B. Stiftner, C.-M. Pfeiler, M. Ruggeri, D. Praetorius, G. Hrkac:

"Computational micromagnetics: A mathematical point of view";

Poster: IEEE 6th International Conference on Microwave Magnetics (ICMM 2018), Exeter; 2018-06-25 - 2018-06-27.

Micromagnetic phenomena on a ferromagnetic sample are often described by the Landau-Lifshitz-Gilbert equation (LLG) which is a nonlinear time-dependent partial differential equation. The sought magnetization is a three-dimensional vector field. From a mathematical point of view, the strong non-linearity of LLG, an (implicit) non-convex modulus constraint, and the non-uniqueness of solutions of LLG aggravate the development and thorough mathematical analysis of numerical integrators. The tangent plane scheme (a.k.a. projection scheme) and the midpoint scheme represent two FEM-based classes of convergent integrators with a rigorous mathematical analysis. We discuss recent developments and our contributions to the latter algorithms. In particular, this includes a convergent tangent plane integrator for the simulation of chiral magnetic skyrmion dynamics. Moreover, we present our open-source and user-friendly Python module commix (based on the FEM software package NGS/Py) for mathematically justified computational micromagntism.

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