{
  "abstract": "We develop an energy-optimal generalized scalar auxiliary variable (EOP-GSAV) framework for nonlinear index-one port-Hamiltonian differential-algebraic equations (pH-DAEs). Exploiting the port-Hamiltonian structure, we separate the nonlinear effort, interconnection, and dissipation terms from a constant implicit core. The resulting BDF-1 and BDF-2 schemes require one linear solve per time step with a reusable factorization, while retaining discrete passivity and accurate tracking of the Hamiltonian. The schemes are compared with the implicit midpoint method equipped with full, modified, and frozen-Jacobian Newton iterations. Numerical experiments ranging from a strongly state-dependent nonlinear stress test to large-scale benchmarks demonstrate robust and competitive performance, with substantial efficiency gains in matched-accuracy regimes. A comparison with SUNDIALS IDA shows comparable work-precision behavior at equal order despite a non-specialized Python/SciPy implementation, while unrestricted variable-order adaptive IDA is faster in the high-accuracy regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05246",
  "author_total": 3,
  "authors": [
    {
      "name": "Aashutosh Sharma"
    },
    {
      "name": "Andreas Bartel"
    },
    {
      "name": "Manuel Schaller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20c13wvy4p95s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05246",
  "fulltext_url": null,
  "id": "20c13wvy4p95s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05246",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7211876517",
  "pdf_url": "https://arxiv.org/pdf/2609.05246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20c13wvy4p95s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Generalized Scalar Auxiliary Variable Method for Structure-Preserving and Efficient Integration of Nonlinear port-Hamiltonian DAEs",
  "title_text": "A Generalized Scalar Auxiliary Variable Method for Structure-Preserving and Efficient Integration of Nonlinear port-Hamiltonian DAEs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/20c13wvy4p95s",
  "venue": "arXiv",
  "versions": []
}