{"id":"https://openalex.org/W1972145837","doi":"https://doi.org/10.1109/tgrs.2011.2166765","title":"A Three-Dimensional Adaptive Integral Method for Scattering From Structures Embedded in Layered Media","display_name":"A Three-Dimensional Adaptive Integral Method for Scattering From Structures Embedded in Layered Media","publication_year":2011,"publication_date":"2011-10-05","ids":{"openalex":"https://openalex.org/W1972145837","doi":"https://doi.org/10.1109/tgrs.2011.2166765","mag":"1972145837"},"language":"en","primary_location":{"id":"doi:10.1109/tgrs.2011.2166765","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2011.2166765","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Geoscience and Remote Sensing","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/A5080870111","display_name":"Kai Yang","orcid":"https://orcid.org/0000-0002-0666-3003"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kai Yang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Texas, Austin, Austin, TX, USA","Dept. of Electr. &, Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Texas, Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"Dept. of Electr. &, Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072461338","display_name":"Ali E. Y\u0131lmaz","orcid":"https://orcid.org/0000-0003-2573-1515"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali E. Yilmaz","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Texas, Austin, Austin, TX, USA","Dept. of Electr. &, Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Texas, Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"Dept. of Electr. &, Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080870111"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":3.2732,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.91925609,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"50","issue":"4","first_page":"1130","last_page":"1139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":1.0,"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":1.0,"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/T11383","display_name":"Advanced Antenna and Metasurface Technologies","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.661331057548523},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5220856070518494},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4648415446281433},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4369465112686157},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.42633721232414246},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.42133161425590515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4128098487854004},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39908185601234436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36545050144195557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29570916295051575},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22442656755447388},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21225914359092712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17507991194725037}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.661331057548523},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5220856070518494},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4648415446281433},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4369465112686157},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.42633721232414246},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.42133161425590515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4128098487854004},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39908185601234436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36545050144195557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29570916295051575},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22442656755447388},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21225914359092712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17507991194725037},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tgrs.2011.2166765","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2011.2166765","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Geoscience and Remote Sensing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310620","display_name":"University of Texas at Austin","ror":"https://ror.org/00hj54h04"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1542178507","https://openalex.org/W1800827217","https://openalex.org/W1962701165","https://openalex.org/W1964379771","https://openalex.org/W1994842411","https://openalex.org/W1997289198","https://openalex.org/W2026139685","https://openalex.org/W2050539045","https://openalex.org/W2054380687","https://openalex.org/W2084385130","https://openalex.org/W2090111309","https://openalex.org/W2097957337","https://openalex.org/W2100338124","https://openalex.org/W2107435904","https://openalex.org/W2108766479","https://openalex.org/W2110660022","https://openalex.org/W2112819334","https://openalex.org/W2114206383","https://openalex.org/W2116266506","https://openalex.org/W2119612139","https://openalex.org/W2120562193","https://openalex.org/W2122933071","https://openalex.org/W2137052588","https://openalex.org/W2143887891","https://openalex.org/W2144781999","https://openalex.org/W2150974273","https://openalex.org/W2154377087","https://openalex.org/W2155150808","https://openalex.org/W2156332776","https://openalex.org/W2162157932","https://openalex.org/W2165720325","https://openalex.org/W2170163309","https://openalex.org/W2171879949","https://openalex.org/W2593527582","https://openalex.org/W6683137818"],"related_works":["https://openalex.org/W2389462125","https://openalex.org/W2091997962","https://openalex.org/W151496359","https://openalex.org/W4220662591","https://openalex.org/W856465872","https://openalex.org/W1969863203","https://openalex.org/W1987843132","https://openalex.org/W1480644286","https://openalex.org/W2359223678","https://openalex.org/W2031400968"],"abstract_inverted_index":{"A":[0],"3-D":[1,50,119],"extension":[2],"of":[3,14,28,42,75,125,131,211,226,228,230,259],"the":[4,37,43,56,61,67,80,86,99,126,129,153,157,178,198,209,214,224,231,238],"adaptive":[5],"integral":[6,45],"method":[7],"(AIM)":[8],"is":[9,142],"presented":[10],"for":[11,69,79,245,262],"fast":[12],"analysis":[13],"scattering":[15],"from":[16],"electrically":[17,20],"large":[18],"perfect":[19],"conducting":[21],"structures":[22,248],"embedded":[23],"inside":[24],"a":[25,29,49],"single":[26],"layer":[27],"planar":[30],"layered":[31,250],"medium.":[32],"The":[33,121],"proposed":[34,239],"scheme":[35,127],"accelerates":[36],"iterative":[38],"method-of-moments":[39],"(MOM)":[40],"solution":[41],"combined-field":[44],"equation":[46],"by":[47,84,117,144,197],"employing":[48],"auxiliary":[51,57,215],"regular":[52],"grid.":[53],"It":[54],"uses":[55],"grid":[58],"to":[59,89,177,257],"execute":[60],"standard":[62],"four-stage":[63],"AIM":[64,81],"procedure;":[65],"unlike":[66],"procedure":[68],"free":[70,263],"space,":[71],"two":[72],"different":[73,137],"sets":[74],"matrices":[76,103],"are":[77,92,104,128],"obtained":[78],"propagation":[82,158],"stage":[83],"decomposing":[85],"Green":[87,139,184],"functions":[88],"terms":[90,147],"that":[91],"in":[93,98,105,156,249],"convolution":[94],"or":[95],"correlation":[96],"form":[97],"stratification":[100],"direction.":[101],"These":[102],"(three":[106],"level)":[107],"block-Toeplitz":[108],"and":[109,113,148,152,187,217,252],"Hankel-(two":[110],"level)-block-Toeplitz":[111],"forms":[112],"can":[114],"be":[115,175],"multiplied":[116],"using":[118,149],"FFTs.":[120],"dominant":[122],"computational":[123,255],"costs":[124,256],"evaluation":[130],"<formula":[132,163,179,188,202,218],"formulatype=\"inline\"":[133,164,180,189,203,219],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[134,165,181,190,204,220],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[135,166,182,191,205,221],"Notation=\"TeX\">$O(N)$</tex></formula>":[136],"layered-medium":[138],"functions,":[140],"which":[141,160],"accelerated":[143],"extracting":[145],"asymptotic":[146],"interpolation":[150],"tables,":[151],"matrix":[154],"multiplications":[155],"stage,":[159],"require":[161],"only":[162],"Notation=\"TeX\">$O(N_{\\rm":[167],"C}\\log":[168],"N_{\\rm":[169],"C})$</tex></formula>":[170],"per":[171,194],"iteration;":[172],"these":[173],"should":[174],"contrasted":[176],"Notation=\"TeX\">$O(N^{2})$</tex></formula>":[183,192],"function":[185],"evaluations":[186],"operations":[193],"iteration":[195],"required":[196],"classical":[199],"MOM.":[200],"Here,":[201],"Notation=\"TeX\">$N_{\\rm":[206],"C}$</tex></formula>":[207],"denotes":[208,223],"number":[210,225],"nodes":[212],"on":[213],"grid,":[216],"Notation=\"TeX\">$N$</tex></formula>":[222],"degrees":[227],"freedom":[229],"surface":[232],"current":[233],"density.":[234],"Numerical":[235],"results":[236],"validate":[237],"method's":[240],"complexity,":[241],"demonstrate":[242],"its":[243,254,260],"accuracy":[244],"several":[246],"large-scale":[247],"media,":[251],"compare":[253],"those":[258],"counterpart":[261],"space.":[264]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
