{
  "abstract": "We present a frequency-domain formulation of Biot's dynamic poroelastic equations with frequency-dependent dissipation (Biot--Allard) for anisotropic, heterogeneous media with memory effects. Two equivalent two-field representations--a displacement-pressure and a velocity-pressure-rate formulation--enable stabilized iterative splitting. While coupling operators generally lack an adjoint or skew-adjoint relationship at finite frequencies, the velocity--pressure-rate representation restores a skew-adjoint structure in the quasi-static limit. We prove continuity of the coupling operators and coercivity of the diagonal blocks, essential for convergence of the L-stabilized splitting scheme. The frequency-domain setting eliminates convolutional memory terms, incorporates attenuation and dispersion via complex-valued parameters, and reduces the time-dependent problem to a family of elliptic boundary-value problems suited for parallel computation and multi-frequency inversion. A conforming Galerkin finite element discretization preserves block structure, and numerical experiments confirm robustness and capture frequency-dependent attenuation. To illustrate discretization independence, we include a large-scale wave simulation using a pseudo-spectral method. This work provides a rigorous and efficient framework for modeling wave phenomena in complex porous media.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07388",
  "author_total": 4,
  "authors": [
    {
      "name": "Morten Jakobsen"
    },
    {
      "name": "Jakob Seierstad Stokke"
    },
    {
      "name": "Kundan Kumar"
    },
    {
      "name": "Florin Adrian Radu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a707pp91evbjg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07388",
  "fulltext_url": null,
  "id": "a707pp91evbjg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07388",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.07388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a707pp91evbjg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Frequency Domain Biot--Allard Equations for Isotropic and Anisotropic Poroelastic Media: Two-field formulations and iterative splitting",
  "title_text": "Frequency Domain Biot--Allard Equations for Isotropic and Anisotropic Poroelastic Media: Two-field formulations and iterative splitting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/a707pp91evbjg",
  "venue": "arXiv",
  "versions": []
}