Parallel computational microhydrodynamics: Communication scheduling strategies

The behavior of multiparticle systems in a viscous fluid, as governed by the Stokes equations, is computed by the coordinated use of multiple processors on a distributed memory parallel computer. The completed double‐layer boundary integral equation method (CDL‐BIEM) is used to convert the hydrodynamic mobility problems to a fixed‐point problem, amenable to either synchronous or asynchronous iterative solution schemes. Parallel computational strategies, based on assigning particles to processors, are considered, and rules are derived to specify how often processors should exchange information. A spectral communication scheduling strategy, based on the spectral radius in pair‐interaction problems, converges with fewer global iterations and effectively reduces the level of interprocessor communications, suggesting algorithm scalability to massively‐parallel computers with hierarchical access to distributed memories. Stochastic schedules, which specify the probability that the information exchange occurs at every iteration, were also considered. For the same test problems, these strategies performed better than the point Jacobi iterations, but not as well as their deterministic counterparts. Scheduling strategies are extrapolated to larger problems, based on projections of memory and performance capabilities of the next generation of high‐performance parallel supercomputers.