Solving the Vlasov equation for one-dimensional models with long range interactions on a GPU

TL;DR

This paper introduces a GPU-based numerical method for solving the one-dimensional Vlasov equation with long-range interactions, demonstrating improved speed and accuracy across multiple models.

Contribution

The paper presents a novel GPU parallel implementation of a second-order time-split algorithm with cubic-spline interpolation for the Vlasov equation in 1D.

Findings

Significant speedups achieved on GPU compared to CPU implementations.

High accuracy maintained across different models and grid resolutions.

Effective application to Hamiltonian Mean Field, Ring, and self-gravitating sheet models.

Abstract

We present a GPU parallel implementation of the numeric integration of the Vlasov equation in one spatial dimension based on a second order time-split algorithm with a local modified cubic-spline interpolation. We apply our approach to three different systems with long-range interactions: the Hamiltonian Mean Field, Ring and the self-gravitating sheet models. Speedups and accuracy for each model and different grid resolutions are presented.