Numerical Methods for the Stray-Field Calculation: A Comparison of recently developed Algorithms

TL;DR

This paper compares various numerical algorithms for calculating the stray field in micromagnetic simulations, evaluating their efficiency, accuracy, and suitability for different geometries.

Contribution

It provides a comprehensive comparison of finite difference, tensor grid, and finite-element methods for stray-field calculations, highlighting their strengths and limitations.

Findings

Integral methods outperform finite-element for cuboid structures.

Tensor grid method is the fastest among the compared algorithms.

Finite-element method is superior for curved structures.

Abstract

Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can be subdivided into integral methods (fast Fourier transform methods, tensor-grid method) which solve the stray field directly and in differential equation methods (finite-element method), which compute the stray field as the solution of a partial differential equation. It turns out that for cuboid structures the integral methods, which work on cuboid grids (fast Fourier transform methods and tensor grid methods) outperform the finite-element method in terms of the ratio of computational effort to accuracy. Among these three methods the tensor grid method is the fastest. However, the use of the tensor grid method in the context of full micromagnetic codes is not well investigated yet. The finite-element method performs best for computations on curved structures.