{"id":"https://openalex.org/W7224316338","doi":"https://doi.org/10.20998/2222-0631.2026.02(11).07","title":"MODELING ELECTROSTATIC FIELD IN COMPLEX NON-AXISYMMETRIC DOMAINS WITH A NON-COMPACT BOUNDARY","display_name":"MODELING ELECTROSTATIC FIELD IN COMPLEX NON-AXISYMMETRIC DOMAINS WITH A NON-COMPACT BOUNDARY","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224316338","doi":"https://doi.org/10.20998/2222-0631.2026.02(11).07"},"language":"en","primary_location":{"id":"doi:10.20998/2222-0631.2026.02(11).07","doi":"https://doi.org/10.20998/2222-0631.2026.02(11).07","is_oa":true,"landing_page_url":"https://doi.org/10.20998/2222-0631.2026.02(11).07","pdf_url":"https://mmtt.khpi.edu.ua/article/download/376899/359639","source":{"id":"https://openalex.org/S4210181089","display_name":"Bulletin of the National Technical University KhPI Series Mathematical modeling in engineering and technologies","issn_l":"2222-0631","issn":["2222-0631"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310322073","host_organization_name":"National Technical University \"Kharkiv Polytechnic Institute\"","host_organization_lineage":["https://openalex.org/P4310322073"],"host_organization_lineage_names":["National Technical University \"Kharkiv Polytechnic Institute\""],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the National Technical University \"KhPI\". Series: Mathematical modeling in engineering and technologies","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://mmtt.khpi.edu.ua/article/download/376899/359639","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009376086","display_name":"A. G. Nikolaev","orcid":"https://orcid.org/0000-0002-7351-1392","observed_orcids":["https://orcid.org/0000-0002-7351-1392"]},"institutions":[{"id":"https://openalex.org/I23686167","display_name":"National Aerospace University \u2013 Kharkiv Aviation Institute","ror":"https://ror.org/048j5n646","country_code":"UA","type":"education","lineage":["https://openalex.org/I23686167"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Oleksii Georhiiovych Nikolaev","raw_affiliation_strings":["National Aerospace University \"Kharkiv Aviation Institute\""],"raw_orcid":"https://orcid.org/0000-0002-7351-1392","affiliations":[{"raw_affiliation_string":"National Aerospace University \"Kharkiv Aviation Institute\"","institution_ids":["https://openalex.org/I23686167"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5160067636","display_name":"Inna Volodymyrivna Lymarenko","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I23686167","display_name":"National Aerospace University \u2013 Kharkiv Aviation Institute","ror":"https://ror.org/048j5n646","country_code":"UA","type":"education","lineage":["https://openalex.org/I23686167"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Inna Volodymyrivna Lymarenko","raw_affiliation_strings":["National Aerospace University \"Kharkiv Aviation Institute\""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Aerospace University \"Kharkiv Aviation Institute\"","institution_ids":["https://openalex.org/I23686167"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I23686167"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.76393089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":"2(11)","first_page":"77","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9286999702453613,"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":0.9286999702453613,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.04479999840259552,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14311","display_name":"Electrical and Electromagnetic Research","score":0.008999999612569809,"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/electrostatic-field","display_name":"electrostatic field","score":0.8880000114440918},{"id":"https://openalex.org/keywords/parabolic-cylinder","display_name":"parabolic cylinder","score":0.9819999933242798},{"id":"https://openalex.org/keywords/generalized-fourier-method","display_name":"generalized Fourier method","score":0.8759999871253967},{"id":"https://openalex.org/keywords/fredholm-operators","display_name":"Fredholm operators","score":0.8880000114440918},{"id":"https://openalex.org/keywords/point-charges","display_name":"point charges","score":0.5619999766349792},{"id":"https://openalex.org/keywords/charge-density-distribution","display_name":"charge density distribution","score":0.8999999761581421},{"id":"https://openalex.org/keywords/capacitance","display_name":"capacitance","score":0.7269999980926514},{"id":"https://openalex.org/keywords/green-s-function","display_name":"Green's function","score":0.9710000157356262},{"id":"https://openalex.org/keywords/laplace-equation","display_name":"Laplace equation","score":0.9639999866485596},{"id":"https://openalex.org/keywords/addition-theorems","display_name":"addition theorems","score":0.9409999847412109},{"id":"https://openalex.org/keywords/coordinate-systems","display_name":"coordinate systems","score":0.39100000262260437}],"concepts":[{"id":"https://openalex.org/C20625954","wikidata":"https://www.wikidata.org/wiki/Q543533","display_name":"Coplanarity","level":2,"score":0.6471999883651733},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6237000226974487},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5534999966621399},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5532000064849854},{"id":"https://openalex.org/C175749648","wikidata":"https://www.wikidata.org/wiki/Q1068091","display_name":"Point particle","level":2,"score":0.5468000173568726},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5133000016212463},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.5049999952316284},{"id":"https://openalex.org/C117626034","wikidata":"https://www.wikidata.org/wiki/Q26336","display_name":"Electrostatics","level":2,"score":0.5045999884605408},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49790000915527344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4896000027656555},{"id":"https://openalex.org/C202374169","wikidata":"https://www.wikidata.org/wiki/Q124291","display_name":"Electrical conductor","level":2,"score":0.48829999566078186},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4869999885559082},{"id":"https://openalex.org/C2986897749","wikidata":"https://www.wikidata.org/wiki/Q231761","display_name":"Potential field","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.44350001215934753},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43880000710487366},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42820000648498535},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35269999504089355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3450999855995178},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.34369999170303345},{"id":"https://openalex.org/C58570533","wikidata":"https://www.wikidata.org/wiki/Q55451","display_name":"Electric potential","level":3,"score":0.3366999924182892},{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C143551052","wikidata":"https://www.wikidata.org/wiki/Q2426155","display_name":"Ewald summation","level":3,"score":0.3163999915122986},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2815999984741211},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C24743483","wikidata":"https://www.wikidata.org/wiki/Q1154848","display_name":"Potential theory","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.266400009393692},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.26409998536109924},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.25999999046325684}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.20998/2222-0631.2026.02(11).07","doi":"https://doi.org/10.20998/2222-0631.2026.02(11).07","is_oa":true,"landing_page_url":"https://doi.org/10.20998/2222-0631.2026.02(11).07","pdf_url":"https://mmtt.khpi.edu.ua/article/download/376899/359639","source":{"id":"https://openalex.org/S4210181089","display_name":"Bulletin of the National Technical University KhPI Series Mathematical modeling in engineering and technologies","issn_l":"2222-0631","issn":["2222-0631"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310322073","host_organization_name":"National Technical University \"Kharkiv Polytechnic Institute\"","host_organization_lineage":["https://openalex.org/P4310322073"],"host_organization_lineage_names":["National Technical University \"Kharkiv Polytechnic Institute\""],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the National Technical University \"KhPI\". Series: Mathematical modeling in engineering and technologies","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.20998/2222-0631.2026.02(11).07","doi":"https://doi.org/10.20998/2222-0631.2026.02(11).07","is_oa":true,"landing_page_url":"https://doi.org/10.20998/2222-0631.2026.02(11).07","pdf_url":"https://mmtt.khpi.edu.ua/article/download/376899/359639","source":{"id":"https://openalex.org/S4210181089","display_name":"Bulletin of the National Technical University KhPI Series Mathematical modeling in engineering and technologies","issn_l":"2222-0631","issn":["2222-0631"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310322073","host_organization_name":"National Technical University \"Kharkiv Polytechnic Institute\"","host_organization_lineage":["https://openalex.org/P4310322073"],"host_organization_lineage_names":["National Technical University \"Kharkiv Polytechnic Institute\""],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of the National Technical University \"KhPI\". Series: Mathematical modeling in engineering and technologies","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224316338.pdf","grobid_xml":"https://content.openalex.org/works/W7224316338.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1977996097","https://openalex.org/W2010286372","https://openalex.org/W2101938740","https://openalex.org/W2133300588","https://openalex.org/W2138994977","https://openalex.org/W2142519853","https://openalex.org/W2579851132","https://openalex.org/W2785771526","https://openalex.org/W2943055953","https://openalex.org/W3123031921","https://openalex.org/W3159892271","https://openalex.org/W4320057317","https://openalex.org/W4394655609","https://openalex.org/W4408156596","https://openalex.org/W4413203168","https://openalex.org/W7125378260","https://openalex.org/W7133330126","https://openalex.org/W7151955035","https://openalex.org/W7159824876"],"related_works":["https://openalex.org/W1926916046","https://openalex.org/W2546976391","https://openalex.org/W4387311020","https://openalex.org/W2053057691","https://openalex.org/W1978610406","https://openalex.org/W2604646087","https://openalex.org/W2995074783","https://openalex.org/W7005767656","https://openalex.org/W1963857841","https://openalex.org/W2081712639"],"abstract_inverted_index":{"Using":[0],"the":[1,5,44,46,63,76,80,104,112,116,118,124,128,147,150,156,166,176,178,183,191,194,212,231,244,258,261,271,275,280,292,303,309,312,316,345,352,356,368,371,378,383],"example":[2],"of":[3,8,11,24,38,65,78,106,115,120,149,158,161,168,182,193,215,218,233,241,253,260,282,291,302,344],"modeling":[4,358,379],"electrostatic":[6],"field":[7,82,214],"a":[9,18,25,31,35,74,86,89,94,159,169,198,216,234,238,264,300,320,328],"system":[10,160,217,295],"charged":[12,219],"parallel":[13,220],"circular":[14,221],"disks":[15,121,222,262],"located":[16,164,236],"near":[17],"conductive":[19,170],"grounded":[20],"screen":[21,171],"in":[22,70,110,126,143,319,338,351,367,382],"theform":[23],"parabolic":[26,346],"cylinder,":[27],"this":[28,61,71,326],"paper":[29,353],"proposes":[30],"method":[32,57,380],"for":[33,60,270,315,334],"solving":[34],"whole":[36],"class":[37,41],"problems.":[39],"This":[40],"simultaneously":[42],"combines":[43],"complexityof":[45],"geometric":[47,113],"domain":[48],"with":[49,98,175],"algorithmic":[50],"and":[51,123,285,370],"computational":[52],"complexities.":[53],"A":[54],"generalized":[55],"Fourier":[56],"was":[58,67,83,130,153,202,225,296,322,332],"used":[59],"purpose,":[62],"mathematicalapparatus":[64],"which":[66,92,111,127],"further":[68],"developed":[69],"paper.":[72],"As":[73,197],"result,":[75,199],"problem":[77,210],"reconstructing":[79],"potential":[81,129,157,213,249,259],"reduced":[84],"to":[85,187,190,257],"resolving":[87],"systemwith":[88],"Fredholm":[90],"operator,":[91],"guaranteed":[93,375],"correct":[95],"approximate":[96],"solution":[97],"sufficient":[99],"accuracy.":[100,376],"The":[101,134,180,266,289],"article":[102,267],"presents":[103],"results":[105,359,373],"an":[107,251],"extensivecomputer":[108],"experiment":[109],"parameters":[114],"problem,":[117],"number":[119],"considered,":[122],"planes":[125],"calculated":[131],"were":[132,185],"varied.":[133],"graphical":[135],"information":[136],"is":[137],"supplemented":[138],"by":[139,250,363],"numerical":[140,287,372],"results,":[141],"summarized":[142],"tables.":[144],"To":[145,325],"verify":[146],"adequacy":[148],"model,":[151],"anotherproblem":[152],"also":[154],"solved:":[155],"point":[162],"charges":[163,184,192,284],"on":[165],"axis":[167],"at":[172,237],"points":[173],"coinciding":[174],"centersof":[177],"disks.":[179,196],"magnitudes":[181,281],"chosen":[186],"be":[188],"equal":[189],"corresponding":[195],"good":[200],"consistency":[201],"achieved":[203],"between":[204,306],"both":[205],"models.":[206],"For":[207,308],"comparison,":[208],"another":[209],"about":[211],"without":[223,263],"ascreen":[224],"solved":[226,350],"separately.":[227],"Calculations":[228],"showed":[229],"that":[230],"presence":[232],"screen,":[235],"relative":[239,256,304],"distance":[240,305],"0.5":[242],"from":[243],"five":[245,364],"disks,":[246,276],"reduces":[247],"thefield":[248],"average":[252],"33":[254],"%":[255],"screen.":[265],"derives":[268],"formulas":[269],"charge":[272],"density":[273],"distributionon":[274],"as":[277,279,299],"well":[278],"these":[283],"their":[286],"values.":[288],"capacitance":[290],"disk-screen":[293],"conductor":[294],"alsodetermined":[297],"separately":[298],"function":[301,314],"them.":[307],"first":[310],"time,":[311],"Green's":[313],"Laplace":[317],"equation":[318],"paraboliccylinder":[321],"obtained":[323],"explicitly.":[324],"end,":[327],"new":[329],"addition":[330],"theorem":[331],"proven":[333,366,385],"basis":[335],"harmonic":[336],"functions":[337],"arbitrarily":[339],"shifted,":[340],"identicallydirected":[341],"coordinate":[342],"systems":[343],"cylinder.":[347],"All":[348],"problems":[349],"are":[354,360],"new,":[355],"theoretical":[357],"rigorously":[361],"substantiated":[362],"theorems":[365],"paper,":[369],"have":[374],"Thus,":[377],"proposed":[381],"articlehas":[384],"its":[386],"high":[387],"effectiveness.":[388]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-30T00:00:00"}
