Fast stray field computation on tensor grids
It addresses the computational bottleneck of stray field calculations for micromagnetic simulations, offering faster scaling than traditional methods.
The paper presents a direct integration algorithm for computing magnetostatic fields and energy on tensor grids, achieving N^(4/3) scaling for N cells and sublinear N^(2/3) scaling when magnetization is in canonical tensor format, with numerical validation.
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.