{"paper":{"title":"Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ansar Calloo, Fran\\c{c}ois Madiot, Henry Lockyer, Luca Zanetti, Matthew Evans, Tristan Pryer","submitted_at":"2024-12-02T16:10:57Z","abstract_excerpt":"We introduce a novel property of bounded Voronoi tessellations that\n  enables cycle-free mesh sweeping algorithms. We prove that a\n  topological sort of the dual graph of any Voronoi tessellation is\n  feasible in any flow direction and dimension, allowing\n  straightforward application to discontinuous Galerkin (DG)\n  discretisations of first-order hyperbolic partial differential\n  equations and the Boltzmann Transport Equation (BTE) without\n  requiring flux-cycle corrections.\n  We also present an efficient algorithm to perform the topological\n  sort on the dual mesh nodes, ensuring a valid swe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01660","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.01660/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}