{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T03:37:54Z","timestamp":1777865874779,"version":"3.51.4"},"reference-count":77,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2026,4,30]]},"DOI":"10.1137\/24m1707523","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:36:42Z","timestamp":1777534602000},"page":"510-536","source":"Crossref","is-referenced-by-count":0,"title":["Complex Scaling for the Helmholtz Equation with Dirichlet Boundary Conditions in a Perturbed Half-Space"],"prefix":"10.1137","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1831-473X","authenticated-orcid":true,"given":"Charles","family":"Epstein","sequence":"first","affiliation":[{"name":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2895-8715","authenticated-orcid":true,"given":"Leslie","family":"Greengard","sequence":"additional","affiliation":[{"name":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeremy","family":"Hoskins","sequence":"additional","affiliation":[{"name":"Department of Statistics and CCAM, University of Chicago, Chicago, IL 60637 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7482-8167","authenticated-orcid":true,"given":"Shidong","family":"Jiang","sequence":"additional","affiliation":[{"name":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5488-3839","authenticated-orcid":true,"given":"Manas","family":"Rachh","sequence":"additional","affiliation":[{"name":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2026,4,30]]},"reference":[{"key":"ref1","unstructured":"F. J. Agocs, T. Goodwill, and J. Hoskins, Complex Scaling for the Junction of Semi-infinite Gratings, preprint, https:\/\/arxiv.org\/abs\/2509.02951, 2025."},{"key":"ref2","unstructured":"S. Ambikasaran and E. Darve, The Inverse Fast Multipole Method, preprint, arXiv:1407.1572, 2014."},{"key":"ref3","unstructured":"T. Askham, et\u00a0al., chunkie:\u00a0A MATLAB Integral Equation Toolbox, https:\/\/github.com\/fastalgorithms\/chunkie, 2024."},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-004-0099-6"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1159"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/21M1459216"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/20M1387122"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/23M1607866"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.01.021"},{"key":"ref10","unstructured":"S. B\u00f6rm, \\(\\mathcal{H}\\)2Lib package, http:\/\/www.h2lib.org\/."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.4171\/091"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0955-7997(02)00152-2"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-015-0233-3"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90171-V"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759528555X"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.11.015"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.03.002"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6714"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2001.0882"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/15M1033782"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139108157"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/0909044"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1002\/mop.4650071304"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.05.007"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4942-3"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/15M1034477"},{"key":"ref27","series-title":"Contemp. Math. 408","first-page":"99","volume-title":"Inverse Problems, Multi-scale Analysis and Effective Medium Theory","author":"Crutchfield W.","year":"2006"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1063\/1.464397"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/200"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(74)90044-8"},{"key":"ref31","unstructured":"C. L. Epstein, Solving the Transmission Problem for Open Wave-Guides II:\u00a0Outgoing Estimates, preprint, https:\/\/arxiv.org\/abs\/2310.05816, 2023."},{"key":"ref32","unstructured":"C. L. Epstein, Solving the Transmission Problem for Open Wave-Guides I:\u00a0Fundamental Solutions and Integral Equations, preprint, arXiv:2302.04353, 2023."},{"key":"ref33","unstructured":"C. L. Epstein, T. Goodwill, J. Hoskins, S. Quinn, and M. Rachh, Complex Scaling for Open Waveguides, preprint, arXiv:2506.10263, 2025."},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.08.031"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-012-0188-3"},{"key":"ref36","unstructured":"H. Ginn and L. N. Trefethen, Lightning Helmholtz Solver, preprint, arXiv:2310.01665, 2023."},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-026-03282-z"},{"key":"ref38","unstructured":"T. Goodwill, L. Greengard, J. Hoskins, M. Rachh, and Y. Wang, Fast Multipole Method with Complex Coordinates, https:\/\/arxiv.org\/abs\/2509.05458, 2025."},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90140-9"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/s006070050015"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59709-1_2"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/PL00021408"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/938167"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1137\/120866683"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1201\/9780367806934"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.2140\/paa.2020.2.447"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2024.101721"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1137\/18M1199034"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2022.3161474"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.22240"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2006.880747"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.01.008"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-9593-2"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2016.10.005"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1137\/17M1112510"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1109\/TMTT.2017.2734090"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.020215.150515sw"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1137\/100786617"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.10.033"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1137\/16M1095949"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2013.04.012"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1121\/1.1819504"},{"key":"ref63","first-page":"857","volume":"12","author":"Odeh F. M.","year":"1963","journal-title":"J. Math. Mech."},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1109\/LMWC.2003.821492"},{"key":"ref65","volume-title":"NIST Handbook of Mathematical Functions","author":"Olver F. W. J.","year":"2010"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.62.5797"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.31.001738"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90107-C"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1609578113"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1991-1115789-9"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1002\/andp.19093330402"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1137\/22M1514040"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1137\/16M1068487"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(96)00016-1"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1016\/S0031-8914(35)90168-9"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1002\/andp.19193652104"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-021-01244-1"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:37:08Z","timestamp":1777534628000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1707523"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,30]]},"references-count":77,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4,30]]}},"alternative-id":["10.1137\/24M1707523"],"URL":"https:\/\/doi.org\/10.1137\/24m1707523","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,30]]}}}