{"paper":{"title":"The Geometry of r-adaptive meshes generated using Optimal Transport Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"C.J. Budd, E. Walsh, R. D. Russell","submitted_at":"2014-09-18T16:16:23Z","abstract_excerpt":"The principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods, and a metric tensor M and mesh metric are useful theoretical tools for understanding a methods level of mesh alignment, or anisotropy. We consider a mesh redistribution method based on the Monge-Ampere equation, which combines equidistribution of a given scalar density function with optimal transport. It does not involve explicit use of a metric tensor M, although such a tensor must exist for the method, and an interesting question to ask is whether or not the alignment produced by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5361","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":""},"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"}