{
  "abstract": "The repeated assembly of the sparse Jacobian matrix constitutes a primary computational bottleneck in the Newton-Raphson power-flow analysis. Through an algebraic equivariance analysis of the Jacobian matrix, this paper proposes a direct sparse Jacobian assembly method based on symbolic permutation. By pre-applying the permutation to the admittance matrix during a one-time symbolic phase, the runtime bus-type projection overhead is entirely eliminated. Consequently, complex Jacobian differentiation and global matrix assembly fuse into a single operation, yielding a single-pass, branchless algorithm that streams values directly into contiguous memory. The framework is realized in the open-source RustPower solver. Benchmarks on IEEE test systems and PEGASE 9241 demonstrate that the proposed assembly is 24.4-30.1x faster than the MATPOWER- style baseline and 6.0-7.8x faster than the Schafer-Braun optimized assembly. End-to-end, the grid-level solve time is 11.7x-154.3x faster than pandapower 3.5.4 with Numba, while leaving numerical results and convergence behavior unchanged. Compared with the native C++ LightSim2Grid 1.0.0, grid-level performance is comparable on IEEE 39 and 1.3x-1.8x faster on IEEE 118 and the PEGASE systems. The method extends directly to general problems where a sparse Jacobian inherits its structure from a static network operator, including transient stability analysis, EMT simulation, and OPF Hessian assembly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12654",
  "author_total": 2,
  "authors": [
    {
      "name": "Tianshi Cheng"
    },
    {
      "name": "Venkata Dinavahi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42jxabmbjgewk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12654",
  "fulltext_url": null,
  "id": "42jxabmbjgewk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12654",
  "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",
      "cs.PF"
    ],
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      "arxiv",
      "cs.SY"
    ],
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      "arxiv",
      "eess.SY"
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    [
      "arxiv",
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    [
      "openalex",
      "2208|Optimal Power Flow Distribution"
    ]
  ],
  "openalex": "W7221522115",
  "pdf_url": "https://arxiv.org/pdf/2610.12654",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42jxabmbjgewk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12654",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12654"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Symbolic-Permutation-Based Direct Sparse Jacobian Assembly for Accelerated Power-Flow Analysis",
  "title_text": "Symbolic-Permutation-Based Direct Sparse Jacobian Assembly for Accelerated Power-Flow Analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/42jxabmbjgewk",
  "venue": "arXiv",
  "versions": []
}