A parallel-in-time solver for nonlinear degenerate time-periodic parabolic problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915176867954688 |
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| author | Egger, Herbert Schafelner, Andreas |
| author_facet | Egger, Herbert Schafelner, Andreas |
| contents | A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based on a fixed-point iteration. Every step of this iteration amounts to the solution of a discretized time-periodic and time-invariant problem for which efficient parallel-in-time methods are available. Global convergence with contraction factors independent of the discretization parameters is established. Together with an appropriate initialization step, a highly efficient and reliable solver is obtained. The applicability and performance of the proposed method is illustrated by simulations of a power transformer. Further comparison is made with other solution strategies proposed in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A parallel-in-time solver for nonlinear degenerate time-periodic parabolic problems Egger, Herbert Schafelner, Andreas Numerical Analysis A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based on a fixed-point iteration. Every step of this iteration amounts to the solution of a discretized time-periodic and time-invariant problem for which efficient parallel-in-time methods are available. Global convergence with contraction factors independent of the discretization parameters is established. Together with an appropriate initialization step, a highly efficient and reliable solver is obtained. The applicability and performance of the proposed method is illustrated by simulations of a power transformer. Further comparison is made with other solution strategies proposed in the literature. |
| title | A parallel-in-time solver for nonlinear degenerate time-periodic parabolic problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.21013 |