{"paper":{"title":"Numerical solution of scattering problems using a Riemann--Hilbert formulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Elena Luca, Stefan G. Llewellyn Smith","submitted_at":"2019-04-07T22:31:43Z","abstract_excerpt":"A fast and accurate numerical method for the solution of scalar and matrix Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as Riemann--Hilbert problems on the real line, and a numerical approach developed for these problems is used. It is shown that the known far-field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results. A number of scalar and matrix Wiener--Hopf problems that generalize the classical Sommerfeld problem of diffraction of plane waves by a semi-infinite plane are solved using the approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03762","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"}