{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03471",
  "author_total": 2,
  "authors": [
    {
      "name": "Yanick Kiechle"
    },
    {
      "name": "Christiane Helzel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d9pqpp1ehkb9j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03471",
  "fulltext_url": null,
  "id": "d9pqpp1ehkb9j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03471",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d9pqpp1ehkb9j.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An Active Flux Method for Maxwell's equations",
  "title_text": "An Active Flux Method for Maxwell's equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/d9pqpp1ehkb9j",
  "venue": "arXiv",
  "versions": []
}