{"id":"https://openalex.org/W4396977115","doi":"https://doi.org/10.1007/s40314-024-02770-y","title":"An adaptive finite element PML method for Helmholtz equations in periodic heterogeneous media","display_name":"An adaptive finite element PML method for Helmholtz equations in periodic heterogeneous media","publication_year":2024,"publication_date":"2024-05-16","ids":{"openalex":"https://openalex.org/W4396977115","doi":"https://doi.org/10.1007/s40314-024-02770-y"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-024-02770-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-024-02770-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","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/A5101762925","display_name":"Xue Jiang","orcid":"https://orcid.org/0000-0002-3160-0282"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]},{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xue Jiang","raw_affiliation_strings":["School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People\u2019s Republic of China","School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-3160-0282","affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37796252","https://openalex.org/I92403157","https://openalex.org/I78675632"]},{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People's Republic of China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101355051","display_name":"Zhongjiang Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]},{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongjiang Sun","raw_affiliation_strings":["School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People\u2019s Republic of China","School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37796252","https://openalex.org/I92403157","https://openalex.org/I78675632"]},{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People's Republic of China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035709239","display_name":"Lijuan Sun","orcid":"https://orcid.org/0000-0003-4915-525X"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]},{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijuan Sun","raw_affiliation_strings":["School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People\u2019s Republic of China","School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37796252","https://openalex.org/I92403157","https://openalex.org/I78675632"]},{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People's Republic of China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100621470","display_name":"Qiang Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiang Ma","raw_affiliation_strings":["College of Mathematics, Sichuan University, Chengdu, 610065, People\u2019s Republic of China","College of Mathematics, Sichuan University, Chengdu, 610065, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics, Sichuan University, Chengdu, 610065, People\u2019s Republic of China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"College of Mathematics, Sichuan University, Chengdu, 610065, People's Republic of China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101762925"],"corresponding_institution_ids":["https://openalex.org/I37796252","https://openalex.org/I78675632","https://openalex.org/I92403157"],"apc_list":null,"apc_paid":null,"fwci":0.1745,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.44581289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"43","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.752354621887207},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.7243549227714539},{"id":"https://openalex.org/keywords/perfectly-matched-layer","display_name":"Perfectly matched layer","score":0.656810462474823},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6566827893257141},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6190499067306519},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5745912790298462},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.5131252408027649},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48707249760627747},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4288105070590973},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4256956875324249},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14691540598869324},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12763327360153198},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.09984073042869568}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.752354621887207},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7243549227714539},{"id":"https://openalex.org/C16895185","wikidata":"https://www.wikidata.org/wiki/Q15101726","display_name":"Perfectly matched layer","level":3,"score":0.656810462474823},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6566827893257141},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6190499067306519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5745912790298462},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5131252408027649},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48707249760627747},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4288105070590973},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4256956875324249},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14691540598869324},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12763327360153198},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.09984073042869568},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-024-02770-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-024-02770-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4870197282","display_name":null,"funder_award_id":"12171017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G560859918","display_name":null,"funder_award_id":"11801387","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1517670975","https://openalex.org/W1520664314","https://openalex.org/W1889079046","https://openalex.org/W1972352449","https://openalex.org/W1981267739","https://openalex.org/W1994751539","https://openalex.org/W1999405023","https://openalex.org/W2002363316","https://openalex.org/W2003017040","https://openalex.org/W2009985306","https://openalex.org/W2013511135","https://openalex.org/W2019681354","https://openalex.org/W2022543060","https://openalex.org/W2027239222","https://openalex.org/W2028426755","https://openalex.org/W2029966922","https://openalex.org/W2030591225","https://openalex.org/W2039924562","https://openalex.org/W2053149981","https://openalex.org/W2056470693","https://openalex.org/W2058891245","https://openalex.org/W2070291256","https://openalex.org/W2091213543","https://openalex.org/W2109362844","https://openalex.org/W2165838836","https://openalex.org/W2338955318","https://openalex.org/W2472641985","https://openalex.org/W2513388925","https://openalex.org/W2522648897","https://openalex.org/W2566228990","https://openalex.org/W2912676481","https://openalex.org/W2919922180","https://openalex.org/W2945655205","https://openalex.org/W2963223245","https://openalex.org/W2963516318","https://openalex.org/W2963691989","https://openalex.org/W2964374283","https://openalex.org/W2969392380","https://openalex.org/W3004625791","https://openalex.org/W3024688492","https://openalex.org/W3041134036","https://openalex.org/W3046457476","https://openalex.org/W3087478199","https://openalex.org/W3157804329","https://openalex.org/W3160675600","https://openalex.org/W3198981003","https://openalex.org/W4232672413","https://openalex.org/W4300943935","https://openalex.org/W6601048702"],"related_works":["https://openalex.org/W2479815380","https://openalex.org/W2145453501","https://openalex.org/W2032794959","https://openalex.org/W138564687","https://openalex.org/W2149804981","https://openalex.org/W4399185739","https://openalex.org/W4367296780","https://openalex.org/W2131186711","https://openalex.org/W277277552","https://openalex.org/W2162587964"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-07T14:30:12.667765","created_date":"2025-10-10T00:00:00"}