{"id":"https://openalex.org/W2072397758","doi":"https://doi.org/10.1109/acc.2007.4282977","title":"A Homotopic Approach to Domain Determination and Solution Refinement for the Fokker-Planck Equation","display_name":"A Homotopic Approach to Domain Determination and Solution Refinement for the Fokker-Planck Equation","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2072397758","doi":"https://doi.org/10.1109/acc.2007.4282977","mag":"2072397758"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282977","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282977","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-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/A5073597636","display_name":"Mrinal Kumar","orcid":"https://orcid.org/0000-0001-9747-9449"},"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":true,"raw_author_name":"Mrinal Kumar","raw_affiliation_strings":["Department of Aerospace Engineering, Texas A and M University, College Station, TX, USA","Texas A&M University\u2013College Station"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Texas A&M University\u2013College Station","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061286389","display_name":"Suman Chakravorty","orcid":"https://orcid.org/0000-0003-3074-3406"},"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":"Suman Chakravorty","raw_affiliation_strings":["Faculty of Aerospace Engineering, Texas A and M University, College Station, TX, USA","Faculty of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA. schakrav@aero.tamu.edu"],"affiliations":[{"raw_affiliation_string":"Faculty of Aerospace Engineering, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Faculty of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA. schakrav@aero.tamu.edu","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046235134","display_name":"John L. Junkins","orcid":"https://orcid.org/0000-0002-8482-4052"},"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":"John L. Junkins","raw_affiliation_strings":["Department of Aerospace Engineering and Holder of the George J Eppright Chair, Texas A and M University, College Station, TX, USA","Distinguished Professor, department of Aerospace Engineering, Holder, George J. Eppright Chair, Texas A&M University, College Station, TX 77843, USA. junkins@tamu.edu"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering and Holder of the George J Eppright Chair, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Distinguished Professor, department of Aerospace Engineering, Holder, George J. Eppright Chair, Texas A&M University, College Station, TX 77843, USA. junkins@tamu.edu","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073597636"],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":null,"apc_paid":null,"fwci":1.52380952,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80645161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1045","last_page":"1050"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.7469333410263062},{"id":"https://openalex.org/keywords/partition-of-unity","display_name":"Partition of unity","score":0.6460838913917542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6092855930328369},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5739412307739258},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5505675077438354},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5376262664794922},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5162999033927917},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4762454330921173},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4349510967731476},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.43338561058044434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4094414710998535},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3305102586746216},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.22223728895187378},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15226033329963684}],"concepts":[{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.7469333410263062},{"id":"https://openalex.org/C102205669","wikidata":"https://www.wikidata.org/wiki/Q191690","display_name":"Partition of unity","level":3,"score":0.6460838913917542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6092855930328369},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5739412307739258},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5505675077438354},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5376262664794922},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5162999033927917},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4762454330921173},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4349510967731476},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.43338561058044434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4094414710998535},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3305102586746216},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.22223728895187378},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15226033329963684},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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:10.1109/acc.2007.4282977","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282977","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8100000023841858}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1595848081","https://openalex.org/W1597988898","https://openalex.org/W1963706464","https://openalex.org/W1989859935","https://openalex.org/W1994513394","https://openalex.org/W2000168014","https://openalex.org/W2017277760","https://openalex.org/W2017959489","https://openalex.org/W2018039791","https://openalex.org/W2023553606","https://openalex.org/W2056907272","https://openalex.org/W2074043910","https://openalex.org/W2089172015","https://openalex.org/W2099538714","https://openalex.org/W2114849571","https://openalex.org/W2123436501","https://openalex.org/W2130709301","https://openalex.org/W2136820585","https://openalex.org/W2145364658","https://openalex.org/W2151982812","https://openalex.org/W2188148017","https://openalex.org/W2917629179","https://openalex.org/W3201678683","https://openalex.org/W4240788980","https://openalex.org/W4285719527","https://openalex.org/W6635783779","https://openalex.org/W6686732616"],"related_works":["https://openalex.org/W2992409218","https://openalex.org/W2963813038","https://openalex.org/W4307127933","https://openalex.org/W2785634710","https://openalex.org/W4301020713","https://openalex.org/W1984215587","https://openalex.org/W2381320429","https://openalex.org/W4299299922","https://openalex.org/W2593957634","https://openalex.org/W2352690124"],"abstract_inverted_index":{"An":[0],"iterative":[1],"homotopic":[2],"approach":[3],"for":[4,60],"the":[5,9,22,25,39,47,61],"solution":[6,48],"refinement":[7],"of":[8,24,34,36,41,52],"stationary":[10],"Fokker-Planck":[11],"equation":[12],"is":[13,16,58],"presented.":[14],"It":[15],"shown":[17],"that":[18],"significant":[19],"improvement":[20],"in":[21],"accuracy":[23],"approximation":[26],"can":[27],"be":[28],"achieved":[29],"with":[30,38],"a":[31,42],"small":[32],"number":[33],"degrees":[35],"freedom":[37],"use":[40],"naturally":[43],"suited":[44],"norm":[45],"on":[46],"domain.":[49],"The":[50],"partition":[51],"unity":[53],"finite":[54],"element":[55],"method":[56],"(PUFEM)":[57],"used":[59],"numerical":[62],"implementation.":[63]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
