{"id":"https://openalex.org/W2152053858","doi":"https://doi.org/10.1109/cdc.2010.5717514","title":"Analytical computation of POD modes and n-width approximations for the heat equation with boundary control","display_name":"Analytical computation of POD modes and n-width approximations for the heat equation with boundary control","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2152053858","doi":"https://doi.org/10.1109/cdc.2010.5717514","mag":"2152053858"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717514","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717514","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","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/A5018560977","display_name":"Tasha N. Fernandez","orcid":null},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T. Fernandez","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107210257","display_name":"Seddik M. Djouadi","orcid":"https://orcid.org/0000-0003-4925-723X"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S.M. Djouadi","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072123379","display_name":"Russell Chris Camphouse","orcid":null},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R.C. Camphouse","raw_affiliation_strings":["Performance Assessment and Decision Analysis Department, Sandia National Laboratories, Carlsbad, NM, USA"],"affiliations":[{"raw_affiliation_string":"Performance Assessment and Decision Analysis Department, Sandia National Laboratories, Carlsbad, NM, USA","institution_ids":["https://openalex.org/I192454743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018560977"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.19317497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"870","last_page":"875"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9970999956130981,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/point-of-delivery","display_name":"Point of delivery","score":0.6995713710784912},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6502245664596558},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6494266390800476},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6308548450469971},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6271864175796509},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.5428228378295898},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5127326250076294},{"id":"https://openalex.org/keywords/heat-kernel","display_name":"Heat kernel","score":0.4933437407016754},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4930133521556854},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.46370750665664673},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4499618709087372},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.43978753685951233},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.4354351758956909},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40588515996932983},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2812480926513672},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10479086637496948},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10164090991020203},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08589810132980347}],"concepts":[{"id":"https://openalex.org/C137776501","wikidata":"https://www.wikidata.org/wiki/Q7208270","display_name":"Point of delivery","level":2,"score":0.6995713710784912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6502245664596558},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6494266390800476},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6308548450469971},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6271864175796509},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5428228378295898},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5127326250076294},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.4933437407016754},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4930133521556854},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.46370750665664673},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4499618709087372},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43978753685951233},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.4354351758956909},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40588515996932983},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2812480926513672},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10479086637496948},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10164090991020203},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08589810132980347},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2010.5717514","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717514","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W419552243","https://openalex.org/W1515569264","https://openalex.org/W1579236455","https://openalex.org/W1845740698","https://openalex.org/W1868559974","https://openalex.org/W1994251552","https://openalex.org/W2004485838","https://openalex.org/W2011464857","https://openalex.org/W2059814274","https://openalex.org/W2062393840","https://openalex.org/W2065313971","https://openalex.org/W2069114279","https://openalex.org/W2098077093","https://openalex.org/W2120756413","https://openalex.org/W2145586686","https://openalex.org/W2147046190","https://openalex.org/W2322736403","https://openalex.org/W2324884288","https://openalex.org/W2330666245","https://openalex.org/W3021722416","https://openalex.org/W3105504410","https://openalex.org/W3195133498","https://openalex.org/W3195435719","https://openalex.org/W4250397849","https://openalex.org/W4285719527","https://openalex.org/W4299521717","https://openalex.org/W6630990112","https://openalex.org/W6667699684","https://openalex.org/W6800164818","https://openalex.org/W6992479258"],"related_works":["https://openalex.org/W1480038316","https://openalex.org/W4383033865","https://openalex.org/W3142541575","https://openalex.org/W2375444032","https://openalex.org/W4313588295","https://openalex.org/W2963145522","https://openalex.org/W2137684886","https://openalex.org/W2086387131","https://openalex.org/W4321473527","https://openalex.org/W2023776688"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"for":[3,20,90],"the":[4,9,21,31,36,45,59,69,78,84,91,95],"purpose":[5],"of":[6,12,30,38,58,77,86],"model":[7],"reduction":[8],"analytical":[10],"expressions":[11],"proper":[13],"orthogonal":[14],"decomposition":[15],"(POD)":[16],"modes":[17,47,65,70,80],"are":[18,51,66],"derived":[19],"heat":[22,92],"equation":[23],"with":[24],"boundary":[25],"control.":[26],"The":[27,62,74],"autocorrelation":[28],"function":[29],"latter":[32],"is":[33],"viewed":[34],"as":[35],"kernel":[37],"a":[39],"self":[40],"adjoint":[41],"compact":[42],"operator,":[43],"and":[44,48,81,99],"POD":[46,64,79],"corresponding":[49],"eigenvalues":[50,82],"computed":[52,63],"by":[53],"solving":[54],"homogeneous":[55],"integral":[56],"equations":[57],"second":[60],"kind.":[61],"compared":[67],"to":[68],"obtained":[71],"from":[72],"snapshots.":[73],"explicit":[75],"computation":[76,85],"allow":[83],"different":[87],"n-widths":[88],"approximations":[89],"equation,":[93],"including":[94],"linear,":[96],"Kolmogorov,":[97],"Gelfand,":[98],"Bernstein":[100],"n-widths.":[101]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}