{"id":"https://openalex.org/W2811272656","doi":"https://doi.org/10.1137/17m1127041","title":"An Entropic Fourier Method for the Boltzmann Equation","display_name":"An Entropic Fourier Method for the Boltzmann Equation","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2811272656","doi":"https://doi.org/10.1137/17m1127041","mag":"2811272656"},"language":"en","primary_location":{"id":"doi:10.1137/17m1127041","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1127041","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-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/A5025938442","display_name":"Zhenning Cai","orcid":"https://orcid.org/0000-0002-7086-7983"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhenning Cai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032790636","display_name":"Yuwei Fan","orcid":"https://orcid.org/0000-0001-9566-6996"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuwei Fan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011918131","display_name":"Lexing Ying","orcid":"https://orcid.org/0000-0003-1547-1457"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lexing Ying","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8506,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.95852345,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"40","issue":"5","first_page":"A2858","last_page":"A2882"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":1.0,"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":1.0,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9995999932289124,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9986000061035156,"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":0.8071161508560181},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7870540618896484},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6191022992134094},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.6015487313270569},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5850157141685486},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5169526934623718},{"id":"https://openalex.org/keywords/discrete-time-fourier-transform","display_name":"Discrete-time Fourier transform","score":0.5085200071334839},{"id":"https://openalex.org/keywords/discrete-fourier-series","display_name":"Discrete Fourier series","score":0.49154457449913025},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.48759570717811584},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.4687500298023224},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45670294761657715},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.4461105763912201},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4380950927734375},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.43112149834632874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33718928694725037},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.16586396098136902},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07137465476989746}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8071161508560181},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7870540618896484},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6191022992134094},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.6015487313270569},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5850157141685486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5169526934623718},{"id":"https://openalex.org/C122444316","wikidata":"https://www.wikidata.org/wiki/Q1440048","display_name":"Discrete-time Fourier transform","level":5,"score":0.5085200071334839},{"id":"https://openalex.org/C175225751","wikidata":"https://www.wikidata.org/wiki/Q15927242","display_name":"Discrete Fourier series","level":5,"score":0.49154457449913025},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.48759570717811584},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.4687500298023224},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45670294761657715},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.4461105763912201},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4380950927734375},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.43112149834632874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33718928694725037},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.16586396098136902},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07137465476989746},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1127041","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1127041","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1974987146","https://openalex.org/W1990352033","https://openalex.org/W1998750192","https://openalex.org/W1998759078","https://openalex.org/W2003443771","https://openalex.org/W2005832942","https://openalex.org/W2015135997","https://openalex.org/W2037783202","https://openalex.org/W2043953726","https://openalex.org/W2051358691","https://openalex.org/W2065686411","https://openalex.org/W2086112279","https://openalex.org/W2116729868","https://openalex.org/W2125505119","https://openalex.org/W2146950839","https://openalex.org/W2162483424","https://openalex.org/W2232401248","https://openalex.org/W2952364624","https://openalex.org/W2963446664","https://openalex.org/W3098469631","https://openalex.org/W3098837341"],"related_works":["https://openalex.org/W198181464","https://openalex.org/W2154898175","https://openalex.org/W3200940340","https://openalex.org/W4353087863","https://openalex.org/W3166675296","https://openalex.org/W337559378","https://openalex.org/W991365525","https://openalex.org/W4239009053","https://openalex.org/W2801154423","https://openalex.org/W2131258459"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2],"entropic":[3],"Fourier":[4,46,70],"method":[5,24,42],"for":[6],"the":[7,11,27,30,55,58,66,78],"numerical":[8,89],"discretization":[9],"of":[10,29,57,65],"Boltzmann":[12],"collision":[13],"operator.":[14],"The":[15],"method,":[16,33,52,71],"which":[17],"is":[18,86],"obtained":[19],"by":[20,88],"modifying":[21],"a":[22,39,45,49,62,69],"Fourier--Galerkin":[23],"to":[25,75],"match":[26],"form":[28],"discrete":[31,40,50,63],"velocity":[32,41,51],"can":[34],"be":[35],"viewed":[36],"both":[37],"as":[38,44],"and":[43,60],"method.":[47],"As":[48,68],"it":[53,72],"preserves":[54],"positivity":[56],"solution":[59],"satisfies":[61],"version":[64],"H-theorem.":[67],"allows":[73],"one":[74],"readily":[76],"apply":[77],"FFT-based":[79],"fast":[80],"algorithms.":[81],"A":[82],"second-order":[83],"convergence":[84],"rate":[85],"validated":[87],"experiments.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
