Micromagnetics problems in two dimensions are formulated in terms of a finite-element description. The free energy, including exchange, anisotropy, external field, and demagnetization contributions, is approximated by means of integrals over linear triangular finite elements and minimized with respect to the nodal variables. By enforcing the constraint that the magnetization vectors at the nodes have constant magnitude, the resulting minimization equations are nonlinear. They are solved using Gauss-Seidel iteration. The finite-element description allows calculations to be performed for arbitrary two-dimensional geometries. In the examples presented, the magnetization distributions obtained were in agreement with expectations based on domain theory.
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