{
  "abstract": "This paper derives a design principle for structure-preserving Galerkin formulations of energy-conserving hyperbolic systems. The aim is to reproduce the modal-energy-exchange structure of the continuous system within a resolved finite-mode space. Total energy conservation follows from this structure. We introduce a state-dependent physical-energy metric H and derive the corresponding energy-compatibility identity. In the infinite-mode exact-integration model, the volume contribution has an antisymmetric representation after H-orthogonalization, yielding pairwise modal energy exchange. Interface contributions take the same exchange form. To reproduce this structure in the practical finite-mode system, we combine two constructions: a Galerkin projection coupled with the physical-energy metric that guarantees the H-metric summation-by-parts identity, and an energy-compatibility closure that removes the component of the compatibility action contributing to the scalar energy residual. With a shared numerical energy flux at interfaces, they close the total-energy balance of the finite-mode system while preserving pairwise modal energy exchange. We also compare the practical operator construction with the finite-mode exact-integration reference and obtain an O(h^p+1) defect estimate. Finally, we derive an equivalent form of the resulting equation in the fixed Galerkin basis for direct implementation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.05781",
  "author_total": 1,
  "authors": [
    {
      "name": "Hirofumi Tomita"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cy071a7kvpyd0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05781",
  "fulltext_url": null,
  "id": "cy071a7kvpyd0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.05781",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7167701936",
  "pdf_url": "https://arxiv.org/pdf/2607.05781",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cy071a7kvpyd0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2607.05781",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05781"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Design Principle for Mode-Consistent Galerkin Closure under a Physical Energy Metric for Hyperbolic Systems",
  "title_text": "Design Principle for Mode-Consistent Galerkin Closure under a Physical Energy Metric for Hyperbolic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/cy071a7kvpyd0",
  "venue": "arXiv",
  "versions": []
}