{"id":"https://openalex.org/W7160089493","doi":"https://doi.org/10.1137/24m1707523","title":"Complex Scaling for the Helmholtz Equation with Dirichlet Boundary Conditions in a Perturbed Half-Space","display_name":"Complex Scaling for the Helmholtz Equation with Dirichlet Boundary Conditions in a Perturbed Half-Space","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7160089493","doi":"https://doi.org/10.1137/24m1707523"},"language":"en","primary_location":{"id":"doi:10.1137/24m1707523","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1707523","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135178239","display_name":"Charles Epstein","orcid":"https://orcid.org/0000-0003-1831-473X"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles Epstein","raw_affiliation_strings":["Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA"],"raw_orcid":"https://orcid.org/0000-0003-1831-473X","affiliations":[{"raw_affiliation_string":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA","institution_ids":["https://openalex.org/I4210107338"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135223269","display_name":"Leslie Greengard","orcid":"https://orcid.org/0000-0003-2895-8715"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leslie Greengard","raw_affiliation_strings":["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"],"raw_orcid":"https://orcid.org/0000-0003-2895-8715","affiliations":[{"raw_affiliation_string":"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","institution_ids":["https://openalex.org/I4210107338"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121185049","display_name":"Jeremy Hoskins","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeremy Hoskins","raw_affiliation_strings":["Department of Statistics and CCAM, University of Chicago, Chicago, IL 60637 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and CCAM, University of Chicago, Chicago, IL 60637 USA","institution_ids":["https://openalex.org/I39422238","https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057037289","display_name":"Shidong Jiang","orcid":"https://orcid.org/0000-0001-7482-8167"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shidong Jiang","raw_affiliation_strings":["Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA"],"raw_orcid":"https://orcid.org/0000-0001-7482-8167","affiliations":[{"raw_affiliation_string":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA","institution_ids":["https://openalex.org/I4210107338"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005247922","display_name":"Manas Rachh","orcid":"https://orcid.org/0000-0001-5488-3839"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Manas Rachh","raw_affiliation_strings":["Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA"],"raw_orcid":"https://orcid.org/0000-0001-5488-3839","affiliations":[{"raw_affiliation_string":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA","institution_ids":["https://openalex.org/I4210107338"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.56140351,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"2","first_page":"510","last_page":"536"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.46299999952316284,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.46299999952316284,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.08060000091791153,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.07100000232458115,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5525000095367432},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.5379999876022339},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5117999911308289},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4740999937057495},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4706000089645386},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.38019999861717224},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.34529998898506165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7263000011444092},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6309000253677368},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5525000095367432},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.5379999876022339},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5117999911308289},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4740999937057495},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4706000089645386},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.38019999861717224},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C103302479","wikidata":"https://www.wikidata.org/wiki/Q1227685","display_name":"Dirichlet conditions","level":5,"score":0.2777999937534332},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C148158259","wikidata":"https://www.wikidata.org/wiki/Q975727","display_name":"Dirichlet's principle","level":4,"score":0.2567000091075897},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2533999979496002},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1707523","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1707523","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400944828987122,"id":"https://metadata.un.org/sdg/13","display_name":"Climate action"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W1425400007","https://openalex.org/W1523113578","https://openalex.org/W1569304948","https://openalex.org/W1602760118","https://openalex.org/W1981045787","https://openalex.org/W1983103429","https://openalex.org/W1990081118","https://openalex.org/W1994751539","https://openalex.org/W1995270405","https://openalex.org/W2003017040","https://openalex.org/W2003646019","https://openalex.org/W2010717035","https://openalex.org/W2014698679","https://openalex.org/W2018419001","https://openalex.org/W2023736082","https://openalex.org/W2029141900","https://openalex.org/W2035247783","https://openalex.org/W2037512470","https://openalex.org/W2040187556","https://openalex.org/W2051083496","https://openalex.org/W2051395078","https://openalex.org/W2067174909","https://openalex.org/W2075458281","https://openalex.org/W2077852080","https://openalex.org/W2080803508","https://openalex.org/W2083206954","https://openalex.org/W2088527939","https://openalex.org/W2089210221","https://openalex.org/W2090717146","https://openalex.org/W2108470252","https://openalex.org/W2114781883","https://openalex.org/W2120660542","https://openalex.org/W2124042568","https://openalex.org/W2133858981","https://openalex.org/W2147056396","https://openalex.org/W2159257047","https://openalex.org/W2160651214","https://openalex.org/W2170585064","https://openalex.org/W2224779109","https://openalex.org/W2472704510","https://openalex.org/W2494125239","https://openalex.org/W2523870537","https://openalex.org/W2531046642","https://openalex.org/W2737367458","https://openalex.org/W2746683429","https://openalex.org/W2799865484","https://openalex.org/W2962927345","https://openalex.org/W2963080259","https://openalex.org/W2963205522","https://openalex.org/W2963446530","https://openalex.org/W2968022604","https://openalex.org/W3015507268","https://openalex.org/W3116788472","https://openalex.org/W3214080486","https://openalex.org/W4205215424","https://openalex.org/W4213212409","https://openalex.org/W4214577052","https://openalex.org/W4226164728","https://openalex.org/W4226380391","https://openalex.org/W4294988936","https://openalex.org/W4388295805","https://openalex.org/W4400787536","https://openalex.org/W4404322945","https://openalex.org/W4405320041","https://openalex.org/W7153263743"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-05-05T00:00:00"}