{"id":"https://openalex.org/W3136522052","doi":"https://doi.org/10.1137/21m1406143","title":"Hyperbolic Quadrature Method of Moments for the One-Dimensional Kinetic Equation","display_name":"Hyperbolic Quadrature Method of Moments for the One-Dimensional Kinetic Equation","publication_year":2022,"publication_date":"2022-04-01","ids":{"openalex":"https://openalex.org/W3136522052","doi":"https://doi.org/10.1137/21m1406143","mag":"3136522052"},"language":"en","primary_location":{"id":"doi:10.1137/21m1406143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1406143","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.10138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039784451","display_name":"Rodney O. Fox","orcid":"https://orcid.org/0000-0003-1944-1861"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rodney O. Fox","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1944-1861","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040283430","display_name":"Fr\u00e9d\u00e9rique Laurent","orcid":"https://orcid.org/0000-0002-7365-1205"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9rique Laurent","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7365-1205","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.4974,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.96888947,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"82","issue":"2","first_page":"750","last_page":"771"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.6797999739646912,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.6797999739646912,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.04740000143647194,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.03420000150799751,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7805672883987427},{"id":"https://openalex.org/keywords/moment-closure","display_name":"Moment closure","score":0.6086378693580627},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5909700989723206},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4721531867980957},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.44071725010871887},{"id":"https://openalex.org/keywords/velocity-moments","display_name":"Velocity Moments","score":0.41351646184921265},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4083611071109772},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12254336476325989},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.09833905100822449}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7805672883987427},{"id":"https://openalex.org/C2778513689","wikidata":"https://www.wikidata.org/wiki/Q6897109","display_name":"Moment closure","level":3,"score":0.6086378693580627},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5909700989723206},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4721531867980957},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.44071725010871887},{"id":"https://openalex.org/C149539972","wikidata":"https://www.wikidata.org/wiki/Q7919290","display_name":"Velocity Moments","level":4,"score":0.41351646184921265},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4083611071109772},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12254336476325989},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.09833905100822449},{"id":"https://openalex.org/C165699331","wikidata":"https://www.wikidata.org/wiki/Q461533","display_name":"Wavefront","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0},{"id":"https://openalex.org/C92423082","wikidata":"https://www.wikidata.org/wiki/Q132146","display_name":"Zernike polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1406143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1406143","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2103.10138","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.10138","pdf_url":"https://arxiv.org/pdf/2103.10138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03171566v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03171566","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Mathematics, 2022, 82 (2), pp.750-771. ⟨10.1137/21m1406143⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.10138","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.10138","pdf_url":"https://arxiv.org/pdf/2103.10138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1580574365","https://openalex.org/W1971818437","https://openalex.org/W1991332489","https://openalex.org/W2000773262","https://openalex.org/W2023141162","https://openalex.org/W2037978467","https://openalex.org/W2051247278","https://openalex.org/W2063430114","https://openalex.org/W2087558637","https://openalex.org/W2131947874","https://openalex.org/W2143008187","https://openalex.org/W2146396721","https://openalex.org/W2312531161","https://openalex.org/W2514639761","https://openalex.org/W2769298387","https://openalex.org/W2910353827","https://openalex.org/W2963128411","https://openalex.org/W2963311102","https://openalex.org/W2984051592","https://openalex.org/W3000282213","https://openalex.org/W3039049215","https://openalex.org/W3045611844","https://openalex.org/W3098675970","https://openalex.org/W3101674322"],"related_works":["https://openalex.org/W2155202381","https://openalex.org/W1851800418","https://openalex.org/W2121476007","https://openalex.org/W2095125040","https://openalex.org/W2782848073","https://openalex.org/W2164786588","https://openalex.org/W1971889155","https://openalex.org/W2964893519","https://openalex.org/W2027651914","https://openalex.org/W4380994390"],"abstract_inverted_index":{"A":[0],"tractable":[1],"solution":[2,216],"is":[3,32,50,83,94,120,212,222],"proposed":[4],"to":[5,21,69,75,87,115,209,217,224],"a":[6,24,122,133,218],"classical":[7],"problem":[8,221],"in":[9,44,54,168],"kinetic":[10,48],"theory,":[11],"namely,":[12],"given":[13],"any":[14],"set":[15],"of":[16,29,64,100,132,144,150,155,159,165,181,188,202,227],"realizable":[17],"velocity":[18,112,134],"moments":[19,65,113,207],"up":[20,74,114,208],"order":[22,30,77,116,203,210],"$2n$,":[23],"closure":[25,93,124,230],"for":[26,34,198],"the":[27,36,41,45,60,98,101,111,130,138,142,151,156,160,163,169,186,195,200,206,228],"moment":[28,37,72,123,145,201],"$2n+1$":[31,204],"constructed":[33],"which":[35],"system":[38,73,161],"found":[39],"from":[40,205],"free-transport":[42],"term":[43],"one-dimensional":[46],"(1-D)":[47],"equation":[49],"globally":[51],"hyperbolic":[52,61],"and":[53,85,125,172,184],"conservative":[55],"form.":[56],"In":[57],"prior":[58],"work,":[59],"quadrature":[62],"method":[63],"(HyQMOM)":[66],"was":[67],"introduced":[68],"close":[70],"this":[71],"fourth":[76],"($n":[78],"\\le":[79],"2$).":[80],"Here,":[81],"HyQMOM":[82,92,119,229],"reformulated":[84],"extended":[86],"arbitrary":[88],"even-order":[89],"moments.":[90,140],"The":[91,177,214],"defined":[95,109],"based":[96,193],"on":[97,129,194],"properties":[99],"monic":[102],"orthogonal":[103],"polynomials":[104],"$Q_n$":[105,173],"that":[106],"are":[107,162],"uniquely":[108],"by":[110],"$2n-1$.":[117],"Thus,":[118],"strictly":[121],"does":[126],"not":[127],"rely":[128],"reconstruction":[131],"distribution":[135],"function":[136],"with":[137,231],"same":[139],"On":[141],"boundary":[143],"space,":[146],"$n$":[147,175],"double":[148],"roots":[149,164,180,187],"characteristic":[152],"polynomial":[153],"$P_{2n+1}$":[154,171,182],"Jacobian":[157],"matrix":[158],"$Q_n$,":[166],"while":[167],"interior,":[170],"share":[174],"roots.":[176],"remaining":[178],"$n+1$":[179],"bound":[183],"separate":[185],"$Q_n$.":[189],"An":[190],"efficient":[191],"algorithm,":[192,197],"Chebyshev":[196],"computing":[199],"$2n$":[211],"developed.":[213],"analytical":[215],"1-D":[219],"Riemann":[220],"used":[223],"demonstrate":[225],"convergence":[226],"increasing":[232],"$n$.":[233]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}