| Autor: |
Egger, Herbert, Engertsberger, Felix, Domenig, Lukas, Roppert, Klaus, Kaltenbacher, Manfred |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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