{"id":"https://openalex.org/W1968327710","doi":"https://doi.org/10.1090/s0025-5718-09-02227-3","title":"The computation of resonances in open systems using a perfectly matched layer","display_name":"The computation of resonances in open systems using a perfectly matched layer","publication_year":2009,"publication_date":"2009-04-27","ids":{"openalex":"https://openalex.org/W1968327710","doi":"https://doi.org/10.1090/s0025-5718-09-02227-3","mag":"1968327710"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02227-3","pdf_url":"https://www.ams.org/mcom/2009-78-267/S0025-5718-09-02227-3/S0025-5718-09-02227-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2009-78-267/S0025-5718-09-02227-3/S0025-5718-09-02227-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013970170","display_name":"Seungil Kim","orcid":"https://orcid.org/0000-0001-7769-6737"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Seungil Kim","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113545293","display_name":"Joseph E. Pasciak","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph E. Pasciak","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843\u20133368","institution_ids":["https://openalex.org/I91045830"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.924,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":74,"citation_normalized_percentile":{"value":0.934506,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"78","issue":"267","first_page":"1375","last_page":"1398"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":1.0,"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":1.0,"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":0.9999,"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":0.9997,"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/helmholtz-equation","display_name":"Helmholtz equation","score":0.7038901},{"id":"https://openalex.org/keywords/perfectly-matched-layer","display_name":"Perfectly Matched Layer","score":0.6410713},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.61472994},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5621},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.47133064},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.43737122}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7038901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6984325},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.67451525},{"id":"https://openalex.org/C16895185","wikidata":"https://www.wikidata.org/wiki/Q15101726","display_name":"Perfectly matched layer","level":3,"score":0.6410713},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.61472994},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5621},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.55096906},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5441481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5204863},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.47133064},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4605078},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.43737122},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.43267006},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.41154063},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24600849},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19927955},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.094472766},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07672915},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02227-3","pdf_url":"https://www.ams.org/mcom/2009-78-267/S0025-5718-09-02227-3/S0025-5718-09-02227-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02227-3","pdf_url":"https://www.ams.org/mcom/2009-78-267/S0025-5718-09-02227-3/S0025-5718-09-02227-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":31,"referenced_works":["https://openalex.org/W1516320851","https://openalex.org/W1523113578","https://openalex.org/W1575147392","https://openalex.org/W1576275398","https://openalex.org/W1582734821","https://openalex.org/W171105080","https://openalex.org/W1889079046","https://openalex.org/W1969524319","https://openalex.org/W1977794655","https://openalex.org/W1989748191","https://openalex.org/W1990669907","https://openalex.org/W1994751539","https://openalex.org/W1998040449","https://openalex.org/W2003017040","https://openalex.org/W2008720207","https://openalex.org/W2010561889","https://openalex.org/W2011655084","https://openalex.org/W2038171602","https://openalex.org/W2046715295","https://openalex.org/W2051437422","https://openalex.org/W2053671897","https://openalex.org/W2069453797","https://openalex.org/W2069665540","https://openalex.org/W2104329699","https://openalex.org/W2124628021","https://openalex.org/W2320571400","https://openalex.org/W2795407492","https://openalex.org/W4253251115","https://openalex.org/W4292027041","https://openalex.org/W4299150230","https://openalex.org/W90568776"],"related_works":["https://openalex.org/W4367296780","https://openalex.org/W4365420316","https://openalex.org/W3193896743","https://openalex.org/W3176862315","https://openalex.org/W3120022531","https://openalex.org/W277277552","https://openalex.org/W2162587964","https://openalex.org/W2149804981","https://openalex.org/W2131186711","https://openalex.org/W2032794959"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,169],"consider":[4],"the":[5,23,41,50,55,77,87,96,102,122,129,139,152,163,171,174],"problem":[6,57,62,71],"of":[7,19,22,43,52,131,154,162,173],"computing":[8],"resonances":[9,16],"in":[10,17,86,180],"open":[11],"systems.":[12],"We":[13,46,125],"first":[14,99,130],"characterize":[15],"terms":[18],"(improper)":[20],"eigenfunctions":[21],"Helmholtz":[24,79],"operator":[25,74,98],"on":[26,64,121],"an":[27,65,73],"unbounded":[28],"domain.":[29,124],"The":[30,160],"perfectly":[31],"matched":[32],"layer":[33],"(PML)":[34],"technique":[35],"has":[36],"been":[37],"successfully":[38],"applied":[39,176],"to":[40,58,94,135,177],"computation":[42],"scattering":[44],"problems.":[45],"shall":[47,126],"see":[48],"that":[49,128,151],"application":[51],"PML":[53],"converts":[54],"resonance":[56,141],"a":[59,83,106,111],"standard":[60],"eigenvalue":[61,70,136],"(still":[63],"infinite":[66,103],"domain).":[67],"This":[68],"new":[69],"involves":[72],"which":[75,143],"resembles":[76],"original":[78],"equation":[80],"transformed":[81],"by":[82,100,105,117],"complex":[84],"shift":[85],"coordinate":[88],"system.":[89],"Our":[90],"goal":[91],"will":[92],"be":[93],"approximate":[95],"shifted":[97],"replacing":[101],"domain":[104,109,156],"finite":[107,119],"(computational)":[108],"with":[110],"convenient":[112],"boundary":[113],"condition":[114],"and":[115,182],"second":[116,164],"applying":[118],"elements":[120],"computational":[123,148,155],"prove":[127],"these":[132],"steps":[133],"leads":[134],"convergence":[137],"(to":[138],"desired":[140],"values)":[142],"is":[144,157,166],"free":[145],"from":[146],"spurious":[147],"eigenvalues":[149],"provided":[150],"size":[153],"sufficiently":[158],"large.":[159],"analysis":[161],"step":[165],"classical.":[167],"Finally,":[168],"illustrate":[170],"behavior":[172],"method":[175],"numerical":[178],"experiments":[179],"one":[181],"two":[183],"spatial":[184],"dimensions.":[185]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1968327710","counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3}],"updated_date":"2025-01-02T09:27:23.741434","created_date":"2016-06-24"}