FFT-based Kronecker product approximation to micromagnetic long-range interactions
Computational Physics
2014-05-23 v1 Numerical Analysis
Abstract
We derive a Kronecker product approximation for the micromagnetic long range interactions in a collocation framework by means of separable sinc quadrature. Evaluation of this operator for structured tensors (Canonical format, Tucker format, Tensor Trains) scales below linear in the volume size. Based on efficient usage of FFT for structured tensors, we are able to accelerate computations to quasi linear complexity in the number of collocation points used in one dimension. Quadratic convergence of the underlying collocation scheme as well as exponential convergence in the separation rank of the approximations is proved. Numerical experiments on accuracy and complexity confirm the theoretical results.
Cite
@article{arxiv.1212.3509,
title = {FFT-based Kronecker product approximation to micromagnetic long-range interactions},
author = {Lukas Exl and Claas Abert and Norbert J. Mauser and Thomas Schrefl and Hans Peter Stimming and Dieter Suess},
journal= {arXiv preprint arXiv:1212.3509},
year = {2014}
}
Comments
4 figures