{"id":"https://openalex.org/W4408108844","doi":"https://doi.org/10.1007/s00211-025-01456-9","title":"The PML-method for a scattering problem for a local perturbation of an open periodic waveguide","display_name":"The PML-method for a scattering problem for a local perturbation of an open periodic waveguide","publication_year":2025,"publication_date":"2025-03-03","ids":{"openalex":"https://openalex.org/W4408108844","doi":"https://doi.org/10.1007/s00211-025-01456-9"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-025-01456-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01456-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01456-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01456-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091107812","display_name":"Andreas Kirsch","orcid":"https://orcid.org/0000-0003-3578-7504"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas Kirsch","raw_affiliation_strings":["Institute of Applied and Numerical Mathematics, Karlsruhe Institute of Technology (KIT), Kaiserstra\u00dfe 12, Karlsruhe, 76131, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied and Numerical Mathematics, Karlsruhe Institute of Technology (KIT), Kaiserstra\u00dfe 12, Karlsruhe, 76131, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"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/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ruming Zhang","raw_affiliation_strings":["Institute of Mathematics, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, Berlin, 10623, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, Berlin, 10623, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091107812"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.5782,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64915274,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"157","issue":"2","first_page":"717","last_page":"748"},"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/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/T11205","display_name":"Numerical methods in inverse problems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6826423406600952},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6044892072677612},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.5781553983688354},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5065122842788696},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5054681301116943},{"id":"https://openalex.org/keywords/waveguide","display_name":"Waveguide","score":0.4741869866847992},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.27663862705230713},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2044248878955841},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10677531361579895}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6826423406600952},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6044892072677612},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.5781553983688354},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5065122842788696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5054681301116943},{"id":"https://openalex.org/C200687136","wikidata":"https://www.wikidata.org/wiki/Q11233438","display_name":"Waveguide","level":2,"score":0.4741869866847992},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.27663862705230713},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2044248878955841},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10677531361579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-025-01456-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01456-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01456-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00211-025-01456-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01456-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01456-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408108844.pdf"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W580567146","https://openalex.org/W1963530630","https://openalex.org/W1990535704","https://openalex.org/W1998406262","https://openalex.org/W2003017040","https://openalex.org/W2015877425","https://openalex.org/W2019466406","https://openalex.org/W2019681354","https://openalex.org/W2023172943","https://openalex.org/W2034815835","https://openalex.org/W2047377882","https://openalex.org/W2103806319","https://openalex.org/W2143932135","https://openalex.org/W2479637896","https://openalex.org/W2511238033","https://openalex.org/W2550437290","https://openalex.org/W2624639708","https://openalex.org/W2726615376","https://openalex.org/W2752072161","https://openalex.org/W2948260758","https://openalex.org/W2954197445","https://openalex.org/W2956137735","https://openalex.org/W2963009834","https://openalex.org/W2963911069","https://openalex.org/W3099119377","https://openalex.org/W3104884639","https://openalex.org/W3129322472","https://openalex.org/W3194651603","https://openalex.org/W4205817443","https://openalex.org/W4225968678","https://openalex.org/W4226105242","https://openalex.org/W4245719435","https://openalex.org/W4288652121","https://openalex.org/W4296679867","https://openalex.org/W4297995665","https://openalex.org/W4322762252","https://openalex.org/W4389347554"],"related_works":["https://openalex.org/W2084997001","https://openalex.org/W1967204941","https://openalex.org/W210855175","https://openalex.org/W2089624481","https://openalex.org/W2106029274","https://openalex.org/W2091948642","https://openalex.org/W3105009518","https://openalex.org/W1987350696","https://openalex.org/W2092363877","https://openalex.org/W1967440439"],"abstract_inverted_index":{"Abstract":[0],"The":[1,118],"perfectly":[2],"matched":[3],"layer":[4],"method":[5,35,215],"(PML":[6],"method)":[7],"is":[8,86,97,120,148,173],"a":[9,90,94,115,161,189,200],"truncation":[10],"technique":[11],"well":[12],"known":[13],"for":[14,36],"the":[15,30,33,37,83,123,128,135,151,157,165,169,176,182,186,196,204,213,221,232],"numerical":[16,226],"treatment":[17],"of":[18,32,93,131,137,185,188,191],"wave":[19,38],"scattering":[20,39],"problems":[21],"in":[22,44],"unbounded":[23],"domains.":[24],"In":[25],"this":[26,146],"paper,":[27],"we":[28,209],"study":[29],"convergence":[31],"PML":[34,214,222],"from":[40,122,127,168],"an":[41],"open":[42],"waveguide":[43],"$$\\mathbb":[45],"{R}^2_+=\\{x\\in":[46],"\\mathbb":[47],"{R}^2:x_2&gt;0\\}$$":[48],"<mml:math":[49,103],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[50,104],"<mml:mrow>":[51,53,60,65],"<mml:msubsup>":[52],"<mml:mi>R</mml:mi>":[54,66],"</mml:mrow>":[55,67,78,79],"<mml:mo>+</mml:mo>":[56],"<mml:mn>2</mml:mn>":[57,68,73],"</mml:msubsup>":[58],"<mml:mo>=</mml:mo>":[59],"<mml:mo>{</mml:mo>":[61],"<mml:mi>x</mml:mi>":[62,72,106],"<mml:mo>\u2208</mml:mo>":[63],"<mml:msup>":[64],"</mml:msup>":[69],"<mml:mo>:</mml:mo>":[70],"<mml:msub>":[71,105],"</mml:msub>":[74,108],"<mml:mo>&gt;</mml:mo>":[75],"<mml:mn>0</mml:mn>":[76],"<mml:mo>}</mml:mo>":[77],"</mml:math>":[80,109],",":[81],"where":[82],"refractive":[84],"index":[85],"assumed":[87],"to":[88,101,112,134,143,149,181,220,230],"be":[89],"local":[91],"perturbation":[92],"function":[95],"which":[96],"periodic":[98,207],"with":[99,145,218],"respect":[100,180,219],"$$x_1$$":[102],"<mml:mn>1</mml:mn>":[107],"and":[110,125,160],"equal":[111],"one":[113],"above":[114,203],"finite":[116],"height.":[117],"problem":[119],"challenging":[121],"theoretical,":[124],"also":[126],"numerical,":[129],"point":[130],"view":[132],"due":[133],"existence":[136],"guided":[138],"waves.":[139],"A":[140],"typical":[141],"way":[142],"deal":[144],"difficulty":[147],"apply":[150],"limiting":[152,170],"absorption":[153,171],"principle.":[154],"Based":[155],"on":[156,199],"Floquet-Bloch":[158,183],"transform":[159],"curve":[162],"deformation":[163],"theory,":[164],"solution,":[166],"derived":[167],"principle,":[172],"rewritten":[174],"as":[175],"line":[177,202],"integral":[178],"(with":[179],"parameter)":[184],"solution":[187],"system":[190],"quasi-periodic":[192],"problems.":[193],"By":[194],"comparing":[195],"Dirichlet-to-Neumann":[197],"maps":[198],"straight":[201],"locally":[205],"perturbed":[206],"layer,":[208],"finally":[210],"show":[211],"that":[212],"converges":[216],"exponentially":[217],"parameter.":[223],"Finally,":[224],"some":[225],"examples":[227],"are":[228],"shown":[229],"illustrate":[231],"theoretical":[233],"results.":[234]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
