{
  "abstract": "We generalize the compact residual-screened local reduced-order model (CL-ROM) from Brinkman-penalized flow to shape optimization with the diffuse domain method (DDM). As with Brinkman penalization, DDM extends evolving-domain problems to a fixed rectangular domain, allowing one grid for discretization and directly compatible snapshots from different designs. Unlike Brinkman penalization, DDM uses a phase field to weight operators and sources and treats Dirichlet, Neumann and Robin conditions through diffuse boundary terms. The CL-ROM mechanism carries over: recent full-order and corrected solutions determine local reduced spaces, while residual screening, correction with retained factors and objective verification decide when a full-order solve is needed. We derive reduced operators, residuals and sensitivities for each diffuse model, using Galerkin projection for the symmetric problems and least-squares Petrov--Galerkin projection for nonlinear flow. For the symmetric problems we prove a local approximation estimate that admits inexact, corrected snapshots. In numerical tests of shape identification, drag minimization in Navier--Stokes channel flow and compliance minimization of a cantilever, CL-ROM uses reduced solutions for nearly all design updates, reproduces the full-order objectives with relative differences below $5\\times10^{-6}$, and is $3.85$ to $7.65$ times faster than a full-order baseline that reuses factorizations as preconditioners.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04864",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiaoping Zhang"
    },
    {
      "name": "Anusooya Vasudevan"
    },
    {
      "name": "Lili Ju"
    },
    {
      "name": "Zhu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ewzhy919a7e0n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04864",
  "fulltext_url": null,
  "id": "ewzhy919a7e0n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04864",
  "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",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04864",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ewzhy919a7e0n.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04864",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04864"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Compact Residual-Screened Local Reduced-Order Model for Diffuse-Domain Shape Optimization",
  "title_text": "A Compact Residual-Screened Local Reduced-Order Model for Diffuse-Domain Shape Optimization",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:38Z",
  "url": "https://research.draconitic.com/paper/ewzhy919a7e0n",
  "venue": "arXiv",
  "versions": []
}