INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections

TL;DR

This paper introduces INFFTM, a MATLAB interface for the NFFT library, enabling fast evaluation of 3D Fourier series at arbitrary points, demonstrated through quantum vortex reconnection simulations.

Contribution

It provides a MATLAB-compatible implementation of NFFT for efficient 3D Fourier series evaluation, filling a gap in computational physics tools.

Findings

Significant reduction in computational cost compared to fine grid simulations.

High accuracy in quantum vortex reconnection analysis.

Effective application of NFFT in MATLAB for physics simulations.

Abstract

Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of \emph{arbitrary} points are quite rare, especially in MATLAB language. Here we employ the Nonequispaced Fast Fourier Transform (NFFT, by J. Keiner, S. Kunis, and D. Potts), a C library designed for this purpose, and provide a Matlab and GNU Octave interface that makes NFFT easily available to the Numerical Analysis community. We test the effectiveness of our package in the framework of quantum vortex reconnections, where pseudospectral Fourier methods are commonly used and local high resolution is required in the post-processing stage. We show that the efficient evaluation of a truncated Fourier series at arbitrary points provides excellent results at a computational cost much smaller than carrying out a numerical simulation of the problem on a sufficiently fine regular grid that can reproduce comparable details of the reconnecting vortices.