{
  "abstract": "In the context of local helioseismology, we present a robust numerical framework based on the Hybridizable Discontinuous Galerkin (HDG) method for solving the linearized equations of stellar oscillations in realistic solar backgrounds, incorporating gravity, stratification, differential rotation, and acoustic attenuation. The governing equations are formulated using the displacement vector and the pressure perturbation as the unknowns and are solved in the frequency domain. The time-independent background model is assumed to be axisymmetric, allowing for a decomposition into azimuthal Fourier modes at each frequency. This leads to a set of 2D decoupled equations in Fourier space, which are numerically solved with the HDG method. We investigate the response to external sources of excitation, particularly Dirac-type sources. At low attenuation levels, we observe the emergence of complex singularity structures (for example in the near-surface layers and in the solar atmosphere). This behaviour follows from the propagation of singularities principles, since in the absence of attenuation the problem is of mixed elliptic-hyperbolic type. To maintain accuracy at small (solar-like) attenuation levels, we develop an HDG stabilization strategy. Our numerical experiments illustrate the accuracy and robustness of the proposed HDG formulation. Our Green's function calculations achieve the high level of accuracy required by passive imaging methods in helioseismology. In particular, we show that the mode frequencies and the rotational splitting coefficients due to differential rotation extracted from the model power spectrum are consistent with solar observations at a level of accuracy better than a tenth of a nanohertz.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "name": "Ha Pham"
    },
    {
      "name": "Florian Faucher"
    },
    {
      "name": "Damien Fournier"
    },
    {
      "name": "Hélène Barucq"
    },
    {
      "name": "Laurent Gizon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85vqj1pftbhrh.bib",
  "cited_by": 0,
  "doi": "10.1016/j.jcp.2026.115506",
  "fulltext_url": null,
  "id": "85vqj1pftbhrh",
  "issns": [
    "0021-9991",
    "1090-2716"
  ],
  "landing_url": "https://inria.hal.science/hal-05847256v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.phys.astr"
    ],
    [
      "hal",
      "2.phys.astr.sr"
    ],
    [
      "openalex",
      "3103|Solar and Space Plasma Dynamics"
    ]
  ],
  "openalex": "W7222847674",
  "pdf_url": "https://inria.hal.science/hal-05847256/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/85vqj1pftbhrh.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:44Z",
      "native_id": "hal-05847256",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05847256v1"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "hal:2.phys.astr.sr",
      "subfield": "stellar"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "Numerical modeling of oscillations for axisymmetric solar backgrounds with differential rotation and gravity",
  "title_text": "Numerical modeling of oscillations for axisymmetric solar backgrounds with differential rotation and gravity",
  "type": "peer-reviewed",
  "updated_at": "2026-11-03T12:20:17Z",
  "url": "https://research.draconitic.com/paper/85vqj1pftbhrh",
  "venue": "Journal of Computational Physics",
  "versions": []
}