{
  "abstract": "We consider the numerical solution of the linear Vlasov transport equation on bounded spatial domains with inflow boundary conditions based on low-rank approximation. We combine a finite volume discretization with a rank-adaptive step-and-truncate scheme for the resulting matrix ODE. The spatial and velocity meshes may be unstructured, while suitable numerical fluxes retain a separated space-velocity representation. For homogeneous inflow, we show that the low-rank scheme inherits the $L_2$ stability and CFL restriction of the underlying full finite volume forward Euler method. In addition, the low-rank approximation error is bounded explicitly in terms of the truncation tolerances, avoiding the modeling error associated with tangent-space projections in dynamical low-rank approximation. Numerical experiments in 1d1v and 2d2v confirm the predicted error behavior. In 2d2v, the method handles an unstructured spatial mesh with nonzero inflow and a full tensor-product discretization of approximately $5.8\\cdot10^{10}$ phase-space cells while the numerical rank is at most twelve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02721",
  "author_total": 2,
  "authors": [
    {
      "name": "André Uschmajew"
    },
    {
      "name": "Andreas Zeiser"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5rj4n9tzg93cw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02721",
  "fulltext_url": null,
  "id": "5rj4n9tzg93cw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02721",
  "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",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7207517600",
  "pdf_url": "https://arxiv.org/pdf/2609.02721",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5rj4n9tzg93cw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02721",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02721"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A stable rank-adaptive step-and-truncate finite volume method for Vlasov transport on domains with piecewise linear boundaries",
  "title_text": "A stable rank-adaptive step-and-truncate finite volume method for Vlasov transport on domains with piecewise linear boundaries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/5rj4n9tzg93cw",
  "venue": "arXiv",
  "versions": []
}