{"id":"https://openalex.org/W2963911069","doi":"https://doi.org/10.1137/16m1067524","title":"A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet--Bloch Transform","display_name":"A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet--Bloch Transform","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2963911069","doi":"https://doi.org/10.1137/16m1067524","mag":"2963911069"},"language":"en","primary_location":{"id":"doi:10.1137/16m1067524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1067524","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/A5003515278","display_name":"Armin Lechleiter","orcid":"https://orcid.org/0000-0002-4346-816X"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Armin Lechleiter","raw_affiliation_strings":["Center for Industrial Mathematics, University of Bremen;"],"affiliations":[{"raw_affiliation_string":"Center for Industrial Mathematics, University of Bremen;","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065643575","display_name":"Ruming Zhang","orcid":"https://orcid.org/0000-0003-2336-1020"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ruming Zhang","raw_affiliation_strings":["Center for Industrial Mathematics, University of Bremen;"],"affiliations":[{"raw_affiliation_string":"Center for Industrial Mathematics, University of Bremen;","institution_ids":["https://openalex.org/I180437899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003515278"],"corresponding_institution_ids":["https://openalex.org/I180437899"],"apc_list":null,"apc_paid":null,"fwci":1.8549,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.8633855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"55","issue":"2","first_page":"713","last_page":"736"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9995999932289124,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.8030610084533691},{"id":"https://openalex.org/keywords/floquet-theory","display_name":"Floquet theory","score":0.7235174775123596},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6322965621948242},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5438939929008484},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.4808562397956848},{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.46581530570983887},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.45989587903022766},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.4355967044830322},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12566924095153809},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11997455358505249},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10365954041481018}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8030610084533691},{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.7235174775123596},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6322965621948242},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5438939929008484},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.4808562397956848},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.46581530570983887},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.45989587903022766},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4355967044830322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12566924095153809},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11997455358505249},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10365954041481018},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1067524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1067524","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":[{"id":"https://metadata.un.org/sdg/11","score":0.7400000095367432,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G8640188844","display_name":null,"funder_award_id":"600411","funder_id":"https://openalex.org/F4320324729","funder_display_name":"Universit\u00e4t Bremen"}],"funders":[{"id":"https://openalex.org/F4320324729","display_name":"Universit\u00e4t Bremen","ror":"https://ror.org/04ers2y35"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1622893263","https://openalex.org/W1963530630","https://openalex.org/W1963799191","https://openalex.org/W1964503974","https://openalex.org/W1995254409","https://openalex.org/W2010002946","https://openalex.org/W2035448837","https://openalex.org/W2035956484","https://openalex.org/W2054094817","https://openalex.org/W2071585412","https://openalex.org/W2079051406","https://openalex.org/W2479637896","https://openalex.org/W2963009834"],"related_works":["https://openalex.org/W1488175704","https://openalex.org/W4286849939","https://openalex.org/W3217258686","https://openalex.org/W2990905476","https://openalex.org/W2037661079","https://openalex.org/W4383815106","https://openalex.org/W4386135338","https://openalex.org/W3158508387","https://openalex.org/W2339191433","https://openalex.org/W2131815370"],"abstract_inverted_index":{"Periodic":[0],"surface":[1,26,39,82],"structures":[2,13],"are":[3,14],"currently":[4],"standard":[5],"building":[6],"blocks":[7],"of":[8,63,95,183,205],"optical":[9],"devices.":[10],"If":[11],"such":[12,145],"illuminated":[15],"by":[16],"aperiodic":[17],"time-harmonic":[18],"incident":[19],"waves,":[20],"e.g.,":[21],"Gaussian":[22],"beams,":[23],"the":[24,37,46,74,80,87,93,98,110,124,161,181,186,203,206],"resulting":[25],"scattering":[27,65,83,171,188],"problem":[28,51,84],"must":[29],"be":[30],"formulated":[31],"in":[32,52,67,109,190],"an":[33,53,60],"unbounded":[34,54,131],"layer":[35],"including":[36],"periodic":[38],"structure.":[40],"An":[41],"obvious":[42],"recipe":[43],"for":[44,144,180],"avoiding":[45],"need":[47,125],"to":[48,57,79,92,97,105,126,150,160,169,185],"discretize":[49],"this":[50,119,134],"domain":[55],"is":[56],"set":[58],"up":[59],"equivalent":[61],"system":[62],"quasi-periodic":[64,99,170,187],"problems":[66,189],"a":[68,146,151,157],"single":[69],"(bounded)":[70],"periodicity":[71,112],"cell":[72],"via":[73,209],"Floquet--Bloch":[75,89,163],"transform.":[76],"The":[77],"solution":[78],"original":[81],"then":[85],"equals":[86],"inverse":[88,162],"transform":[90,164],"applied":[91,149],"family":[94,182],"solutions":[96,108,184],"problems,":[100],"which":[101],"simply":[102],"requires":[103],"us":[104],"integrate":[106],"these":[107],"quasi":[111],"parameter.":[113],"A":[114],"numerical":[115,207,211],"scheme":[116,147,208],"derived":[117],"from":[118],"representation":[120],"hence":[121],"completely":[122],"avoids":[123],"tackle":[127],"differential":[128],"equations":[129],"on":[130],"domains.":[132],"In":[133],"paper,":[135],"we":[136],"provide":[137],"rigorous":[138],"convergence":[139],"analysis":[140,174],"and":[141,165],"error":[142,198],"bounds":[143,199],"when":[148],"two-dimensional":[152],"model":[153],"problem,":[154],"relying":[155],"upon":[156,177],"quadrature-based":[158],"approximation":[159],"finite":[166],"element":[167],"approximations":[168],"problems.":[172],"Our":[173],"essentially":[175],"relies":[176],"regularity":[178],"results":[179],"suitable":[191],"mixed":[192],"Sobolev":[193],"spaces.":[194],"We":[195],"illustrate":[196],"our":[197],"as":[200,202],"well":[201],"efficiency":[204],"several":[210],"examples.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
