{"id":"https://openalex.org/W3012261688","doi":"https://doi.org/10.1007/s11075-020-00889-7","title":"Preconditioners and their analyses for edge element saddle-point systems arising from time-harmonic Maxwell\u2019s equations","display_name":"Preconditioners and their analyses for edge element saddle-point systems arising from time-harmonic Maxwell\u2019s equations","publication_year":2020,"publication_date":"2020-03-16","ids":{"openalex":"https://openalex.org/W3012261688","doi":"https://doi.org/10.1007/s11075-020-00889-7","mag":"3012261688"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-020-00889-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00889-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5100414176","display_name":"Ying Liang","orcid":"https://orcid.org/0000-0002-2594-3318"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Ying Liang","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People\u2019s Republic of China","Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People\u2019s Republic of China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People's Republic of China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043042295","display_name":"Hua Xiang","orcid":"https://orcid.org/0000-0002-5094-2376"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hua Xiang","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People\u2019s Republic of China","School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People's Republic of China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030584853","display_name":"Shiyang Zhang","orcid":"https://orcid.org/0000-0001-6229-3652"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shiyang Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People\u2019s Republic of China","School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People's Republic of China","institution_ids":["https://openalex.org/I37461747"]}]},{"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":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Jun Zou","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People\u2019s Republic of China","Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-4809-7724","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People\u2019s Republic of China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People's Republic of China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090609331"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.35,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52221027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"86","issue":"1","first_page":"281","last_page":"302"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8506635427474976},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7623157501220703},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7375369668006897},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7206501960754395},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.5612420439720154},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5599800944328308},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5054891109466553},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4918496608734131},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4588068723678589},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.42616838216781616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4261399209499359},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.42052221298217773},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.414753258228302},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25346726179122925},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1841152310371399},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16103467345237732},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14087438583374023}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8506635427474976},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7623157501220703},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7375369668006897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7206501960754395},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.5612420439720154},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5599800944328308},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5054891109466553},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4918496608734131},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4588068723678589},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.42616838216781616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4261399209499359},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.42052221298217773},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.414753258228302},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25346726179122925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1841152310371399},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16103467345237732},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14087438583374023},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-020-00889-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00889-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/13"}],"awards":[{"id":"https://openalex.org/G5205719177","display_name":null,"funder_award_id":"11471253.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8496995922","display_name":null,"funder_award_id":"11571265","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W592911714","https://openalex.org/W1528783519","https://openalex.org/W1970432716","https://openalex.org/W1987199740","https://openalex.org/W1992234740","https://openalex.org/W2003550247","https://openalex.org/W2005047411","https://openalex.org/W2015272191","https://openalex.org/W2021402826","https://openalex.org/W2039371973","https://openalex.org/W2047861338","https://openalex.org/W2062618977","https://openalex.org/W2065938796","https://openalex.org/W2066637873","https://openalex.org/W2067527388","https://openalex.org/W2072247902","https://openalex.org/W2083175038","https://openalex.org/W2094877794","https://openalex.org/W2095471433","https://openalex.org/W2099359799","https://openalex.org/W2141870784","https://openalex.org/W2143783905","https://openalex.org/W2157059822"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W1572705989","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2087062149"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}