{"id":"https://openalex.org/W4415785563","doi":"https://doi.org/10.1137/24m168533x","title":"Two-Level Hybrid Schwarz Preconditioners for the Helmholtz Equation with High Wave Number","display_name":"Two-Level Hybrid Schwarz Preconditioners for the Helmholtz Equation with High Wave Number","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415785563","doi":"https://doi.org/10.1137/24m168533x"},"language":"en","primary_location":{"id":"doi:10.1137/24m168533x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/24m168533x","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1137/24m168533x","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066744320","display_name":"Peipei Lu","orcid":"https://orcid.org/0000-0003-4937-9499"},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Peipei Lu","raw_affiliation_strings":["Department of Mathematics Sciences, Soochow University, Suzhou 215006, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Sciences, Soochow University, Suzhou 215006, China","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100742189","display_name":"Xuejun Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuejun Xu","raw_affiliation_strings":["School of Mathematical Sciences, Tongji University, Shanghai 200092, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020708321","display_name":"Bowen Zheng","orcid":"https://orcid.org/0009-0003-0352-8257"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bowen Zheng","raw_affiliation_strings":["LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"],"affiliations":[{"raw_affiliation_string":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090609331","display_name":"Jun Zou","orcid":"https://orcid.org/0000-0002-4809-7724"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Zou","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066744320"],"corresponding_institution_ids":["https://openalex.org/I3923682"],"apc_list":null,"apc_paid":null,"fwci":1.4942,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.84951408,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"63","issue":"6","first_page":"2187","last_page":"2220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.34790000319480896,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.34790000319480896,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.20200000703334808,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.05900000035762787,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.637499988079071},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4602999985218048},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.39340001344680786},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.36000001430511475},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.29910001158714294},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.2773999869823456}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.758400022983551},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.637499988079071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5202000141143799},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4602999985218048},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.39340001344680786},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.36000001430511475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3456000089645386},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.29910001158714294},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.2630000114440918},{"id":"https://openalex.org/C3019722297","wikidata":"https://www.wikidata.org/wiki/Q4440864","display_name":"High dimensional","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m168533x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/24m168533x","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/24m168533x","is_oa":true,"landing_page_url":"https://doi.org/10.1137/24m168533x","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1548589512","https://openalex.org/W1720292799","https://openalex.org/W1970622200","https://openalex.org/W1976538983","https://openalex.org/W1980404981","https://openalex.org/W1987152170","https://openalex.org/W2024381649","https://openalex.org/W2024949119","https://openalex.org/W2029966922","https://openalex.org/W2031027147","https://openalex.org/W2032941427","https://openalex.org/W2041226551","https://openalex.org/W2051043245","https://openalex.org/W2063228755","https://openalex.org/W2068395392","https://openalex.org/W2080212747","https://openalex.org/W2084463157","https://openalex.org/W2098102734","https://openalex.org/W2114535880","https://openalex.org/W2117866703","https://openalex.org/W2161243591","https://openalex.org/W2164119610","https://openalex.org/W2398465244","https://openalex.org/W2592456637","https://openalex.org/W2767278683","https://openalex.org/W2951927487","https://openalex.org/W2963691989","https://openalex.org/W2963726548","https://openalex.org/W2963961138","https://openalex.org/W3087680391","https://openalex.org/W3209752110","https://openalex.org/W4292027041","https://openalex.org/W4380741142","https://openalex.org/W4409337324"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-11-03T00:00:00"}