Load Balancing in Strongly Inhomogeneous Simulations -- a Vlasiator Case Study

TL;DR

This paper compares various load balancing methods for large-scale simulations, demonstrating that Hilbert space filling curves, especially the Beta curve, offer superior load distribution in a magnetospheric simulation case study.

Contribution

It introduces and evaluates six 3D Hilbert curves for load balancing, highlighting their effectiveness over traditional hypergraph and geometric methods.

Findings

HSFC method provides optimal load balance

RIB and PHG methods perform well, RCB less so

Beta Hilbert curve outperforms standard curves

Abstract

Parallelization is a necessity for large-scale simulations due to the amount of data processed. In this article we investigate different load balancing methods using Vlasiator, a global magnetospheric simulation as our case study. The theoretical basis for load balancing is the (hyper)graph partitioning problem, modeling simulation units as vertices and their data dependencies as edges. As it is an NP-hard problem, heuristics are necessary for dynamic runtime balancing. We consider first hypergraph partitioning via an algorithm called parallel hypergraph partitioner (PHG); this is done by partitioning a simplified grid and then attempting to optimize the solution on the finer grid. The second and third are the geometric methods of recursive coordinate bisection (RCB) and recursive inertial bisection (RIB). Finally we consider the method of Hilbert space filling curves (HSFC). The algorithm projects simulation cells along a Hilbert curve and makes cuts along the curve. This works well due to the excellent locality of Hilbert curves, and can be optimized further by choice of curve. We introduce and investigate six three-dimensional Hilbert curves in total. Our findings on runs of two different scales indicate the HSFC method provides optimal load balance, followed by RIB and PHG methods and finally by RCB. Of the Hilbert curves evaluated, the Beta curve outperformed the most commonly used curve by a few percent.