{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T17:09:27Z","timestamp":1769274567613,"version":"3.49.0"},"reference-count":69,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Exascale Computing Project","award":["17-SC-20-SC"],"award-info":[{"award-number":["17-SC-20-SC"]}]},{"DOI":"10.13039\/100017223","name":"National Energy Research Scientific Computing Center","doi-asserted-by":"crossref","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}],"id":[{"id":"10.13039\/100017223","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2012046"],"award-info":[{"award-number":["2012046"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2152011"],"award-info":[{"award-number":["2152011"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["AC02-05CH11231"],"award-info":[{"award-number":["AC02-05CH11231"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2023,3,31]]},"DOI":"10.1137\/21m1450422","type":"journal-article","created":{"date-parts":[[2023,2,23]],"date-time":"2023-02-23T11:57:36Z","timestamp":1677153456000},"page":"269-308","source":"Crossref","is-referenced-by-count":6,"title":["A Fast Butterfly-Compressed Hadamard\u2013Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources"],"prefix":"10.1137","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3750-1178","authenticated-orcid":true,"given":"Yang","family":"Liu","sequence":"first","affiliation":[{"name":"Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Michigan State University, East Lansing, MI 48824 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Burridge","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianliang","family":"Qian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Michigan State University, East Lansing, MI 48824 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2023,2,25]]},"reference":[{"key":"ref1","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz M.","year":"1965"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/120903476"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160160402"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(65)90021-2"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(95)00890-X"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994269186"},{"key":"ref7","series-title":"Lect. Notes Comput. Sci. Eng. 63","volume-title":"Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems","author":"Bebendorf M.","year":"2008"},{"key":"ref8","series-title":"Lecture notes","volume-title":"Hierarchical Matrices","author":"Boerm S.","year":"2006"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/080734339"},{"key":"ref11","volume":"10","author":"Chen Z.","year":"2013","journal-title":"Int. J. Numer. Anal. Model."},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/130917144"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1145\/992200.992206"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1145\/356044.356047"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1093\/gji\/ggaa503"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20358"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/100804644"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21755"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.03.011"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1186\/s40687-017-0098-9"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.05.029"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/0710032"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6903"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/LAWP.2012.2234433"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2017.2727511"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1002\/mop.31166"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1121\/1.387099"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.11.007"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/18M1218078"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-57-02471-7"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1145\/779359.779361"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1137\/16M1074941"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/15M1007173"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/20M1349667"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/LAWP.2016.2626786"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1137\/20M1315853"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109014"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1137\/15M1052469"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.02.048"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1137\/17M1130381"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.03.066"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1137\/120901696"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1002\/mop.4650071707"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/8.511816"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(98)00326-0"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.02.002"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2009.08.005"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1190\/1.2759835"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1137\/19M1294873"},{"key":"ref53","first-page":"1774","volume-title":"Prestack Depth Migration and Velocity Model Building","author":"Pica A.","year":"1997"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1137\/15M1013158"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1137\/20M1322224"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-015-0111-7"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2021.3137193"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.1984.1143193"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.01.039"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025380731197"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1190\/segam2016-13848017.1"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.05.004"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.02.015"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1137\/110848062"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-010-9345-6"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.02.044"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1137\/08071291X"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1016\/j.jqsrt.2007.01.034"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.11.040"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1137\/16M1064660"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2005.02626.x"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-005-9014-3"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-04-01678-3"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T14:18:37Z","timestamp":1694614717000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1450422"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,25]]},"references-count":69,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,3,31]]}},"alternative-id":["10.1137\/21M1450422"],"URL":"https:\/\/doi.org\/10.1137\/21m1450422","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,25]]}}}