{
  "abstract": "Significant spatial heterogeneity and nonlocal history-dependent attenuation jointly govern wave propagation in composite materials, making full-scale direct numerical simulation (DNS) computationally prohibitive. This study proposed a high-order multi-scale (HOMS) method for nonlocal-in-time fractionally damped wave problems with highly oscillatory and discontinuous material coefficients. Using a multi-scale asymptotic expansion approach, the macroscopic homogenized equation, and first- and second-order correction terms are derived to construct the high-accuracy HOMS solution. Moreover, a local pointwise error analysis identifies the leading residual eliminated by this HOMS solution and validates its local physical balance preservation. Then, a global energy-norm error estimate establishes the $O(\\varepsilon)$-order convergence rate for the HOMS solution. Subsequently, an efficient spatiotemporal multi-scale algorithm integrating the finite element and finite difference methods is designed, which employs a novel fully discrete $L2\\text{-}1_σ$-Newmark scheme, and corresponding unconditional shifted-energy stability and explicit convergence rates are also obtained for the macroscopic homogenized displacement and velocity, respectively. Both two- and three-dimensional examples are presented to demonstrate the accuracy, efficiency, reduced cost, and robustness of the proposed HOMS method. This work provides an effective multi-scale tool for nonlocal-in-time wave simulation in engineering applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29451",
  "author_total": 4,
  "authors": [
    {
      "name": "Gehao Wang"
    },
    {
      "name": "Hao Dong"
    },
    {
      "name": "Yufeng Nie"
    },
    {
      "name": "Junzhi Cui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cs81azz886w19.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29451",
  "fulltext_url": null,
  "id": "cs81azz886w19",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29451",
  "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",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7223247399",
  "pdf_url": "https://arxiv.org/pdf/2610.29451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cs81azz886w19.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A high-order multi-scale method and its error analysis for nonlocal-in-time fractionally damped wave problems in composite materials",
  "title_text": "A high-order multi-scale method and its error analysis for nonlocal-in-time fractionally damped wave problems in composite materials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/cs81azz886w19",
  "venue": "arXiv",
  "versions": []
}