{"id":"https://openalex.org/W3195387697","doi":"https://doi.org/10.1137/20m1380788","title":"Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit","display_name":"Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3195387697","doi":"https://doi.org/10.1137/20m1380788","mag":"3195387697"},"language":"en","primary_location":{"id":"doi:10.1137/20m1380788","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1380788","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5026906318","display_name":"Zhiyan Ding","orcid":"https://orcid.org/0000-0001-8863-403X"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhiyan Ding","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019445901","display_name":"Lukas Einkemmer","orcid":"https://orcid.org/0000-0002-8798-2304"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Lukas Einkemmer","raw_affiliation_strings":["Department of Mathematics, University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100438891","display_name":"Qin Li","orcid":"https://orcid.org/0000-0001-9210-8948"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I2802999273","display_name":"Wisconsin Institutes for Discovery","ror":"https://ror.org/05gbven85","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2802999273"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qin Li","raw_affiliation_strings":["Department of Mathematics and Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI, 53706, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I2802999273","https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026906318"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":2.2318,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.8868223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"4","first_page":"2254","last_page":"2285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"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":0.9987000226974487,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980999827384949,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7016820907592773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6832217574119568},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6033684611320496},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5824005603790283},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.5756192207336426},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.49875879287719727},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.4581931531429291},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4316052496433258},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3221091628074646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.297635018825531},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13404271006584167}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7016820907592773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6832217574119568},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6033684611320496},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5824005603790283},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5756192207336426},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.49875879287719727},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.4581931531429291},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4316052496433258},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3221091628074646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.297635018825531},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13404271006584167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"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/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1380788","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1380788","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3080512194","display_name":null,"funder_award_id":"1740707","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G382852709","display_name":null,"funder_award_id":"TRIPODS: 1740707","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4403718343","display_name":null,"funder_award_id":"DMS-1750488","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6203420807","display_name":null,"funder_award_id":"TRIPODS","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7005066020","display_name":null,"funder_award_id":"1619778","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7747989704","display_name":null,"funder_award_id":"1107291","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8569211670","display_name":null,"funder_award_id":"DMS-1619778","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1580989833","https://openalex.org/W1945958945","https://openalex.org/W1967562270","https://openalex.org/W1974987146","https://openalex.org/W1988996307","https://openalex.org/W2001032670","https://openalex.org/W2001859599","https://openalex.org/W2002633056","https://openalex.org/W2013637933","https://openalex.org/W2031008300","https://openalex.org/W2032827682","https://openalex.org/W2049887960","https://openalex.org/W2050873954","https://openalex.org/W2051456448","https://openalex.org/W2055048779","https://openalex.org/W2060331029","https://openalex.org/W2061170466","https://openalex.org/W2067067855","https://openalex.org/W2080330641","https://openalex.org/W2096434207","https://openalex.org/W2101644050","https://openalex.org/W2102688209","https://openalex.org/W2115402677","https://openalex.org/W2118115288","https://openalex.org/W2120208332","https://openalex.org/W2121827693","https://openalex.org/W2144965994","https://openalex.org/W2152279941","https://openalex.org/W2155073557","https://openalex.org/W2165335881","https://openalex.org/W2257781909","https://openalex.org/W2294357336","https://openalex.org/W2411900373","https://openalex.org/W2793973608","https://openalex.org/W2962793222","https://openalex.org/W2962883250","https://openalex.org/W2964036597","https://openalex.org/W2964241805","https://openalex.org/W2968110048","https://openalex.org/W2979430961","https://openalex.org/W3099008000","https://openalex.org/W3100470592","https://openalex.org/W3104117848","https://openalex.org/W3104755947","https://openalex.org/W3104980255","https://openalex.org/W3105340407","https://openalex.org/W4232904039"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W3106318770","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2377513064","https://openalex.org/W2016990342"],"abstract_inverted_index":{"Dynamical":[0],"low-rank":[1,11,36,53,106,139,163,194,209],"algorithms":[2,54,164],"are":[3,101],"a":[4,24,137,207,213],"class":[5],"of":[6,13,34,47,108,158,161],"numerical":[7,114,123],"methods":[8,100],"that":[9,98,185],"compute":[10],"approximations":[12],"dynamical":[14,52,138,162,208],"systems.":[15],"This":[16,196],"is":[17,125,174],"accomplished":[18],"by":[19],"projecting":[20],"the":[21,29,35,88,91,99,105,109,143,156,159,186,201],"dynamics":[22],"onto":[23],"low-dimensional":[25],"manifold":[26],"and":[27,72,90,111,181,190],"writing":[28],"solution":[30,110],"directly":[31],"in":[32,58,151,170],"terms":[33],"factors.":[37],"The":[38,168],"approach":[39],"has":[40],"been":[41,56],"successfully":[42],"applied":[43,141,211],"to":[44,83,103,142,154,165,176,212],"many":[45],"types":[46],"differential":[48],"equations.":[49],"Recently,":[50],"efficient":[51],"have":[55],"proposed":[57],"[L.":[59],"Einkemmer,":[60],"A":[61],"Low-Rank":[62],"Algorithm":[63],"for":[64,136,206],"Weakly":[65],"Compressible":[66],"Flow,":[67],"arXiv:1804.04561,":[68],"2018;":[69],"L.":[70],"Einkemmer":[71],"C.":[73],"Lubich,":[74],"SIAM":[75],"J.":[76],"Sci.":[77],"Comput.,":[78],"40":[79],"(2018),":[80],"pp.":[81],"B1330--B1360]":[82],"treat":[84],"kinetic":[85,152,166,214],"equations,":[86],"including":[87],"Vlasov--Poisson":[89],"Boltzmann":[92,146],"equation.":[93],"There":[94],"it":[95],"was":[96],"demonstrated":[97],"able":[102],"capture":[104,192],"structure":[107],"significantly":[112],"reduce":[113],"cost,":[115],"while":[116],"often":[117],"maintaining":[118],"high":[119],"accuracy.":[120],"However,":[121],"no":[122],"analysis":[124,135,205],"currently":[126],"available.":[127],"In":[128],"this":[129,193],"paper,":[130],"we":[131,182],"perform":[132],"an":[133],"error":[134,204],"algorithm":[140],"multiscale":[144],"linear":[145],"equation":[147],"(a":[148],"classical":[149],"model":[150],"theory)":[153],"showcase":[155],"validity":[157],"application":[160],"theory.":[167],"equation,":[169],"its":[171],"parabolic":[172],"regime,":[173],"known":[175],"be":[177],"rank":[178],"1":[179],"theoretically,":[180],"will":[183],"prove":[184],"scheme":[187],"can":[188],"dynamically":[189],"automatically":[191],"structure.":[195],"work":[197],"thus":[198],"serves":[199],"as":[200],"first":[202],"mathematical":[203],"approximation":[210],"problem.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
