On nonlinear magnetic field solvers using local Quasi-Newton updates
<|reference_start|>On nonlinear magnetic field solvers using local Quasi-Newton updates: Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton updates to construct appropriate linearizations of the material behavior during the nonlinear iteration. The resulting scheme shows similar fast convergence as the Newton-method but, like the fixed-point methods, does not require derivative information of the underlying material law. As a consequence, the method can be used for the efficient solution of models with hysteresis which involve nonsmooth material behavior. The implementation of the proposed scheme can be realized in standard finite-element codes in parallel to the fixed-point and the Newton method. A full convergence analysis of all three methods is established proving global mesh-independent convergence. The theoretical results and the performance of the nonlinear iterative schemes are evaluated by computational tests for a typical benchmark problem.<|reference_end|>
@article{egger2024on,
    title={On nonlinear magnetic field solvers using local Quasi-Newton updates},
    author={Herbert Egger, Felix Engertsberger, Lukas Domenig, Klaus Roppert,
  Manfred Kaltenbacher},
    journal={arXiv preprint arXiv:2409.01015},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01015},
    primaryClass={math.NA cs.NA}
}