Mapping the Arnold web with a GPU-supercomputer

TL;DR

This paper demonstrates that using GPU-supercomputers significantly accelerates the mapping of the Arnold web, a complex resonance structure in phase space of non-integrable Hamiltonian systems, enabling faster exploration of the system's dynamics.

Contribution

The study introduces GPU-based computational methods to efficiently map the Arnold web, achieving two orders of magnitude speedup over traditional CPU methods.

Findings

GPU-supercomputers enable rapid mapping of the Arnold web.

Speedup of two orders of magnitude compared to CPU simulations.

Facilitates detailed exploration of resonance channels in phase space.

Abstract

The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is $M \geq 3$. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the whole energy shell. The Arnold diffusion is a slow process; consequently the mapping of the web presents a very time-consuming task. We demonstrate that the exploration of the Arnold web by use of a graphic processing unit (GPU)-supercomputer can result in distinct speedups of two orders of magnitude as compared to standard CPU-based simulations.