A projection method for phase field models in micromagnetics

Magnetic materials have been finding increasingly wider areas of application in industry and therefore, as indicated by the reviews [1], [2] and [3], there is an increased interest in the efficient modeling of such materials that have an inherent coupling between the magnetic and mechanical characteristics. A particular challenge in the modeling of such materials is the algorithmic preservation of the geometric constraint on the magnetization field, that remains constant in magnitude [4]. In earlier works, [5] and [6], we presented a phase field model within a geometrically exact incremental variational framework where the geometric property of the magnetization director is exactly preserved pointwise by nonlinear rotational updates at the nodes. In the current work however, we present an alternative approach that involves an operator split along with a projection step for the magnetization vector. This method provides significant advantages in terms of speed and ease of implementation at the cost of the maximum time step size used. The current work therefore presents comparative study of the the two methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)