Finite element micromagnetic simulations with adaptive mesh refinement

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Abstract
The finite element method has recently been employed in investigating magnetization processes in materials with an irregular microstructure. In order to improve the accuracy of the solution, a method based on an adaptive refinement scheme is clearly desirable. Error control is essential if accuracy of results is to be optimal. We have applied an adaptive scheme to a system of interacting two-dimensional polycrystalline grains. The error estimator is based on the divergence and curl of both the magnetization and demagnetizing field. It is shown that increasing levels of discretization improve the micromagnetic solution, and the spatial localization of the additional nodes demonstrates the importance of the adaptive meshing technique.