{"paper":{"title":"Variable Order, Directional H2-Matrices for Helmholtz Problems with Complex Frequency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Maria Lopez-Fernandez, Stefan Sauter, Steffen B\\\"orm","submitted_at":"2019-03-07T10:03:04Z","abstract_excerpt":"The sparse approximation of high-frequency Helmholtz-type integral operators has many important physical applications such as problems in wave propagation and wave scattering. The discrete system matrices are huge and densely populated; hence their sparse approximation is of outstanding importance. In our paper we will generalize the directional $\\mathcal{H}^{2}$-matrix techniques from the \\textquotedblleft pure\\textquotedblright\\ Helmholtz operator $\\mathcal{L}u=-\\Delta u+\\zeta^{2}u$ with $\\zeta=-\\operatorname*{i}k$, $k\\in\\mathbb{R}$, to general complex frequencies $\\zeta\\in\\mathbb{C}$ with $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02803","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"}