Fast stray field computation on tensor grids

TL;DR

This paper introduces a fast, tensor-based algorithm for computing magnetostatic fields and energies on non-uniform grids, significantly reducing computational complexity and enabling efficient simulations.

Contribution

It presents a novel tensor approximation method for magnetostatic calculations that improves efficiency and scalability over traditional approaches.

Findings

Algorithm scales with N^(4/3) complexity

Achieves N^(2/3) complexity with tensor format

Numerical examples confirm theoretical efficiency and accuracy

Abstract

A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N^(4/3) for N computational cells used and with N^(2/3) (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.