A high-order finite volume method for Maxwell's equations in heterogeneous and time-varying media

TL;DR

This paper introduces a high-order finite volume method for solving Maxwell's equations in media with spatially and temporally varying properties, offering improved accuracy and efficiency over traditional methods.

Contribution

The paper presents a novel high-order finite volume approach capable of accurately modeling Maxwell's equations in dynamic, heterogeneous media, including both conservative and non-conservative formulations.

Findings

High-order methods resolve fine structures effectively.

The proposed method outperforms traditional 2nd-order FDTD in efficiency.

Numerical examples validate the method's accuracy and robustness.

Abstract

We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately resolve fine structures that develop due to the varying material properties. Numerical examples demonstrate the effectiveness of the proposed method in handling temporal variation and its efficiency relative to traditional 2nd-order FDTD.