{"id":"https://openalex.org/W3107641740","doi":"https://doi.org/10.1515/jnma-2020-0067","title":"Acceleration of nonlinear solvers for natural convection problems","display_name":"Acceleration of nonlinear solvers for natural convection problems","publication_year":2020,"publication_date":"2020-11-30","ids":{"openalex":"https://openalex.org/W3107641740","doi":"https://doi.org/10.1515/jnma-2020-0067","mag":"3107641740"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2020-0067","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2020-0067","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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/A5008374349","display_name":"Sara Pollock","orcid":"https://orcid.org/0000-0001-7896-350X"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sara Pollock","raw_affiliation_strings":["Department of Mathematics , University of Florida , Gainesville , FL 32611 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Florida , Gainesville , FL 32611 , USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028355904","display_name":"Leo G. Rebholz","orcid":"https://orcid.org/0000-0002-5173-5731"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leo G. Rebholz","raw_affiliation_strings":["School of Mathematical and Statistical Sciences , Clemson University , Clemson , SC 29634 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences , Clemson University , Clemson , SC 29634 , USA","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055423311","display_name":"Mengying Xiao","orcid":"https://orcid.org/0000-0003-1181-052X"},"institutions":[{"id":"https://openalex.org/I83683471","display_name":"University of West Florida","ror":"https://ror.org/002w4zy91","country_code":"US","type":"education","lineage":["https://openalex.org/I83683471"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mengying Xiao","raw_affiliation_strings":["Department of Mathematics and Statistics , University of West Florida , Pensacola , FL 32514 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , University of West Florida , Pensacola , FL 32514 , USA","institution_ids":["https://openalex.org/I83683471"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028355904"],"corresponding_institution_ids":["https://openalex.org/I8078737"],"apc_list":null,"apc_paid":null,"fwci":1.2602,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.77086117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"29","issue":"4","first_page":"323","last_page":"341"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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":0.9991999864578247,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9987999796867371,"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/acceleration","display_name":"Acceleration","score":0.7969937324523926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7636497020721436},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6403031349182129},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.6122437715530396},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5701389908790588},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5648646950721741},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.523621141910553},{"id":"https://openalex.org/keywords/fixed-point-iteration","display_name":"Fixed-point iteration","score":0.49344339966773987},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4382103681564331},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.436691015958786},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3502534031867981},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33751991391181946},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.28226906061172485},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20345842838287354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1437181830406189},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.0907348096370697},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08059605956077576}],"concepts":[{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.7969937324523926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7636497020721436},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6403031349182129},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6122437715530396},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5701389908790588},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5648646950721741},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.523621141910553},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.49344339966773987},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4382103681564331},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.436691015958786},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3502534031867981},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33751991391181946},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.28226906061172485},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20345842838287354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1437181830406189},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0907348096370697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08059605956077576},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2020-0067","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2020-0067","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W209265777","https://openalex.org/W272184100","https://openalex.org/W1966801132","https://openalex.org/W1973212083","https://openalex.org/W1994892733","https://openalex.org/W2004140015","https://openalex.org/W2038281434","https://openalex.org/W2041108136","https://openalex.org/W2049914863","https://openalex.org/W2054034220","https://openalex.org/W2071486596","https://openalex.org/W2100514507","https://openalex.org/W2141870784","https://openalex.org/W2345742189","https://openalex.org/W2395188625","https://openalex.org/W2702148523","https://openalex.org/W2802921497","https://openalex.org/W2898027306","https://openalex.org/W2963743617","https://openalex.org/W2998796568","https://openalex.org/W3004198084","https://openalex.org/W3007299075","https://openalex.org/W3120161765","https://openalex.org/W3204708751","https://openalex.org/W4231405723"],"related_works":["https://openalex.org/W2361607624","https://openalex.org/W3154013474","https://openalex.org/W2049942793","https://openalex.org/W1998059688","https://openalex.org/W3000466668","https://openalex.org/W2183298476","https://openalex.org/W1979581525","https://openalex.org/W2995335048","https://openalex.org/W2125984153","https://openalex.org/W4230493222"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"develops":[3],"an":[4],"efficient":[5],"and":[6,42,116,142],"robust":[7],"solution":[8],"technique":[9],"for":[10,53,61,67,138,153],"the":[11,28,34,48,62,68,75,79,84,87,92,104,114,135,139,145,148],"steady":[12],"Boussinesq":[13,69,140],"model":[14],"of":[15,94,122],"non-isothermal":[16],"flow":[17],"using":[18],"Anderson":[19,54,63,123,131],"acceleration":[20,132,146],"applied":[21,133],"to":[22,37,134,151],"a":[23,58,119,165],"Picard":[24,65],"iteration.":[25],"After":[26],"analyzing":[27],"fixed":[29],"point":[30],"operator":[31],"associated":[32],"with":[33,164],"nonlinear":[35],"iteration":[36,66,137,150],"prove":[38],"that":[39,74,99,112,118,144,158],"certain":[40],"stability":[41],"regularity":[43],"properties":[44],"hold,":[45],"we":[46],"apply":[47],"authors\u2019":[49],"recently":[50],"constructed":[51],"theory":[52],"acceleration,":[55,162],"which":[56],"yields":[57],"convergence":[59],"result":[60,72],"accelerated":[64],"system.":[70],"The":[71],"shows":[73],"leading":[76],"term":[77],"in":[78,86],"residual":[80,105],"is":[81,106],"improved":[82],"by":[83],"gain":[85],"optimization":[88],"problem,":[89],"but":[90],"at":[91],"cost":[93],"additional":[95],"higher":[96,155],"order":[97],"terms":[98],"can":[100,125],"be":[101,126],"significant":[102],"when":[103],"large.":[107],"We":[108,128],"perform":[109],"numerical":[110],"tests":[111],"illustrate":[113],"theory,":[115],"show":[117],"2-stage":[120],"choice":[121],"depth":[124],"advantageous.":[127],"also":[129],"consider":[130],"Newton":[136,149],"equations,":[141],"observe":[143],"allows":[147],"converge":[152],"significantly":[154],"Rayleigh":[156],"numbers":[157],"it":[159],"could":[160],"without":[161],"even":[163],"standard":[166],"line":[167],"search.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}