Efficient micromagnetic–elastic simulations based on a perturbed Lagrangian function

Abstract

Micromagnetic simulations require the numerically challenging preservation of the Euclidean norm during the whole simulation. This can be accomplished by applying a priori length preserving methods, renormalization algorithms, or penalization strategies. The latter one includes both the penalty method and the Lagrangian multiplier. The penalty method requires the definition of a penalty parameter during the initiation of the simulation which, depending on its size, can lead to an unsatisfied constraint or stiff and difficult to solve systems of equations. The Lagrange multiplier always penalizes in problem-dependent intensity, hence, an additional degree of freedom is added to the system of equations to the drawback of higher computational costs. This paper proposes a method that utilizes a perturbed Lagrangian multiplier and an element level static condensation to condensate the additional degree of freedom. This guarantees fast simulations, and no parameter fitting in advance. Suitable numerical examples are conducted to prove the workability of the outlined scheme and to highlight the efficiency compared to the non-condensed formulation.