{
  "abstract": "This paper presents a residual-constrained topology optimization framework that controls interface transition bandwidth without requiring external density filters. The steady conserved Allen--Cahn (AC) equation is formulated as an equality residual constraint and solved via a mass-weighted Augmented Lagrangian Method (ALM) coupled with the Method of Moving Asymptotes (MMA). A closed-form chemical potential projection eliminates the constant residual mode, ensuring algebraic compatibility with external volume targets. Variational sensitivity analysis reveals a symmetric-plus-rank-one Jacobian that yields matrix-free sensitivities without additional adjoint PDE solves, reducing residual sensitivity overhead to only 0.11% of the state elasticity solve time in 3D. Systematic 2D benchmarks confirm that interface bandwidth is governed intrinsically by reaction--diffusion parameters across mesh refinements. While diffuse interfaces incur a continuous compliance elevation (1.4%--12.3%), a volume-preserving 0/1 post-processing audit across 48 benchmark cases demonstrates that this gap stems primarily from intermediate-density penalization: binarized AC-ALM designs achieve equal or superior stiffness in 45 configurations (averaging 1.2% stiffer than SIMP). Simultaneously, single-node hinges and strut fragmentation are substantially suppressed compared to unregularized baselines. Three-dimensional benchmarks further demonstrate practical spatial viability for complex structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02375",
  "author_total": 4,
  "authors": [
    {
      "name": "Run Du"
    },
    {
      "name": "Xuan Xiao"
    },
    {
      "name": "Wenming Cheng"
    },
    {
      "name": "Zeqiang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09evrvrbnm8vv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02375",
  "fulltext_url": null,
  "id": "09evrvrbnm8vv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02375",
  "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.CE"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02375",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09evrvrbnm8vv.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02375",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02375"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Allen--Cahn Residual-Constrained Topology Optimization via an Augmented Lagrangian Method",
  "title_text": "Allen--Cahn Residual-Constrained Topology Optimization via an Augmented Lagrangian Method",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/09evrvrbnm8vv",
  "venue": "arXiv",
  "versions": []
}