[P8, Praetorius] is concerned with time-dependent micromagnetics which is modeled by the Landau-Lifshitz-Gilbert equation (LLG) coupled to other PDEs, e.g., the Maxwell equations, the conservation of elastic momentum, or the continuity equations for the electric current and spin densities. For these complex PDE systems, we aim to investigate the existence of weak solutions (globally in time) and strong solutions (locally in time) as well as the effective (i.e., implementationally attractive and computationally cheap) and reliable (i.e., unconditionally convergent) numerical integration. In particular, the latter will benefit from the derivation and mathematical analysis of limit problems to bridge, e.g., different time-scales.
To this end, [P8, Praetorius] clusters all activities of the SFB related to micromagnetics: First, the coupling of LLG with the Maxwell equations and the derivation of an effective self-consisted model for the interaction of magnetization and electron spin accumulation is a joint work package with [P2, Jüngel]. Second, magnetostrictive effects will be studied together with [P11, Stefanelli]. Third, fast numerical solvers for LLG are developed and analyzed together with [P5, Mauser] and [P10, Schöberl]. All findings will be implemented in the SFB joint software platform. At the same time, [P8, Praetorius] will benefit from interactions with an already strongly linked international cooperation network including L. Banas (Bielefeld), C. Carstensen (Berlin), and T. Tran (Sydney) as well as interdisciplinary cooperations with G. Hrkac (Exeter) and D. Suess (Wien).