Fast computation of magnetostatic fields by Non-uniform Fast Fourier Transforms

TL;DR

This paper introduces a Non-uniform Fast Fourier Transform algorithm that significantly accelerates the computation of magnetostatic fields in micromagnetic simulations, matching the efficiency of regular grid FFTs while maintaining FEM flexibility and accuracy.

Contribution

It presents a novel NUFFT-based method that achieves N logN convergence for finite element methods in magnetostatic field calculations, improving computational speed without sacrificing accuracy.

Findings

Achieves N logN computational complexity for FEM-based magnetostatic calculations.

Maintains high accuracy comparable to traditional FEM methods.

Significantly reduces computation time in micromagnetic simulations.

Abstract

The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite element methods (FEM) are bounded to N^4/3 in the best case. We report the implementation of a Non-uniform Fast Fourier Transform algorithm which brings a N logN convergence to FEM, with no loss of accuracy in the results.