Parallel SPH modeling using dynamic domain decomposition and load balancing displacement of Voronoi subdomains

Abstract

A highly adaptive load balancing algorithm for parallel simulations using particle methods, such as molecular dynamics and smoothed particle hydrodynamics (SPH), is developed. Our algorithm is based on the dynamic spatial decomposition of simulated material samples between Voronoi subdomains, where each subdomain with all its particles is handled by a single computational process which is typically run on a single CPU core of a multiprocessor computing cluster.The algorithm displaces the positions of neighbor Voronoi subdomains in accordance with the local load imbalance between the corresponding processes. It results in particle transfers from heavy-loaded processes to less-loaded ones. Iteration of the algorithm puts into alignment the processor loads. Convergence to a well-balanced decomposition from imbalanced one is improved by the usage of multi-body terms in the balancing displacements.The high adaptability of the balancing algorithm to simulation conditions is illustrated by SPH modeling of the dynamic behavior of materials under extreme conditions, which are characterized by large pressure and velocity gradients, as a result of which the spatial distribution of particles varies greatly in time. The higher parallel efficiency of our algorithm in such conditions is demonstrated by comparison with the corresponding static decomposition of the computational domain. Our algorithm shows almost perfect strong scalability in tests using from tens to several thousand processes.

Subsonic and supersonic gas flows to condensation surface

“…The number of atoms is not fixed in simulations, but on an average the MD box contains the order of 2 × 10 6 atoms. MD simulations were performed with our in-house parallel code MD-VD 3 using the Voronoi dynamic domain decomposition 12,13 .…”

Towards Informed Partitioning for Load Balancing: a Proof-of-Concept

“…Then, using geometric constructions, the algorithm divides the space into subdomains, focusing on providing a high load imbalance correction capability at a low CPU time cost. For instance, some researchers proposed to use Voronoï tessellations [7,8,9], some divided the space into cuboids [10], or improved classical algorithms such as RCB [3] by allowing multisections instead of bisections [11].…”

“…More recently, novel geometric partitioning techniques have been proposed. Zhakhovskii et al [7], Fattebert et al [8], and later Egorova et al [9] introduced partitioning methods based on Voronoï tesselations for molecular dynamic applications (particle sim-ulations). In particular, Zhakhovskii et al [7] load balances at regular intervals by replacing the Voronoi site according to the local mass center combined with that of the Voronoï neighbors that move, while Fattebert et al [8] employ a gradient method and an estimation of the work per volume to adjust the processing elements' workload by moving Voronoï sites.…”

“…Note that Fattebert et al [8] were the first to propose such a partitioning method in 3D. Finally, Egorova et al [9] consider Voronoï sites as weighted bodies, where the weight depends on the processing element's load. They compute the displacement required by a Voronoï site to be balanced with respect to the neighboring domains using multi-body terms.…”

SPH Modeling of Water-Related Natural Hazards

“…The work in [97] evaluated the efficiency of a neighbor search algorithm based on a quad-tree partitioning on 32 processors. The SPH method has also been implemented for distributed memory systems using MPI for WCSPH [99,[103][104][105][106], and MPI for ISPH [107,108]. The execution on distributed systems requires the division of the simulation domain into multiple subdomains.…”