Distributing and Load Balancing Sparse Fluid Simulations

Abstract

This paper describes a general algorithm and a system for load balancing sparse fluid simulations. Automatically distributing sparse fluid simulations efficiently is challenging because the computational load varies across the simulation domain and time. A key challenge with load balancing is that optimal decision making requires knowing the fluid distribution across partitions for future time steps, but computing this state for an arbitrary simulation requires running the simulation itself. The key insight of this paper is that it is possible to predict future load by running a speculative low resolution simulation in parallel. We mathematically formulate the problem of load balancing over multiple time steps and present a polynomial time algorithm to compute an approximate solution to it. Our experimental results show that distributing and speculatively load balancing sparse FLIP simulations over 8 nodes speeds them up by 5.3× to 7.9×, and that speculative load balancing generates assignments that perform within 20% of optimal.

Accelerating Distributed Graphical Fluid Simulations with Micro‐partitioning

“…FLIP (sparse grids on OpenVDB) . We implement a FLIP simulation application with the same setup used to evaluate the Speculative algorithm [SHQL18]. The simulation workflow is revised for better visual quality.…”

“…When most computation happens on a tiny portion (less than 10%) of the entire domain, this approach gives an order of magnitude speedup over static and uniform partitioning. For example, a speculative load balancing algorithm [SHQL18] runs a low‐resolution fluid simulation alongside the actual one in order to estimate load distribution, uses the estimate to decide how to assign partitions and achieves 5–8 times speedup over static and uniform partitioning.…”

“…In addition, Birdshot scheduling can in some cases outperform dynamic load balancing algorithms. In a FLIP simulation, Birdshot scheduling is only 21% slower than a state-of-art dynamic load balancing algorithm [SHQL18], but it is much simpler.…”

“…This paper proposes a new scheduling approach for distributed graphical fluid simulations, called Birdshot scheduling. Birdshot scheduling performs almost as well as state‐of‐the‐art dynamic scheduling algorithms based on speculative execution [SHQL18], but has no control overhead, does not need to dynamically migrate data and generates a deterministic, repeatable schedule. Birdshot scheduling works on simulations with an underlying Eulerian geometry, such as uniform grids and sparse data structures, like OpenVDB [Mus13] or sparse paged grids [SABS14].…”

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

“…An important step in minimizing the cost of system assembly is to scalably parallelize sparse matrix‐matrix multiplication, for which we use the algorithm of Saad [Saa03]. In the future, we are interested in implementing load balancing strategies such as the simple speculative load balancing approach of [SHQL18], particularly for free surface flows. We note that our implementation enables high‐resolution simulations such as that in Figure 2 at relatively modest computational cost (see Table 3).…”