{"paper":{"title":"Optimal additive Schwarz methods for the $hp$-BEM: the hypersingular integral operator in 3D on locally refined meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Rieder, Dirk Praetorius, Jens Markus Melenk, Thomas F\\\"uhrer","submitted_at":"2014-12-05T15:14:05Z","abstract_excerpt":"We propose and analyze an overlapping Schwarz preconditioner for the $p$ and $hp$ boundary element method for the hypersingular integral equation in 3D. We consider surface triangulations consisting of triangles. The condition number is bounded uniformly in the mesh size $h$ and the polynomial order $p$. The preconditioner handles adaptively refined meshes and is based on a local multilevel preconditioner for the lowest order space. Numerical experiments on different geometries illustrate its robustness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2024","kind":"arxiv","version":2},"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"}