On nonlinear magnetic field solvers using local Quasi-Newton updates
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917772170100736 |
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| author | Egger, Herbert Engertsberger, Felix Domenig, Lukas Roppert, Klaus Kaltenbacher, Manfred |
| author_facet | Egger, Herbert Engertsberger, Felix Domenig, Lukas Roppert, Klaus Kaltenbacher, Manfred |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On nonlinear magnetic field solvers using local Quasi-Newton updates Egger, Herbert Engertsberger, Felix Domenig, Lukas Roppert, Klaus Kaltenbacher, Manfred Numerical Analysis 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. |
| title | On nonlinear magnetic field solvers using local Quasi-Newton updates |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.01015 |