2024/09/02 by Herbert Egger, Felix Engertsberger, Egger, Herbert +7 · 1 citation
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2409.01015
openalex publication_date 2024/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.