Molecular dynamics for long-range interacting systems on Graphic Processing Units

TL;DR

This paper develops GPU-accelerated symplectic integrators for long-range interacting N-body systems, achieving significant speedups while maintaining energy accuracy across large particle simulations.

Contribution

It introduces GPU implementations of a fourth-order symplectic integrator for long-range N-body models, demonstrating high speedups and energy conservation.

Findings

Speedups up to 140 times over serial code

Energy errors comparable to CPU implementations

Able to simulate up to 50 million particles

Abstract

We present implementations of a fourth-order symplectic integrator on graphic processing units for three $N$-body models with long-range interactions of general interest: the Hamiltonian Mean Field, Ring and two-dimensional self-gravitating models. We discuss the algorithms, speedups and errors using one and two GPU units. Speedups can be as high as 140 compared to a serial code, and the overall relative error in the total energy is of the same order of magnitude as for the CPU code. The number of particles used in the tests range from 10,000 to 50,000,000 depending on the model.