A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations
By: Yann-Meing Law , Zhichao Peng , Daniel Appelö and more
Potential Business Impact:
Simulates light waves faster and more accurately.
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.
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