{"id":"https://openalex.org/W4225998070","doi":"https://doi.org/10.1137/21m1458247","title":"Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes","display_name":"Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes","publication_year":2023,"publication_date":"2023-11-01","ids":{"openalex":"https://openalex.org/W4225998070","doi":"https://doi.org/10.1137/21m1458247"},"language":"en","primary_location":{"id":"doi:10.1137/21m1458247","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1458247","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/21M1458247?download=true","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/21M1458247?download=true","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kailiang Wu","orcid":"https://orcid.org/0000-0001-7482-5062"},"institutions":[{"id":"https://openalex.org/I200296433","display_name":"Chinese Academy of Medical Sciences & Peking Union Medical College","ror":"https://ror.org/02drdmm93","country_code":"CN","type":"education","lineage":["https://openalex.org/I200296433"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kailiang Wu","raw_affiliation_strings":["\\dagger Department of Mathematics , SUSTech International Center for Mathematics , Southern Univer- sity of Science and Technology , and National Center for Applied Mathematics Shenzhen (NCAMS) , Shenzhen , Guangdong 518055 , China"],"raw_orcid":"https://orcid.org/0000-0001-7482-5062","affiliations":[{"raw_affiliation_string":"\\dagger Department of Mathematics , SUSTech International Center for Mathematics , Southern Univer- sity of Science and Technology , and National Center for Applied Mathematics Shenzhen (NCAMS) , Shenzhen , Guangdong 518055 , China","institution_ids":["https://openalex.org/I200296433","https://openalex.org/I3045169105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047035333","display_name":"Chi\u2010Wang Shu","orcid":"https://orcid.org/0000-0001-7720-9564"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chi-Wang Shu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7720-9564","affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01182318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"4","first_page":"1031","last_page":"1073"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13497","display_name":"Hermeneutics and Narrative Identity","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T13497","display_name":"Hermeneutics and Narrative Identity","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13695","display_name":"Aging, Elder Care, and Social Issues","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/3600","display_name":"General Health Professions"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T13099","display_name":"Health, Medicine and Society","score":0.95660001039505,"subfield":{"id":"https://openalex.org/subfields/3600","display_name":"General Health Professions"},"field":{"id":"https://openalex.org/fields/36","display_name":"Health Professions"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6742710471153259},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6106822490692139},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6008477210998535},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5990545749664307},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48212504386901855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47776877880096436},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.42197558283805847},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4167459011077881},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3850049376487732},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38215136528015137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2105289101600647},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11995059251785278},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09374332427978516}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6742710471153259},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6106822490692139},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6008477210998535},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5990545749664307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48212504386901855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47776877880096436},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.42197558283805847},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4167459011077881},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3850049376487732},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38215136528015137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2105289101600647},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11995059251785278},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09374332427978516},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1458247","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1458247","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/21M1458247?download=true","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/21m1458247","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1458247","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/21M1458247?download=true","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2918700403","display_name":null,"funder_award_id":"12171227","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G36446433","display_name":null,"funder_award_id":"FA9550-20-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G427217464","display_name":null,"funder_award_id":"DMS-2010107","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4837876779","display_name":null,"funder_award_id":"FA9550-20-1-0055.","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5729145195","display_name":null,"funder_award_id":"FA9550-20","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6137477588","display_name":null,"funder_award_id":"12171227","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8215495876","display_name":"High Order Schemes: Robustness, Efficiency, and Stochastic Effects","funder_award_id":"2010107","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"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4225998070.pdf","grobid_xml":"https://content.openalex.org/works/W4225998070.grobid-xml"},"referenced_works_count":116,"referenced_works":["https://openalex.org/W10764281","https://openalex.org/W752645271","https://openalex.org/W1966239316","https://openalex.org/W1969395389","https://openalex.org/W1974099477","https://openalex.org/W1980103755","https://openalex.org/W1987675555","https://openalex.org/W1987937688","https://openalex.org/W1990790313","https://openalex.org/W1993538940","https://openalex.org/W1994955324","https://openalex.org/W2004302354","https://openalex.org/W2004898338","https://openalex.org/W2005768635","https://openalex.org/W2008166083","https://openalex.org/W2008956940","https://openalex.org/W2021275151","https://openalex.org/W2023948158","https://openalex.org/W2024099978","https://openalex.org/W2024361440","https://openalex.org/W2026894631","https://openalex.org/W2032343734","https://openalex.org/W2033525926","https://openalex.org/W2034029678","https://openalex.org/W2038007684","https://openalex.org/W2042177365","https://openalex.org/W2054597080","https://openalex.org/W2054988599","https://openalex.org/W2055880686","https://openalex.org/W2055887270","https://openalex.org/W2057662384","https://openalex.org/W2058765828","https://openalex.org/W2061088299","https://openalex.org/W2071701027","https://openalex.org/W2072099237","https://openalex.org/W2072150166","https://openalex.org/W2074900879","https://openalex.org/W2078033075","https://openalex.org/W2088718866","https://openalex.org/W2090061427","https://openalex.org/W2091178963","https://openalex.org/W2092584883","https://openalex.org/W2092910485","https://openalex.org/W2094818681","https://openalex.org/W2094894029","https://openalex.org/W2095470955","https://openalex.org/W2096324403","https://openalex.org/W2098364742","https://openalex.org/W2098451156","https://openalex.org/W2105387413","https://openalex.org/W2116729868","https://openalex.org/W2120966574","https://openalex.org/W2126479355","https://openalex.org/W2161783230","https://openalex.org/W2318861708","https://openalex.org/W2409693504","https://openalex.org/W2492545630","https://openalex.org/W2507484451","https://openalex.org/W2525391476","https://openalex.org/W2530159564","https://openalex.org/W2530252398","https://openalex.org/W2530578203","https://openalex.org/W2530847379","https://openalex.org/W2558642297","https://openalex.org/W2568579702","https://openalex.org/W2574003032","https://openalex.org/W2579422625","https://openalex.org/W2597037285","https://openalex.org/W2611618900","https://openalex.org/W2745476525","https://openalex.org/W2777191004","https://openalex.org/W2787270748","https://openalex.org/W2789108710","https://openalex.org/W2794063120","https://openalex.org/W2798719855","https://openalex.org/W2805719800","https://openalex.org/W2809858621","https://openalex.org/W2851699097","https://openalex.org/W2897418613","https://openalex.org/W2901277663","https://openalex.org/W2902098003","https://openalex.org/W2914074116","https://openalex.org/W2924663918","https://openalex.org/W2945798956","https://openalex.org/W2946480467","https://openalex.org/W2952800475","https://openalex.org/W2955676493","https://openalex.org/W2962833397","https://openalex.org/W2962976992","https://openalex.org/W2963562886","https://openalex.org/W2964177232","https://openalex.org/W2964325435","https://openalex.org/W2980240043","https://openalex.org/W3000033894","https://openalex.org/W3012705530","https://openalex.org/W3025882857","https://openalex.org/W3029281960","https://openalex.org/W3048822804","https://openalex.org/W3086430718","https://openalex.org/W3092625540","https://openalex.org/W3110724176","https://openalex.org/W3133356548","https://openalex.org/W3159048616","https://openalex.org/W3159813613","https://openalex.org/W3160679425","https://openalex.org/W3164691581","https://openalex.org/W3171856336","https://openalex.org/W3172003963","https://openalex.org/W3187402050","https://openalex.org/W3215639577","https://openalex.org/W4210398350","https://openalex.org/W4235926700","https://openalex.org/W4250589301","https://openalex.org/W4253408650","https://openalex.org/W4292070096","https://openalex.org/W4313549260"],"related_works":["https://openalex.org/W1369132","https://openalex.org/W102507","https://openalex.org/W2970780","https://openalex.org/W12173359","https://openalex.org/W15972590","https://openalex.org/W12544505","https://openalex.org/W2679833","https://openalex.org/W3451101","https://openalex.org/W4450723","https://openalex.org/W11272930"],"abstract_inverted_index":{"Solutions":[0],"to":[1,47,104,128,134,175],"many":[2,81],"partial":[3,179],"differential":[4,180],"equations":[5,20,181],"satisfy":[6],"certain":[7],"bounds":[8],"or":[9,206],"constraints.":[10,56,87,121],"For":[11],"example,":[12],"the":[13,26,29,36,146,155,172],"density":[14],"and":[15,24,65,100,149,161,182,186,197],"pressure":[16],"are":[17],"positive":[18],"for":[19,80,115,167,189],"of":[21,38,125,152,158,178],"fluid":[22,30],"dynamics,":[23],"in":[25,70],"relativistic":[27],"case":[28],"velocity":[31],"is":[32,45,127],"upper":[33],"bounded":[34],"by":[35,137,204],"speed":[37],"light,":[39],"etc.":[40],"As":[41],"widely":[42],"realized,":[43],"it":[44],"crucial":[46],"develop":[48],"bound-preserving":[49,59,117,191],"numerical":[50],"methods":[51,166],"that":[52],"preserve":[53],"such":[54],"intrinsic":[55],"Exploring":[57],"provably":[58],"schemes":[60],"has":[61,66],"attracted":[62],"much":[63],"attention":[64],"been":[67],"actively":[68],"studied":[69],"recent":[71],"years.":[72],"This":[73],"is,":[74],"however,":[75],"still":[76],"a":[77,111,176],"challenging":[78,195],"task":[79],"systems,":[82],"especially":[83],"those":[84],"involving":[85],"nonlinear":[86,120,132],"Based":[88],"on":[89],"some":[90,140],"key":[91],"insights":[92],"from":[93],"geometry,":[94],"we":[95],"systematically":[96],"propose":[97,162],"an":[98],"innovative":[99],"general":[101,150],"framework,":[102],"referred":[103],"as":[105],"geometric":[106,156],"quasilinearization":[107],"(GQL),":[108],"which":[109,199],"paves":[110],"new":[112],"effective":[113,165],"way":[114],"studying":[116,190],"problems":[118],"with":[119],"The":[122],"essential":[123],"idea":[124],"GQL":[126,153,173],"equivalently":[129],"transform":[130],"all":[131],"constraints":[133],"linear":[135],"ones,":[136],"properly":[138],"introducing":[139],"free":[141],"auxiliary":[142],"variables.":[143],"We":[144,170],"establish":[145],"fundamental":[147],"principle":[148],"theory":[151],"via":[154],"properties":[157],"convex":[159],"regions":[160],"three":[163],"simple":[164],"constructing":[168],"GQL.":[169],"apply":[171],"approach":[174],"variety":[177],"demonstrate":[183],"its":[184],"effectiveness":[185],"remarkable":[187],"advantages":[188],"schemes,":[192],"using":[193],"diverse":[194],"examples":[196],"applications":[198],"cannot":[200],"be":[201],"easily":[202],"handled":[203],"direct":[205],"traditional":[207],"approaches.":[208]},"counts_by_year":[],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2022-05-05T00:00:00"}