{"paper":{"title":"Algebraic dual polynomials for the equivalence of curl-curl problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Artur Palha, Marc Gerritsma, Varun Jain, Yi Zhang","submitted_at":"2018-04-30T22:11:28Z","abstract_excerpt":"In this paper we will consider two curl-curl equation in two dimensions. One curl-curl problem for a scalar quantity $F$ and one problem for a vector field $\\bf{E}$. For Dirichlet boundary conditions $\\bf{n} \\times \\bf{E} =$ $ \\hat{E}_{\\dashv}$ on $\\bf{E}$ and Neumann boundary conditions $\\bf{n} \\times \\mbox{curl}$ $F=\\hat{E}_{\\dashv}$, we expect the solutions to satisfy $\\bf{E}=\\mbox{curl}$ $F$. When we use algebraic dual polynomial representations, these identities continue to hold at the discrete level. Equivalence will be proved and illustrated with a computational example."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00114","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"}