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arXiv · 2611.03471

An Active Flux Method for Maxwell's equations

Yanick Kiechle·Christiane Helzel
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Abstract

We present a novel Active Flux method and a divergence-free method using exact evolution operators for solving Maxwell's equations in three space dimensions on Cartesian grids. The proposed methods are fully discrete, third-order accurate and rely on a truly multidimensional evolution operator based on Kirchhoff's formula for the electromagnetic wave equation. The first method is a classical Active Flux method with globally continuous reconstruction while the second method is an adaptation of the Active Flux method to a locally divergence-free reconstruction by Balsara. The applied reconstruction is built from facial degrees of freedom and is no longer globally continuous. The classical method keeps the divergence error bounded. The divergence-free method with face averages initialized by a potential keeps the constraints at round-off. We compare the accuracy of both methods for smooth and discontinuous test problems.

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Yanick Kiechle, Christiane Helzel. 2026-11-02. An Active Flux Method for Maxwell's equations. https://arxiv.org/abs/2611.03471

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