A comparative study of finite element schemes for micromagnetic mechanically coupled simulations

Abstract

Magnetic materials find wide applications in modern technology. For further materials design and optimization, physics-grounded micromagnetic simulations play a critical role, as predictions of properties, regarding the materials to be examined, can be made on the basis of in silico characterizations. However, micromagnetism, in particular, the Landau–Lifshitz–Gilbert equation, poses an interesting but challenging numerical issue, particularly the constraint of the preserved magnetization magnitude far below Curie temperature. Since this requirement is not fulfilled a priori, additional measures must be considered. In this work, four different methods for conserving the length of the magnetization vector in the framework of the finite element method are compared, namely, a projection method, penalty method, a Lagrange multiplier, and the approximation of the magnetization vectors using arithmetical and circular spherical coordinates. By applying the described methods to appropriate numerical examples, the different advantages and disadvantages are worked out so that a clear recommendation for the perturbed Lagrange method can be derived.