Parallel-vector algorithms for particle simulations on shared-memory multiprocessors

Over the last few decades, the computational demands of massive particle-based simulations for both scientific and industrial purposes have been continuously increasing. Hence, considerable efforts are being made to develop parallel computing techniques on various platforms. In such simulations, particles freely move within a given space, and so on a distributed-memory system, load balancing, i.e., assigning an equal number of particles to each processor, is not guaranteed. However, shared-memory systems achieve better load balancing for particle models, but suffer from the intrinsic drawback of memory access competition, particularly during (1) paring of contact candidates from among neighboring particles and (2) force summation for each particle. Here, novel algorithms are proposed to overcome these two problems. For the first problem, the key is a pre-conditioning process during which particle labels are sorted by a cell label in the domain to which the particles belong. Then, a list of contact candidates is constructed by pairing the sorted particle labels. For the latter problem, a table comprising the list indexes of the contact candidate pairs is created and used to sum the contact forces acting on each particle for all contacts according to Newton’s third law. With just these methods, memory access competition is avoided without additional redundant procedures. The parallel efficiency and compatibility of these two algorithms were evaluated in discrete element method (DEM) simulations on four types of shared-memory parallel computers: a multicore multiprocessor computer, scalar supercomputer, vector supercomputer, and graphics processing unit. The computational efficiency of a DEM code was found to be drastically improved with our algorithms on all but the scalar supercomputer. Thus, the developed parallel algorithms are useful on shared-memory parallel computers with sufficient memory bandwidth.