{
  "abstract": "In this work, we develop a two-level overlapping preconditioner for time-dependent problems in high-contrast multiscale media. We present a coarse-space construction based on multiscale methods, with emphasis on the relaxed nonlocal multicontinuum (NLMC) method. The NLMC space can be separated into components representing the high-permeability regions and the low-permeability background. We show that the complete NLMC space effectively preconditions the heterogeneous stiffness operator, whereas the high-permeability component alone captures the contrast-dependent global modes. For suitable small time-step sizes, the mass matrix controls the low-permeability contribution and only the high-permeability component in NLMC space is required for the global coarse correction in the two-level preconditioner. For general time-step sizes, performance can be maintained by using the full NLMC space or augmenting the high-permeability component with a standard multiscale space. The proposed coarse-space construction lowers the computational cost while preserving robustness with respect to coefficient contrast and fine-scale resolution. To further improve efficiency, the multiscale basis functions can be constructed by iteratively solving the relaxed energy-minimizing formulation. We demonstrate the robustness, efficiency and scalability of the proposed method through several numerical experiments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27958",
  "author_total": 3,
  "authors": [
    {
      "name": "Yating Wang"
    },
    {
      "name": "Yibao Li"
    },
    {
      "name": "Wing Tat Leung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c220a1qs9w5w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27958",
  "fulltext_url": null,
  "id": "6c220a1qs9w5w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27958",
  "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": "W7204815184",
  "pdf_url": "https://arxiv.org/pdf/2608.27958",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c220a1qs9w5w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27958",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27958"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Two-Level Preconditioner Based on Dominant Components for Time-Dependent Multiscale High-Contrast Problem",
  "title_text": "A Two-Level Preconditioner Based on Dominant Components for Time-Dependent Multiscale High-Contrast Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/6c220a1qs9w5w",
  "venue": "arXiv",
  "versions": []
}