{"paper":{"title":"The method of 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":"2014-10-22T04:04:02Z","abstract_excerpt":"We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as $\\mathcal{O}(\\frac{N}{L})$, where $N$ is the number of volume unknowns, and $L$ is the number of processors, as long as $L$ grows at most like a small fractional power of $N$. The solver decomposes the domain into layers, and uses transmission conditions in boundary integral form to explicitly define \"polarized traces\", i.e., up- and down-going waves sampled at interfaces. Local direct solvers are used in each layer to precompute traces of l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5910","kind":"arxiv","version":3},"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"}