{"id":"https://openalex.org/W754905802","doi":"https://doi.org/10.1137/140969907","title":"An Adaptive Finite Element Method for the Diffraction Grating Problem with Transparent Boundary Condition","display_name":"An Adaptive Finite Element Method for the Diffraction Grating Problem with Transparent Boundary Condition","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W754905802","doi":"https://doi.org/10.1137/140969907","mag":"754905802"},"language":"en","primary_location":{"id":"doi:10.1137/140969907","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969907","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/A5101999545","display_name":"Zhoufeng Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhoufeng Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018497995","display_name":"Gang Bao","orcid":"https://orcid.org/0000-0003-1591-8095"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gang Bao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013234925","display_name":"Jiaqing Li","orcid":"https://orcid.org/0000-0002-7993-7706"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiaqing Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100742532","display_name":"Peijun Li","orcid":"https://orcid.org/0000-0001-5119-6435"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peijun Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034214957","display_name":"Haijun Wu","orcid":"https://orcid.org/0000-0003-1787-5973"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haijun Wu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101999545"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6803,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.87995279,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"53","issue":"3","first_page":"1585","last_page":"1607"},"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":0.9994999766349792,"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":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.7877603769302368},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6644123196601868},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5812183618545532},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.5699132084846497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5624123811721802},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5326290726661682},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5286736488342285},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.4655535817146301},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.45118552446365356},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4257686734199524},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38592350482940674},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05883106589317322}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7877603769302368},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6644123196601868},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5812183618545532},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.5699132084846497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5624123811721802},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5326290726661682},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5286736488342285},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.4655535817146301},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.45118552446365356},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4257686734199524},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38592350482940674},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05883106589317322},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140969907","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969907","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.703.4462","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.703.4462","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.purdue.edu/%7Elipeijun/paper/2015/WBLLW_SINUM_2015.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W653136046","https://openalex.org/W1492378095","https://openalex.org/W1513869700","https://openalex.org/W1659382607","https://openalex.org/W1933261278","https://openalex.org/W1972343484","https://openalex.org/W1972352449","https://openalex.org/W1977490503","https://openalex.org/W1983072269","https://openalex.org/W1988440346","https://openalex.org/W1989594010","https://openalex.org/W1995254409","https://openalex.org/W1995479616","https://openalex.org/W2003017040","https://openalex.org/W2003349146","https://openalex.org/W2009985306","https://openalex.org/W2016720639","https://openalex.org/W2019681354","https://openalex.org/W2028751448","https://openalex.org/W2033698269","https://openalex.org/W2039924562","https://openalex.org/W2042598996","https://openalex.org/W2056366812","https://openalex.org/W2056598374","https://openalex.org/W2058891245","https://openalex.org/W2068790309","https://openalex.org/W2071928229","https://openalex.org/W2072811159","https://openalex.org/W2079051406","https://openalex.org/W2081137717","https://openalex.org/W2084743165","https://openalex.org/W2088366347","https://openalex.org/W2091213543","https://openalex.org/W2095685733","https://openalex.org/W2107813568","https://openalex.org/W4232672413"],"related_works":["https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W138907054","https://openalex.org/W2536422707","https://openalex.org/W24145419","https://openalex.org/W2044869171","https://openalex.org/W1590887574"],"abstract_inverted_index":{"The":[0,76],"diffraction":[1,122],"grating":[2,123],"problem":[3,10],"is":[4,25,74,118,130],"modeled":[5],"by":[6,12,42],"a":[7,13,21,63,77,109,113],"boundary":[8,18,33,95],"value":[9],"governed":[11],"Helmholtz":[14],"equation":[15],"with":[16,100],"transparent":[17],"conditions.":[19],"An":[20],"posteriori":[22,78,110],"error":[23,79,89,93,111,135],"estimate":[24,80],"derived":[26],"when":[27],"the":[28,31,39,43,46,55,71,85,91,103,108,121,127,133,137,146,157,161],"truncation":[29,92,104,128,134],"of":[30,82,94,160],"nonlocal":[32],"operators":[34,96],"takes":[35],"place.":[36],"To":[37],"overcome":[38],"difficulty":[40],"caused":[41],"fact":[44],"that":[45,126],"truncated":[47],"Dirichlet-to-Neumann":[48],"(DtN)":[49],"mapping":[50,58],"does":[51],"not":[52],"converge":[53],"to":[54,102,155],"original":[56],"DtN":[57],"in":[59],"its":[60],"operator":[61],"norm,":[62],"duality":[64],"argument":[65],"without":[66],"assuming":[67],"more":[68],"regularity":[69],"than":[70],"weak":[72],"solution":[73],"applied.":[75],"consists":[81],"two":[83],"parts,":[84],"finite":[86,114,147],"element":[87,115,148],"discretization":[88,149],"and":[90,136],"which":[97],"decays":[98],"exponentially":[99],"respect":[101],"parameter.":[105],"Based":[106],"on":[107],"control,":[112],"adaptive":[116,163],"strategy":[117],"established":[119],"for":[120,140],"problem,":[124],"such":[125],"parameter":[129],"determined":[131],"through":[132,145],"mesh":[138],"elements":[139],"local":[141],"refinements":[142],"are":[143,153],"marked":[144],"error.":[150],"Numerical":[151],"experiments":[152],"presented":[154],"illustrate":[156],"competitive":[158],"behavior":[159],"proposed":[162],"algorithm.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
