INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections
This work offers a practical tool for computational physicists and numerical analysts who need efficient evaluation of Fourier series at arbitrary points, particularly in post-processing of pseudospectral simulations.
The authors provide a MATLAB/GNU Octave interface for the Nonequispaced Fast Fourier Transform (NFFT) library, enabling fast evaluation of 3D Fourier series at arbitrary points. They demonstrate its effectiveness in quantum vortex reconnection simulations, achieving high resolution at lower computational cost than fine-grid simulations.
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.