{"paper":{"title":"A new extrapolation cascadic multigrid method for 3D elliptic boundary value problems on rectangular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dongdong He, Hongling Hu, Kejia Pan","submitted_at":"2015-06-09T16:24:36Z","abstract_excerpt":"In this paper, we develop a new extrapolation cascadic multigrid (ECMG$_{jcg}$) method, which makes it possible to solve 3D elliptic boundary value problems on rectangular domains of over 100 million unknowns on a desktop computer in minutes. First, by combining Richardson extrapolation and tri-quadratic Serendipity interpolation techniques, we introduce a new extrapolation formula to provide a good initial guess for the iterative solution on the next finer grid, which is a third order approximation to the finite element (FE) solution. And the resulting large sparse linear system from the FE d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02983","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"}