Various applications ranging from spintronic devices, giant magnetoresistance sensors, and magnetic storage devices, include magnetic parts on very different length scales. Since the consideration of the Landau–Lifshitz–Gilbert equation (LLG) constrains the maximum element size to the exchange length within the media, it is numerically not attractive to simulate macroscopic parts with this approach. On the other hand, the magnetostatic Maxwell equations do not constrain the element size, but cannot describe the short-range exchange interaction accurately. A combination of both methods allows one to describe magnetic domains within the micromagnetic regime by use of LLG and also considers the macroscopic parts by a nonlinear material law using the Maxwell equations. In our work, we prove that under certain assumptions on the nonlinear material law, this multiscale version of LLG admits weak solutions. Our proof is constructive in the sense that we provide a linear-implicit numerical integrator for the multiscale model such that the numerically computable finite element solutions admit weak H1-convergence (at least for a subsequence) towards a weak solution.
Bruckner F., Suess D., Feischl M., Führer T., Goldenits P., Page M., et al. (2014). Multiscale modeling in micromagnetics: Existence of solutions and numerical integration. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 24(13), 2627-2662 [10.1142/S0218202514500328].
Multiscale modeling in micromagnetics: Existence of solutions and numerical integration
Ruggeri M.
2014
Abstract
Various applications ranging from spintronic devices, giant magnetoresistance sensors, and magnetic storage devices, include magnetic parts on very different length scales. Since the consideration of the Landau–Lifshitz–Gilbert equation (LLG) constrains the maximum element size to the exchange length within the media, it is numerically not attractive to simulate macroscopic parts with this approach. On the other hand, the magnetostatic Maxwell equations do not constrain the element size, but cannot describe the short-range exchange interaction accurately. A combination of both methods allows one to describe magnetic domains within the micromagnetic regime by use of LLG and also considers the macroscopic parts by a nonlinear material law using the Maxwell equations. In our work, we prove that under certain assumptions on the nonlinear material law, this multiscale version of LLG admits weak solutions. Our proof is constructive in the sense that we provide a linear-implicit numerical integrator for the multiscale model such that the numerically computable finite element solutions admit weak H1-convergence (at least for a subsequence) towards a weak solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.