{"id":"https://openalex.org/W2014876600","doi":"https://doi.org/10.1002/ecjb.4420780508","title":"Discussions on numerical accuracy of the vector finite element methods using the vector\u2010shape function","display_name":"Discussions on numerical accuracy of the vector finite element methods using the vector\u2010shape function","publication_year":1995,"publication_date":"1995-05-01","ids":{"openalex":"https://openalex.org/W2014876600","doi":"https://doi.org/10.1002/ecjb.4420780508","mag":"2014876600"},"language":"en","primary_location":{"id":"doi:10.1002/ecjb.4420780508","doi":"https://doi.org/10.1002/ecjb.4420780508","is_oa":false,"landing_page_url":"https://doi.org/10.1002/ecjb.4420780508","pdf_url":null,"source":{"id":"https://openalex.org/S4210198954","display_name":"Electronics and Communications in Japan (Part II Electronics)","issn_l":"1520-6432","issn":["1520-6432","8756-663X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronics and Communications in Japan (Part II: Electronics)","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5015286781","display_name":"M. Ohtaka","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I111966504","display_name":"University of Fukui","ror":"https://ror.org/00msqp585","country_code":"JP","type":"education","lineage":["https://openalex.org/I111966504"]},{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP","US"],"is_corresponding":false,"raw_author_name":"Masato Ohtaka","raw_affiliation_strings":["Faculty of Engineering, Fukui University, Fukui, Japan 910","Masato Ohtaka: received his B. E. and Dr. of Eng. degrees in 1970 and 1976, respectively, from Osaka University. In 1976, he became a Research Associate in the Department of Electrical Engineering, Fukui University, where he was promoted to Associate Professor in 1986. In 1989\u201390, he was on leave at the University of Southern California, Center for Laser Studies, as a Visiting Associate Professor. Presently, he is in the Department of Electrical and Electronics Engineering, Division of Materials and Devices, Opto-Electronics Group. He has been engaged in research and education on numerical analysis of electromagnetic waves and electron waves, integral transforms, and analysis of dynamic characteristics of laser diodes. He is a member of the Japan Society of Applies Physics and the IEEE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Fukui University, Fukui, Japan 910","institution_ids":["https://openalex.org/I111966504"]},{"raw_affiliation_string":"Masato Ohtaka: received his B. E. and Dr. of Eng. degrees in 1970 and 1976, respectively, from Osaka University. In 1976, he became a Research Associate in the Department of Electrical Engineering, Fukui University, where he was promoted to Associate Professor in 1986. In 1989\u201390, he was on leave at the University of Southern California, Center for Laser Studies, as a Visiting Associate Professor. Presently, he is in the Department of Electrical and Electronics Engineering, Division of Materials and Devices, Opto-Electronics Group. He has been engaged in research and education on numerical analysis of electromagnetic waves and electron waves, integral transforms, and analysis of dynamic characteristics of laser diodes. He is a member of the Japan Society of Applies Physics and the IEEE","institution_ids":["https://openalex.org/I111966504","https://openalex.org/I1174212","https://openalex.org/I98285908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101492864","display_name":"Takao Kobayashi","orcid":"https://orcid.org/0000-0001-6266-3764","observed_orcids":["https://orcid.org/0000-0001-6266-3764"]},"institutions":[{"id":"https://openalex.org/I111966504","display_name":"University of Fukui","ror":"https://ror.org/00msqp585","country_code":"JP","type":"education","lineage":["https://openalex.org/I111966504"]},{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]},{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]},{"id":"https://openalex.org/I4210132896","display_name":"The Physical Society of Japan","ror":"https://ror.org/04845gv95","country_code":"JP","type":"nonprofit","lineage":["https://openalex.org/I4210132896"]},{"id":"https://openalex.org/I4405254567","display_name":"The Laser Society of Japan","ror":"https://ror.org/01z745x67","country_code":"JP","type":"nonprofit","lineage":["https://openalex.org/I4405254567"]},{"id":"https://openalex.org/I4405255286","display_name":"The Institute of Electrical Engineers of Japan","ror":"https://ror.org/02tzt1z19","country_code":"JP","type":"nonprofit","lineage":["https://openalex.org/I4405255286"]}],"countries":["JP","US"],"is_corresponding":false,"raw_author_name":"Takao Kobayashi","raw_affiliation_strings":["Faculty of Engineering, Fukui University, Fukui, Japan 910","Takao Kobayashi: received his B. E. and M.S. degrees in 1964 and 1966, respectively, from the Department of Communication Engineering, Tohoku University, and his Dr. of Eng. degree later. In 1967, he became a Research Associate of Tohoku University, Research Institute of Electrical Communications. In 1979\u201380, he was on leave at Yale University. In 1981, he became an Associate Professor at Tohoku University, and that same year, Professor at Fukui University (Department of Electrical Engineering). Presently, he is in charge of Optoelectronics at the Department of Electrical and Electronics Engineering. He has been engaged in research and education on various lasers, nonlinear wavelength transformation, laser radar, optical information measurement, and environmental electronics. He is a member of the Japan Society of Applied Physics; Japan Physical Society; Japan Spectroscopy Society; Institute of Electrical Engineers of Japan; Laser Society; and IEEE","IEEE","Institute of Electrical Engineers of Japan","Japan Physical Society","Japan Spectroscopy Society","Laser Society","Takao Kobayashi:  received his B. E. and M.S. degrees in 1964 and 1966, respectively, from the Department of Communication Engineering, Tohoku University, and his Dr. of Eng. degree later. In 1967, he became a Research Associate of Tohoku University, Research Institute of Electrical Communications. In 1979\u201380, he was on leave at Yale University. In 1981, he became an Associate Professor at Tohoku University, and that same year, Professor at Fukui University (Department of Electrical Engineering). Presently, he is in charge of Optoelectronics at the Department of Electrical and Electronics Engineering. He has been engaged in research and education on various lasers, nonlinear wavelength transformation, laser radar, optical information measurement, and environmental electronics. He is a member of the Japan Society of Applied Physics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Fukui University, Fukui, Japan 910","institution_ids":["https://openalex.org/I111966504"]},{"raw_affiliation_string":"Takao Kobayashi: received his B. E. and M.S. degrees in 1964 and 1966, respectively, from the Department of Communication Engineering, Tohoku University, and his Dr. of Eng. degree later. In 1967, he became a Research Associate of Tohoku University, Research Institute of Electrical Communications. In 1979\u201380, he was on leave at Yale University. In 1981, he became an Associate Professor at Tohoku University, and that same year, Professor at Fukui University (Department of Electrical Engineering). Presently, he is in charge of Optoelectronics at the Department of Electrical and Electronics Engineering. He has been engaged in research and education on various lasers, nonlinear wavelength transformation, laser radar, optical information measurement, and environmental electronics. He is a member of the Japan Society of Applied Physics; Japan Physical Society; Japan Spectroscopy Society; Institute of Electrical Engineers of Japan; Laser Society; and IEEE","institution_ids":["https://openalex.org/I111966504","https://openalex.org/I201537933"]},{"raw_affiliation_string":"IEEE","institution_ids":[]},{"raw_affiliation_string":"Institute of Electrical Engineers of Japan","institution_ids":["https://openalex.org/I4405255286"]},{"raw_affiliation_string":"Japan Physical Society","institution_ids":["https://openalex.org/I4210132896"]},{"raw_affiliation_string":"Japan Spectroscopy Society","institution_ids":[]},{"raw_affiliation_string":"Laser Society","institution_ids":["https://openalex.org/I4405254567"]},{"raw_affiliation_string":"Takao Kobayashi:  received his B. E. and M.S. degrees in 1964 and 1966, respectively, from the Department of Communication Engineering, Tohoku University, and his Dr. of Eng. degree later. In 1967, he became a Research Associate of Tohoku University, Research Institute of Electrical Communications. In 1979\u201380, he was on leave at Yale University. In 1981, he became an Associate Professor at Tohoku University, and that same year, Professor at Fukui University (Department of Electrical Engineering). Presently, he is in charge of Optoelectronics at the Department of Electrical and Electronics Engineering. He has been engaged in research and education on various lasers, nonlinear wavelength transformation, laser radar, optical information measurement, and environmental electronics. He is a member of the Japan Society of Applied Physics","institution_ids":["https://openalex.org/I201537933","https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4635,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58422058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"78","issue":"5","first_page":"71","last_page":"80"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9038000106811523,"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":0.9038000106811523,"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":0.08560000360012054,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.006800000090152025,"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/vector-finite-element-method","display_name":"vector finite element method","score":0.9950000047683716},{"id":"https://openalex.org/keywords/electromagnetic-waveguides","display_name":"electromagnetic waveguides","score":0.7860000133514404},{"id":"https://openalex.org/keywords/numerical-accuracy","display_name":"numerical accuracy","score":0.7649999856948853},{"id":"https://openalex.org/keywords/waveguide-modes","display_name":"waveguide modes","score":0.7950000166893005},{"id":"https://openalex.org/keywords/propagation-constant","display_name":"propagation constant","score":0.9350000023841858},{"id":"https://openalex.org/keywords/spurious-modes","display_name":"spurious modes","score":0.5400000214576721},{"id":"https://openalex.org/keywords/longitudinal-field-component","display_name":"longitudinal field component","score":0.6389999985694885},{"id":"https://openalex.org/keywords/numerical-efficiency","display_name":"numerical efficiency","score":0.45100000500679016}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6960036754608154},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6597023606300354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5666518807411194},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.5438748598098755},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5243282914161682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4973912537097931},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.45263564586639404},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42997950315475464},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4239156246185303},{"id":"https://openalex.org/C2456702","wikidata":"https://www.wikidata.org/wiki/Q1375954","display_name":"Vector-valued function","level":2,"score":0.41167110204696655},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29475730657577515},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28943759202957153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21805429458618164},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.12533581256866455},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/ecjb.4420780508","doi":"https://doi.org/10.1002/ecjb.4420780508","is_oa":false,"landing_page_url":"https://doi.org/10.1002/ecjb.4420780508","pdf_url":null,"source":{"id":"https://openalex.org/S4210198954","display_name":"Electronics and Communications in Japan (Part II Electronics)","issn_l":"1520-6432","issn":["1520-6432","8756-663X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronics and Communications in Japan (Part II: Electronics)","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1561829173","https://openalex.org/W2029220867","https://openalex.org/W2056600736","https://openalex.org/W2086279850","https://openalex.org/W2112843438","https://openalex.org/W2130644324","https://openalex.org/W2141521951","https://openalex.org/W2149881152"],"related_works":["https://openalex.org/W7162966486","https://openalex.org/W2092921117","https://openalex.org/W7162962946","https://openalex.org/W2220957026","https://openalex.org/W7007365832","https://openalex.org/W1974391339","https://openalex.org/W2025658542","https://openalex.org/W2107337797","https://openalex.org/W2140955036","https://openalex.org/W2161363688"],"abstract_inverted_index":{"Abstract":[0],"With":[1],"respect":[2],"to":[3,52],"the":[4,12,15,19,40,53,59,64,79,87,92,106,113,133,136,142,148,153,163,167,176,179,190,198],"vector":[5,33],"finite":[6,34],"element":[7,35],"method":[8,111,188,191],"for":[9,24,86,129],"analysis":[10],"of":[11,27,63,74,78,97,105,135,147,166,170,178,202],"electromagnetic":[13,60,107],"waveguide,":[14,45],"numerical":[16,20,164],"accuracy":[17,165],"and":[18,43,55,58,91,144,156,161],"efficiency":[21],"are":[22,37,48,159],"investigated":[23],"three":[25,154],"types":[26,96],"variational":[28,80,150],"expressions":[29,81,151],"with":[30,50,116],"which":[31],"spurious\u2010free":[32],"analyses":[36],"possible.":[38],"For":[39],"linear,":[41],"isotropic,":[42],"lossless":[44],"these":[46],"methods":[47,99,204],"compared":[49],"regard":[51],"physical":[54,143],"mathematical":[56,145],"properties":[57,146],"field":[61,108,181],"construction":[62],"guided":[65,172],"mode":[66,173],"using":[67,152,192,197],"vector\u2010shape":[68],"functions":[69,85,115],"represented":[70],"by":[71,103],"complete":[72],"polynomials":[73],"identical":[75,117],"form.":[76],"Two":[77],"use":[82],"different\u2010order":[83],"shape":[84,114],"two":[88,149],"transverse":[89,121,155,194],"components":[90,158,182],"longitudinal":[93,157,180],"component.":[94],"Four":[95],"computation":[98,187,203],"can":[100,205],"be":[101,206],"constructed":[102],"selection":[104,201],"components.":[109,122,195],"Another":[110],"uses":[112],"orders":[118],"in":[119,184],"four":[120,193],"Numerical":[123],"computations":[124],"have":[125],"been":[126],"carried":[127],"out":[128],"various":[130],"waveguides.":[131],"From":[132],"results":[134],"computations,":[137],"it":[138],"is":[139],"shown":[140],"that":[141,162],"equivalent":[160],"propagation":[168],"constant":[169],"each":[171],"depends":[174],"on":[175],"magnitude":[177],"used":[183],"an":[185],"actual":[186],"unlike":[189],"By":[196],"results,":[199],"optimum":[200],"realized.":[207]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}