Abstract
SummaryThe simulation of vast numbers of rigid bodies of non‐analytical shapes and of tremendously different sizes that collide with each other is computationally challenging. A bottleneck is the identification of all particle contact points per time step. We propose a tree‐based multilevel meta data structure to administer the particles. The data structure plus a purpose‐made tree traversal identifying the contact points introduce concurrency to the particle comparisons, whilst they keep the absolute number of particle‐to‐particle comparisons low. Furthermore, a novel adaptivity criterion allows explicit time stepping to work with comparably large time steps. It optimises both toward low algorithmic complexity per time step and low numbers of time steps. We study three different parallelisation strategies exploiting our traversal's concurrency. The fusion of two of them yields promising speedups once we rely on maximally asynchronous task‐based realisations. Our work shows that new computer architecture can push the boundary of rigid particle computability, yet if and only if the right data structures and data processing schemes are chosen.
Highlights
Granular flows are subject of computational studies in many application fields such as soil assessment in agriculture, powder mixture in engineering or the stability analysis of rocky slopes, and ice sheets
Our dynamically adaptive approach based upon spacetrees serves this purpose whilst a data movement minimisation, ie, we strive for single-touch algorithms where each particle data is read from the main memory per time step only once, implies that particle data is to be exchanged only once through message passing if the present strategies are translated into a shared memory world.In this context, we emphasise that our realisation relies on Peano[32] for which excellent memory behaviour is validated.[19]
Some regions of the tree already might have been subject of collision checks, whilst other regions have not been traversed yet.As the different aspects particle bookkeeping and Discrete Element Method (DEM) physics have differing concurrency characteristics, we found it advantageous to realise the position updates through the descends within the tree, whilst we embed the actual physics into the traversal backtracking
Summary
The simulation of vast numbers of rigid bodies of non-analytical shapes and of tremendously different sizes that collide with each other is computationally challenging. A bottleneck is the identification of all particle contact points per time step. We propose a tree-based multilevel meta data structure to administer the particles. The data structure plus a purpose-made tree traversal identifying the contact points introduce concurrency to the particle comparisons, whilst they keep the absolute number of particle-to-particle comparisons low. A novel adaptivity criterion allows explicit time stepping to work with comparably large time steps. It optimises both toward low algorithmic complexity per time step and low numbers of time steps. Our work shows that new computer architecture can push the boundary of rigid particle computability, yet if and only if the right data structures and data processing schemes are chosen. KEYWORDS computational geometry, discrete element method, dynamically adaptive cartesian grids, shared memory parallelisation, vectorisation
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