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Introduction
Abstract
We have investigated the domain patterns in Nd2Fe14B particles using a finite element method with adaptive mesh refinement in three space dimensions. This technique is suitable to improve the micromagnetic solution and reduce the discretisation error. As the magnetisation and its derivatives vary markedly at the domain boundaries, non-uniform meshes are warranted in the interest of computational accuracy and efficiency. Suitable refinement patterns avoid degenerated elements and deteriorating convergence rates. The mesh is refined or partially coarsened where the solution is found to be smooth. Adaptive mesh refinement at run-time of the simulation allows the area of local refinement to move together with occurring domain walls.
Discretization Error
The discretization error can be estimated by calculating the difference between the magnetization vectors on a common edge. Above, its norm is plotted for different refinement levels. Refinement in those areas where the discretization error is large reduces the discretization error and improves the solution calculated with the FE method.
Werner Scholz
