apply a Verlet buffer method to (X)DEM simulations regardless of which broad phase algorithm is used. We rely on the fact that such DEM simulations are temporal coherent: the neighborhood only changes slightly from the last time-step to the current time-step. We use the Verlet buffer method to extend the list of pairs returned by the broad phase by stretching the particles bounding volume with an extension range. This allows re-using the result of the broad phase for several time-steps before an update is required once again and thereby its reduce the number of times the broad phase is executed. We have implemented a condition based on particles displacements to ensure the validity of the broad phase: a new one is executed to update the list of colliding particles only when necessary. This guarantees identical results because approximations introduced in the broad phase by our approach are corrected in the narrow phase which is executed at every time-steps anyway. We perform an extensive study to evaluate the influence of the Verlet extension range on the performance of the execution in terms of computation time and memory consumption. We consider different test-cases, partitioners (ORB, Zoltan, METIS, SCOTCH, ...), broad phase algorithms (Link cell, Sweep and prune, ...) and grid configurations (fine, coarse), sequential and parallel (up to 280 cores). While a larger Verlet buffer increases the cost of the broad phase and narrow phase, it also allows skipping a significant number of broad phase execution (> 99 \%). As a consequence, our first results show that this approach can speeds up the total .execution time up to a factor of 5 for sequential executions, and up to a factor of 3 parallel executions on 280 cores while maintaining a reasonable memory consumption.

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