{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:59:00Z","timestamp":1787504340616,"version":"build-2736575974"},"reference-count":45,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2024,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper presents a novel boundary integral equation (BIE) formulation for the two-dimensional time-harmonic water-waves problem. It utilizes a complex-scaled Laplace free-space Green\u2019s function, resulting in a BIE posed on the infinite boundaries of the domain. The perfectly matched layer (PML) coordinate stretching that is used to render propagating waves exponentially decaying allows for the effective truncation and discretization of the BIE unbounded domain. We show through a variety of numerical examples that, despite the logarithmic growth of the complex-scaled Laplace free-space Green\u2019s function, the truncation errors are exponentially small with respect to the truncation length. Our formulation uses only simple function evaluations (e.g., complex logarithms and square roots), hence avoiding the need to compute the involved water-wave Green\u2019s function. Finally, we show that the proposed approach can also be used to find complex resonances through a linear eigenvalue problem since the Green\u2019s function is frequency-independent.<\/jats:p>","DOI":"10.1137\/23m1607866","type":"journal-article","created":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T04:01:31Z","timestamp":1721275291000},"page":"1532-1556","source":"Crossref","is-referenced-by-count":10,"title":["A Complex-Scaled Boundary Integral Equation for Time-Harmonic Water Waves"],"prefix":"10.1137","volume":"84","author":[{"given":"Anne-Sophie Bonnet-Ben","family":"Dhia","sequence":"first","affiliation":[{"name":"POEMS, CNRS, Inria, ENSTA Paris, Institut Polytechnique de Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8090-934X","authenticated-orcid":true,"given":"Luiz M.","family":"Faria","sequence":"additional","affiliation":[{"name":"POEMS, CNRS, Inria, ENSTA Paris, Institut Polytechnique de Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1647-4019","authenticated-orcid":true,"given":"Carlos","family":"P\u00e9rez-Arancibia","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Twente, Enschede, The Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,7,18]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597325141"},{"key":"ref2","unstructured":"T. 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