FFT-based solution of 2D and 3D magnetization problems in type-II superconductivity

TL;DR

This paper develops and compares FFT-based numerical methods for 2D and 3D magnetization problems in type-II superconductors, demonstrating improved stability, efficiency, and applicability over existing finite element approaches.

Contribution

It introduces a new FFT-based method for 3D bulk magnetization problems using a magnetic field formulation, enhancing stability and ease of implementation.

Findings

Modified FFT method ensures stable convergence.

New 3D FFT-based method is simple and efficient.

Numerical simulations demonstrate the method's effectiveness.

Abstract

We consider the Fast Fourier Transform (FFT) based numerical method for thin film magnetization problems [Vestg{\aa}rden and Johansen, SuST, 25 (2012) 104001], compare it with the finite element methods, and evaluate its accuracy. Proposed modifications of this method implementation ensure stable convergence of iterations and enhance its efficiency. A new method, also based on the FFT, is developed for 3D bulk magnetization problems. This method is based on a magnetic field formulation, different from the popular h-formulation of eddy current problems typically employed with the edge finite elements. The method is simple, easy to implement, and can be used with a general current-voltage relation; its efficiency is illustrated by numerical simulations.