{"paper":{"title":"An algorithmic exploration of the existence of high-order summation by parts operators with diagonal norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Joshua Klarmann, Nathan Albin","submitted_at":"2014-03-23T13:18:43Z","abstract_excerpt":"This paper explores a common class of diagonal-norm summation by parts (SBP) operators found in the literature, which can be parameterized by an integer triple $(s,t,r)$ representing the interior order of accuracy ($2s)$, the boundary order of accuracy ($t$), and the dimension of the boundary closure ($r$). There is no simple formula for determining whether or not an SBP operator exists for a given triple of parameters. Instead, one must check that certain compatibility conditions are met: namely that a particular linear system of equations has a positive solution. Partly because of the comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5750","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"}