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

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 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. Program summaryProgram Title: INFFTMProgram Files doi:http://dx.doi.org/10.17632/nx5zzp5xxj.1Licensing provisions: GNU GPLv3Programming language: MATLAB/GNU OctaveNature of problem: Evaluation of 3d Fourier series at arbitrary rectilinear grids or sets of arbitrary points, with application to quantum vortex reconnection.Solution method: Fast n-dimensional linear transform of an n-d tensor (rectilinear grids), NFFT (Nonuniform Fast Fourier Transform, arbitrary points), time splitting spectral Fourier method (Gross–Pitaevskii equation for superfluids).External routines/libraries: NFFT (optional but recommended).