Norbert J. Mauser

Carl-Martin Pfeiler, Michele Ruggeri, Bernhard Stiftner et al.

We present our open-source Python module Commics for the study of the magnetization dynamics in ferromagnetic materials via micromagnetic simulations. It implements state-of-the-art unconditionally convergent finite element methods for the numerical integration of the Landau-Lifshitz-Gilbert equation. The implementation is based on the multiphysics finite element software Netgen/NGSolve. The simulation scripts are written in Python, which leads to very readable code and direct access to extensive post-processing. Together with documentation and example scripts, the code is freely available on GitLab.

Lukas Exl, Claas Abert, Norbert J. Mauser et al.

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.

Lukas Exl, Norbert J. Mauser, Yong Zhang

We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation of the singular convolution kernel and Taylor expansion of the density. Starting from the convolution formulation, for smooth and fast decaying densities, we make a full use of the Fourier pseudospectral (plane wave) approximation of the density and a separable Gaussian-sum approximation of the kernel in an interval where the singularity (the origin) is excluded. Hence, the potential is separated into a regular integral and a near-field singular correction integral, where the first integral is computed with the Fourier pseudospectral method and the latter singular one can be well resolved utilizing a low-order Taylor expansion of the density. Both evaluations can be accelerated by fast Fourier transforms (FFT). The new method is accurate (14-16 digits), efficient ($O(N \log N)$ complexity), low in storage, easily adaptable to other different kernels, applicable for anisotropic densities and highly parallelable.