Tree method for quantum vortex dynamics

TL;DR

This paper introduces a fast tree-based numerical method for simulating vortex filament evolution in superfluid helium, significantly reducing computational costs while maintaining accuracy across various vortex configurations.

Contribution

A novel tree algorithm for vortex dynamics that accelerates Biot-Savart integral calculations from N^2 to N log N, enabling efficient simulations of complex vortex systems.

Findings

Computational cost scales as N log N instead of N squared.

Method accurately reproduces vortex dynamics compared to Biot-Savart law.

Effective for diverse vortex configurations, including vortex rings and tangles.

Abstract

We present a numerical method to compute the evolution of vortex filaments in superfluid helium. The method is based on a tree algorithm which considerably speeds up the calculation of Biot-Savart integrals. We show that the computational cost scales as Nlog{(N) rather than N squared, where $N$ is the number of discretization points. We test the method and its properties for a variety of vortex configurations, ranging from simple vortex rings to a counterflow vortex tangle, and compare results against the Local Induction Approximation and the exact Biot-Savart law.