{
  "abstract": "In this work, we develop a second-order, linear, decoupled, and structure-preserving numerical scheme for the modified Landau--de Gennes model of smectic-A (SmA) liquid crystals. The main contributions are threefold. First, to the best of our knowledge, we propose the first integration of the generalized scalar auxiliary variable (GSAV) approach with a second-order exponential time-differencing Runge--Kutta (ETDRK2) discretization, leading to a second-order GSAV--ETD2 scheme. Second, we prove that the proposed scheme satisfies an unconditional energy-dissipation law, thereby closing the theoretical gap in the energy-stability analysis of second-order GSAV exponential integrators of this class. Third, by deriving a coercive discrete reformulation, we establish a fully discrete error estimate without imposing any coupling condition between $τ$ and $h$, achieving the optimal convergence rate $\\mathcal{O}(τ^2+h^2)$. Numerical experiments are presented to verify our theoretical results and to simulate the self-assembly dynamics of the SmA phase.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21175",
  "author_total": 3,
  "authors": [
    {
      "name": "Wenshuai Hu"
    },
    {
      "name": "Guanghua Ji"
    },
    {
      "name": "Xiao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/et8jshq8qent5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21175",
  "fulltext_url": null,
  "id": "et8jshq8qent5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21175",
  "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",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7213957068",
  "pdf_url": "https://arxiv.org/pdf/2609.21175",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/et8jshq8qent5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2609.21175",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21175"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Energy stability and error estimates for a second-order structure-preserving exponential integrator method for smectic-A liquid crystals",
  "title_text": "Energy stability and error estimates for a second-order structure-preserving exponential integrator method for smectic-A liquid crystals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/et8jshq8qent5",
  "venue": "arXiv",
  "versions": []
}