arXiv Open Access 2025

A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations

Yann-Meing Law Zhichao Peng Daniel Appelö Thomas Hagstrom

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Abstrak

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.

Topik & Kata Kunci

math.NA

Penulis (4)

Yann-Meing Law

Zhichao Peng

Daniel Appelö

Thomas Hagstrom

Format Sitasi

APA MLA BibTeX

Law, Y., Peng, Z., Appelö, D., Hagstrom, T. (2025). A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations. https://arxiv.org/abs/2504.09269

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓