{
  "abstract": "The paper presents a higher-order global multi-trace integral equation for time-harmonic electromagnetic scattering by composite objects. The higher-order multi-trace formulation is preconditioned with a Calderón multiplicative preconditioner using higher-order quasi-Helmholtz projectors. The higher-order quasi-Helmholtz projectors separate the solenoidal and non-solenoidal components of the basis functions. Separate access to the Helmholtz components circumvents the explicit inversion of an ill-conditioned mixed Gram matrix. This enables the application of Calderón multiplicative preconditioning without refining the mesh and resorting to dual basis functions. Furthermore, it enables low-frequency stabilization, as the solenoidal and non-solenoidal components can be rescaled individually. The higher-order quasi-Helmholtz projectors are computed iteratively, enabling iterative solvers to efficiently solve the preconditioned matrix system, yielding accurate solutions in a few dozen iterations. Numerical experiments are conducted for composite dielectric bodies, confirming the effectiveness of the proposed preconditioner for the global multi-trace formulation discretized with higher-order basis functions for dense meshes and at very low frequencies",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17252",
  "author_total": 4,
  "authors": [
    {
      "name": "Cedric Münger"
    },
    {
      "name": "Alessandro Zuccotti"
    },
    {
      "name": "Van Chien Le"
    },
    {
      "name": "Kristof Cools"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bqyqx0rcet1q8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17252",
  "fulltext_url": null,
  "id": "bqyqx0rcet1q8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17252",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3107|Electromagnetic Scattering and Analysis"
    ]
  ],
  "openalex": "W7213417504",
  "pdf_url": "https://arxiv.org/pdf/2609.17252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bqyqx0rcet1q8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Quasi-Helmholtz Calderón Multiplicative Preconditioning for Higher-Order Global Multi-Trace Integral Equations",
  "title_text": "Quasi-Helmholtz Calderón Multiplicative Preconditioning for Higher-Order Global Multi-Trace Integral Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/bqyqx0rcet1q8",
  "venue": "arXiv",
  "versions": []
}