{"paper":{"title":"Asymptotic Preserving scheme for strongly anisotropic parabolic equations for arbitrary anisotropy direction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jacek Narski, Maurizio Ottaviani","submitted_at":"2013-03-21T10:31:27Z","abstract_excerpt":"This paper deals with the numerical study of a strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. Furthermore, the recently proposed Asymptotic-Preserving method [arXiv:1203.6739] allows to perform simulations regardless of the anisotropy strength but its application is limited to the case, where the anisotropy direction is given by a field with all field lines open. In this paper we introduce a new Asymptotic-Preserving method, which overcomes those limitations without any loss of precision or increase in the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5219","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}