Proven Distributed Memory Parallelization of Particle Methods

TL;DR

This paper presents a mathematically proven parallelization scheme for particle methods on distributed-memory systems, ensuring correctness and equivalence to sequential algorithms, thus providing a solid theoretical foundation for existing and future implementations.

Contribution

It offers the first formal proof of correctness for distributed-memory parallelization of particle methods, extending prior shared-memory proofs to a broader class of algorithms.

Findings

Proven equivalence of parallel and sequential particle methods on distributed systems

Applicable to widely used particle algorithms like SPH, DEM, and MD

Provides a theoretical foundation for practical parallel software implementations

Abstract

We provide a mathematically proven parallelization scheme for particle methods on distributed-memory computer systems. Particle methods are a versatile and widely used class of algorithms for computer simulations and numerical predictions in various applications, ranging from continuum fluid dynamics and granular flows, using methods such as Smoothed Particle Hydrodynamics (SPH) and Discrete Element Methods (DEM) to Molecular Dynamics (MD) simulations in molecular modeling. Particle methods naturally lend themselves to implementation on parallel-computing hardware. So far, however, a mathematical proof of correctness and equivalence to sequential implementations was only available for shared-memory parallelism. Here, we leverage a formal definition of the algorithmic class of particle methods to provide a proven parallelization scheme for distributed-memory computers. We prove that these parallelized particle methods on distributed memory computers are formally equivalent to their sequential counterpart for a well-defined class of particle methods. Notably, the here analyzed parallelization scheme is well-known and commonly used. Our analysis is, therefore, of immediate practical relevance to existing and new parallel software implementations of particle methods and places them on solid theoretical grounds.