A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917984116670464 |
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| author | Law, Yann-Meing Peng, Zhichao Appelö, Daniel Hagstrom, Thomas |
| author_facet | Law, Yann-Meing Peng, Zhichao Appelö, Daniel Hagstrom, Thomas |
| contents | In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small local linear systems for which the dimension is independent of the order. The implementation of order adaptive algorithms is straightforward in this setting, making the resulting p-adaptive Hermite method appealing for the simulations of soliton-like wave propagation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations Law, Yann-Meing Peng, Zhichao Appelö, Daniel Hagstrom, Thomas Numerical Analysis 35Q61, 65M70, 78M22 In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small local linear systems for which the dimension is independent of the order. The implementation of order adaptive algorithms is straightforward in this setting, making the resulting p-adaptive Hermite method appealing for the simulations of soliton-like wave propagation. |
| title | A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations |
| topic | Numerical Analysis 35Q61, 65M70, 78M22 |
| url | https://arxiv.org/abs/2504.09269 |