FFT-based Kronecker product approximation to micromagnetic long-range interactions

By Lukas Exl, Claas Abert, Norbert J. Mauser, Thomas Schrefl, Hans Peter Stimming, Dieter Suess. 2012

11 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Computational Mathematics, Mechanics of Materials

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…• the solution of high-dimensional Schr¨odinger equations [46,160,172,184,192,193]; • computational tasks in micromagnetics [80,81]; • rational approximation problems [242]; • computational homogenization [42,96,176]; • computational finance [134,137]; • the approximation of…”