{
  "abstract": "We propose an approach using matrix symmetry to accelerate hierarchical low-rank compression for wave transmission scattering. For Helmholtz transmission problems, we introduce a symmetric Müller-like boundary integral equation formulation. Although not of the second kind, this formulation creates no difficulties for direct solvers. A one-point corrected quadrature in a Nyström discretization preserves the complex symmetry of the discretized system. This formulation is integrated into a variant of a hierarchical semiseparable direct solver. Within this framework, the computational workload of the low-rank approximation in the proxy method is halved by exploiting the symmetric relationship between the left and right coefficients. Furthermore, we extend this symmetry-exploiting approach to elastic transmission problems by using a symmetric Galerkin boundary element method. Numerical experiments on a multi-node computing cluster demonstrate that the symmetric Müller-like formulation for Helmholtz scattering achieves on average a 1.41-fold speedup compared to the non-symmetric baseline while maintaining third-order convergence. Furthermore, the symmetry-aware solver for elastic scattering is more than 1.5 times faster.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33216",
  "author_total": 4,
  "authors": [
    {
      "name": "Yasuhiro Matsumoto"
    },
    {
      "name": "Taizo Maruyama"
    },
    {
      "name": "Qianxiang Ma"
    },
    {
      "name": "Rio Yokota"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0xp6nnn6s8qj9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33216",
  "fulltext_url": null,
  "id": "0xp6nnn6s8qj9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33216",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.33216",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0xp6nnn6s8qj9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33216",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33216"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Hierarchical low-rank compression exploiting symmetric boundary integral equations in transmission scattering",
  "title_text": "Hierarchical low-rank compression exploiting symmetric boundary integral equations in transmission scattering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/0xp6nnn6s8qj9",
  "venue": "arXiv",
  "versions": []
}