The Hermite-Taylor Correction Function Method for Maxwell's Equations

TL;DR

This paper introduces the Hermite-Taylor Correction Function method, a systematic approach for implementing boundary conditions in the Hermite-Taylor method applied to Maxwell's equations, enhancing its accuracy and applicability.

Contribution

The paper develops a systematic correction function approach for boundary conditions in the Hermite-Taylor method, specifically applied to Maxwell's equations.

Findings

Improved handling of boundary conditions in Hermite-Taylor method.

Enhanced accuracy and efficiency for Maxwell's equations.

Method extendable to other hyperbolic systems.

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.