The Hermite-Taylor Correction Function Method for Maxwell's Equations
Numerical Analysis
2023-03-20 v2 Numerical Analysis
Abstract
The Hermite-Taylor method, introduced in 2005 by Goodrich, Hagstrom and Lorenz, is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor Correction Function method, which provides exactly such a systematic approach for handing boundary conditions. Here we focus on Maxwell's equations but note that the method is easily extended to other hyperbolic problems.
Cite
@article{arxiv.2210.07134,
title = {The Hermite-Taylor Correction Function Method for Maxwell's Equations},
author = {Yann-Meing Law and Daniel Appelö},
journal= {arXiv preprint arXiv:2210.07134},
year = {2023}
}