{
  "abstract": "Finite-element analysis (FEA) flux maps are widely used in reduced electrical-machine lookup-table (LUT) models. However, the local dynamics of an implemented LUT representation need not match those inferred from separately interpolated derivative maps. This study develops a representation-aware numerical analysis workflow for a 100 kW externally excited synchronous machine. A formal atlas of 10,230 grid–knot matrices is compared with the audited trilinear representation at grid knots and at 5000 strictly off-grid cell-center equilibria. Although interior-knot constructions agree closely, the Jacobian of the implemented LUT representation is non-Hurwitz at 488 of 5000 within-cell equilibrium centers (9.76%), whereas the derivative-consistent comparator is Hurwitz at all centers. An extended nine-point audit of 1660 center-admissible geometric cells at five speeds (8300 cell-speed groups) retains 73,900 current-limit-valid design locations; within this finite design, 16,526 of 73,900 implemented-model Jacobians (22.36%) are non-Hurwitz, compared with 0% for the derivative-consistent representation. Interpolation-family and grid-resolution sensitivities preserve the qualitative operator-order effect. On the 832-point common strict-domain subset, Heun and classical fourth-order Runge–Kutta (RK4) remain markedly more accurate than Euler-based alternatives. The results show that interpolation–differentiation consistency should be established before interpreting model-predicted local continuous-time stability and fixed-step numerical admissibility. These percentages describe two distinct finite designs and do not estimate continuous-domain prevalence.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Electricity and Energy, Bigadiç Vocational School, Balıkesir University, 10440 Bigadiç, Türkiye"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Oktay Karakaya",
      "orcid": "0000-0003-3871-1724"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkmp7d9mfbbx7.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213880",
  "fulltext_url": null,
  "id": "dkmp7d9mfbbx7",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3880",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2208|Electric Motor Design and Analysis"
    ]
  ],
  "openalex": "W7223667707",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/dkmp7d9mfbbx7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14213880",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3880"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Interpolation–Differentiation Mismatch and Local Stability in FEA-Based Electrical-Machine Lookup Tables",
  "title_text": "Interpolation–Differentiation Mismatch and Local Stability in FEA-Based Electrical-Machine Lookup Tables",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/dkmp7d9mfbbx7",
  "venue": "Mathematics",
  "versions": []
}