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

Published: April 12, 2025 | arXiv ID: 2504.09269v1

By: Yann-Meing Law , Zhichao Peng , Daniel Appelö and more

Potential Business Impact:

Simulates light waves faster and more accurately.

Business Areas:
Telecommunications Hardware

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.

Country of Origin
🇨🇦 🇭🇰 🇺🇸 Hong Kong, Canada, United States

Page Count
22 pages

Category
Mathematics:
Numerical Analysis (Math)