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J. Kraus, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, B. Stiftner:
"Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics";
in: "ASC Report 21/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 35.

The tangent plane scheme is a time-marching scheme for the numerical
solution of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which describes the time evolution of ferromagnetic configurations. Exploiting the geometric structure of LLG, the tangent plane scheme requires only the solution of one linear variational form per time-step, which is posed in the discrete tangent space determined by the nodal values of the current magnetization.
We develop an effective solution strategy for the arising constrained linear system, which is based on appropriate Householder reflections. We derive possible preconditioners, which are (essentially) independent of the time-step, and prove that the preconditioned GMRES algorithm leads to linear convergence. Numerical experiments underpin the theoretical findings.

http://www.asc.tuwien.ac.at/preprint/2018/asc21x2018.pdf