{"paper":{"title":"Nested domain decomposition with polarized traces for the 2D Helmholtz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Laurent Demanet, Leonardo Zepeda-N\\'u\\~nez","submitted_at":"2015-10-07T05:42:19Z","abstract_excerpt":"We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media, with online parallel complexity that scales empirically as $\\mathcal{O}(\\frac{N}{P})$, where $N$ is the number of volume unknowns, and $P$ is the number of processors, as long as $P = \\mathcal{O}(N^{1/5})$. This sublinear scaling is achieved by domain decomposition, not distributed linear algebra, and improves on the $P =\\mathcal{O}(N^{1/8})$ scaling reported earlier in [L. Zepeda-N\\'u\\~nez and L. Demanet, J. Comput. Phys., 308 (2016), pp. 347-388 ]. The solver relies on a two-l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01831","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"}