{"id":"https://openalex.org/W4415678610","doi":"https://doi.org/10.1515/cmam-2024-0200","title":"Anderson\u2013Picard Based Nonlinear Preconditioning of the Newton Iteration for Non-Isothermal Flow Simulations","display_name":"Anderson\u2013Picard Based Nonlinear Preconditioning of the Newton Iteration for Non-Isothermal Flow Simulations","publication_year":2025,"publication_date":"2025-10-29","ids":{"openalex":"https://openalex.org/W4415678610","doi":"https://doi.org/10.1515/cmam-2024-0200"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2024-0200","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0200","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"Computational Methods in Applied 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/A5110460255","display_name":"Elizabeth Hawkins","orcid":"https://orcid.org/0009-0006-7413-9533"},"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":"Elizabeth Hawkins","raw_affiliation_strings":["School of Mathematical and Statistical Sciences , 2545 Clemson University , Clemson , SC 29364 , USA"],"raw_orcid":"https://orcid.org/0009-0006-7413-9533","affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences , 2545 Clemson University , Clemson , SC 29364 , USA","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110460255"],"corresponding_institution_ids":["https://openalex.org/I8078737"],"apc_list":null,"apc_paid":null,"fwci":1.0663,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.79430977,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"26","issue":"1","first_page":"69","last_page":"88"},"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":0.5400000214576721,"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":0.5400000214576721,"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":0.10249999910593033,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.08959999680519104,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.7035999894142151},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6843000054359436},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6370000243186951},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5871999859809875},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5605999827384949},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44929999113082886},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.43700000643730164},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4205000102519989}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742000222206116},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.7035999894142151},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6843000054359436},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6370000243186951},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6248999834060669},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5871999859809875},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5605999827384949},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.43700000643730164},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.40290001034736633},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.40070000290870667},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.38830000162124634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35100001096725464},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.289000004529953},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.272599995136261},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2700999975204468},{"id":"https://openalex.org/C173443657","wikidata":"https://www.wikidata.org/wiki/Q7606635","display_name":"Steffensen's method","level":5,"score":0.267300009727478},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2615000009536743}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2024-0200","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0200","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1439490531","display_name":null,"funder_award_id":"DMS-2011490","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":21,"referenced_works":["https://openalex.org/W209265777","https://openalex.org/W612879516","https://openalex.org/W1528988129","https://openalex.org/W1586538875","https://openalex.org/W1918988090","https://openalex.org/W2041108136","https://openalex.org/W2042280353","https://openalex.org/W2051490992","https://openalex.org/W2054034220","https://openalex.org/W2071486596","https://openalex.org/W2128105562","https://openalex.org/W2130756427","https://openalex.org/W2142484159","https://openalex.org/W2540191835","https://openalex.org/W2963743617","https://openalex.org/W3007299075","https://openalex.org/W3120161765","https://openalex.org/W4231405723","https://openalex.org/W4252104256","https://openalex.org/W4283267821","https://openalex.org/W4410774320"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,19],"propose,":[2],"analyze,":[3],"and":[4,41,57,96,115],"test":[5],"a":[6,35],"nonlinear":[7,72,126],"preconditioning":[8,73],"technique":[9],"to":[10,79],"improve":[11],"the":[12,39,54,62,66,69,80,87,103,119,130],"Newton":[13,30,81,128],"iteration":[14,82],"for":[15,107],"non-isothermal":[16],"flow":[17],"simulations.":[18],"prove":[20],"that":[21,129],"by":[22],"first":[23],"applying":[24],"an":[25],"Anderson":[26],"accelerated":[27],"Picard":[28,114],"step,":[29],"becomes":[31],"unconditionally":[32],"stable":[33],"(under":[34],"uniqueness":[36],"condition":[37],"on":[38,53,98],"data)":[40],"its":[42],"quadratic":[43,94],"convergence":[44,95,106,121],"is":[45],"retained":[46],"but":[47],"has":[48],"less":[49],"restrictive":[50],"sufficient":[51],"conditions":[52],"Rayleigh":[55,110],"number":[56,111],"initial":[58],"condition\u2019s":[59],"accuracy.":[60],"Since":[61],"Anderson\u2013Picard":[63,124],"step":[64],"decouples":[65],"equations":[67],"in":[68],"system,":[70],"this":[71,93],"adds":[74],"relatively":[75],"little":[76],"extra":[77],"cost":[78],"(which":[83],"does":[84],"not":[85],"decouple":[86],"equations).":[88],"Our":[89],"numerical":[90],"tests":[91,104],"illustrate":[92],"stability":[97],"multiple":[99],"benchmark":[100],"problems.":[101],"Furthermore,":[102],"show":[105],"significantly":[108],"higher":[109],"than":[112],"both":[113],"Newton,":[116],"which":[117],"illustrates":[118],"larger":[120],"basin":[122],"of":[123],"based":[125],"preconditioned":[127],"theory":[131],"predicts.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-30T00:00:00"}