{
  "abstract": "We present an efficient wideband construction of directional $\\mathcal{H}^2$-matrices for the electrical field integral equation that, in contrast to existing constructions, supports not only box trees but also geometry-adaptive cluster trees. To accommodate geometry-adaptive cluster trees, we determine the number of directions from the electrical size of each cluster (instead of the level of a box tree), construct the directions using Spherical-Fibonacci points, and establish a hierarchy between the direction sets of a cluster and its children through an angular nearest-neighbor mapping. We construct the nested directional representation using the incomplete adaptive cross approximation, for which we introduce a robustified tree-mimicry pivoting strategy that prevents premature convergence for block-structured matrices arising from certain geometries and meshes. Numerical results demonstrate that the proposed approach achieves the desired accuracy, requires no more storage than the octree-based construction and substantially less when the geometry or discretization is poorly matched to octree clustering, and exhibits the expected $\\mathcal{O}(N\\log N)$ scaling for high-frequency problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19431",
  "author_total": 2,
  "authors": [
    {
      "name": "Joshua M. Tetzner"
    },
    {
      "name": "Simon B. Adrian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvm0g64f8kwry.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19431",
  "fulltext_url": null,
  "id": "fvm0g64f8kwry",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19431",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3107|Electromagnetic Scattering and Analysis"
    ]
  ],
  "openalex": "W7213612954",
  "pdf_url": "https://arxiv.org/pdf/2609.19431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvm0g64f8kwry.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Wideband Directional $\\mathcal{H}^2$-Matrix Compression for the Electric Field Integral Equation with Geometry-Adaptive Cluster Trees",
  "title_text": "Wideband Directional ℋ^2-Matrix Compression for the Electric Field Integral Equation with Geometry-Adaptive Cluster Trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/fvm0g64f8kwry",
  "venue": "arXiv",
  "versions": []
}