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arXiv · 2301.01752

The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems

Yann-Meing Law·Daniel Appelö·Thomas Hagstrom
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Abstract

We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$ in each Cartesian coordinate. This makes the development of a systematic approach to enforce boundary and interface conditions difficult. Here we use the correction function method to update the numerical solution where the Hermite-Taylor method cannot be applied directly. Time derivatives of boundary and interface conditions, converted into spatial derivatives, are enforced to obtain a stable method and relax the time-step size restriction of the Hermite-Taylor correction function method. The proposed high-order method offers a flexible systematic approach to handle embedded boundary and interface problems, including problems with discontinuous solutions at the interface. This method is also easily adaptable to other first order hyperbolic systems.

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Yann-Meing Law, Daniel Appelö, Thomas Hagstrom. 2023-01-04. The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems. https://arxiv.org/abs/2301.01752

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