{
  "abstract": "This work develops tensor-train (TT) formulations for solving large-scale three-dimensional linear elasticity problems discretized by isogeometric analysis. By exploiting the tensor-product structure of the basis functions and the low-rank structure of geometry-dependent coefficient fields, the stiffness operator, mass operator, force vector, and displacement solution are represented in TT format. Two solution strategies are investigated: a block-operator formulation, in which the coupled elasticity operator is stored as separated TT blocks, and a single-operator formulation, in which the full coupled system is stored as one monolithic TT operator. A matrix-free three-field TT conjugate-gradient solver is introduced for the block formulation, while AMEn is used for the single-operator formulation. Numerical examples demonstrate substantial compression of both operators and solutions compared with conventional sparse full-grid representations, showing that TT-based formulations provide an efficient and scalable approach for large-scale three-dimensional elasticity simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23595",
  "author_total": 4,
  "authors": [
    {
      "name": "Quoc Thai Tran"
    },
    {
      "name": "Duc P. Truong"
    },
    {
      "name": "William Dai"
    },
    {
      "name": "Kim Ø. Rasmussen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hzxs5n3yc2dk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23595",
  "fulltext_url": null,
  "id": "6hzxs5n3yc2dk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23595",
  "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",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7204241386",
  "pdf_url": "https://arxiv.org/pdf/2608.23595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hzxs5n3yc2dk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.23595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Tensor-Train Isogeometric Analysis for Large-Scale Three-Dimensional Linear Elasticity",
  "title_text": "Tensor-Train Isogeometric Analysis for Large-Scale Three-Dimensional Linear Elasticity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/6hzxs5n3yc2dk",
  "venue": "arXiv",
  "versions": []
}