{"id":"https://openalex.org/W2055976205","doi":"https://doi.org/10.1137/0915044","title":"Towards Polyalgorithmic Linear System Solvers for Nonlinear Elliptic Problems","display_name":"Towards Polyalgorithmic Linear System Solvers for Nonlinear Elliptic Problems","publication_year":1994,"publication_date":"1994-05-01","ids":{"openalex":"https://openalex.org/W2055976205","doi":"https://doi.org/10.1137/0915044","mag":"2055976205"},"language":"en","primary_location":{"id":"doi:10.1137/0915044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915044","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/A5061539614","display_name":"Alexandre Ern","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexandre Ern","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084153097","display_name":"Vincent Giovangigli\u2225","orcid":"https://orcid.org/0000-0001-6624-6941"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vincent Giovangigli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021283893","display_name":"David E. Keyes","orcid":"https://orcid.org/0000-0002-4052-7224"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David E. Keyes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078993938","display_name":"Mitchell D. Smooke","orcid":"https://orcid.org/0000-0002-7900-2134"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mitchell D. Smooke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2192,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.92768444,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"3","first_page":"681","last_page":"703"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"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/T11416","display_name":"Numerical methods for differential equations","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.7497560977935791},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5588424205780029},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5207486152648926},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5190927982330322},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.494853675365448},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.49462029337882996},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.49000826478004456},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4894057810306549},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.48614880442619324},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.46869778633117676},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.42181625962257385},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.385250449180603},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3165132701396942},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29404711723327637},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.12385225296020508},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10358202457427979}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7497560977935791},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5588424205780029},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5207486152648926},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5190927982330322},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.494853675365448},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.49462029337882996},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.49000826478004456},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4894057810306549},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.48614880442619324},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.46869778633117676},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.42181625962257385},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.385250449180603},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3165132701396942},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29404711723327637},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.12385225296020508},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10358202457427979},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0915044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915044","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W170399909","https://openalex.org/W2015105467","https://openalex.org/W2021810545","https://openalex.org/W2023880860","https://openalex.org/W2049644675","https://openalex.org/W2054808747","https://openalex.org/W2061345018","https://openalex.org/W2066063303","https://openalex.org/W2078816762","https://openalex.org/W2082286426","https://openalex.org/W2085259167","https://openalex.org/W2095445354","https://openalex.org/W2137029533","https://openalex.org/W2140153041","https://openalex.org/W2155216327","https://openalex.org/W2326641952","https://openalex.org/W2336720422","https://openalex.org/W3021593381","https://openalex.org/W4242364743"],"related_works":["https://openalex.org/W2159515580","https://openalex.org/W4229577910","https://openalex.org/W2371322831","https://openalex.org/W2081820376","https://openalex.org/W2800324324","https://openalex.org/W2640255794","https://openalex.org/W2026707481","https://openalex.org/W2791597622","https://openalex.org/W2091325992","https://openalex.org/W2743060302"],"abstract_inverted_index":{"The":[0,36,187],"authors":[1],"investigate":[2],"the":[3,45,51,54,65,69,75,83,90,93,96,102,115,142,157,165,184,196,204],"performance":[4,94],"of":[5,24,53,68,74,89,95,104,106,117,172,189,198,210],"several":[6],"preconditioned":[7,162],"conjugate":[8],"gradient-like":[9],"algorithms":[10,128],"and":[11,48,178],"a":[12,29,39,118,131,152,170,199,207,223],"standard":[13,143],"stationary":[14],"iterative":[15],"method":[16,108],"(block-line":[17],"successive":[18],"overrelaxation":[19],"(SOR))":[20],"on":[21,164],"linear":[22,98],"systems":[23],"equations":[25],"that":[26,43,58],"arise":[27],"from":[28,77],"nonlinear":[30,120],"elliptic":[31,80],"flame":[32],"sheet":[33],"problem":[34,46],"simulation.":[35],"nonlinearity":[37],"forces":[38],"pseudotransient":[40,185],"continuation":[41],"process":[42],"makes":[44],"parabolic":[47,78],"thus":[49],"compacts":[50],"spectrum":[52],"Jacobian":[55],"matrix":[56],"so":[57],"simple":[59],"relaxation":[60],"methods":[61],"are":[62,179],"viable":[63],"in":[64,87,203],"initial":[66],"stages":[67],"solution":[70,121],"process.":[71],"However,":[72],"because":[73],"transition":[76],"to":[79,141,195],"character":[81],"as":[82,101],"timestep":[84],"is":[85,109,192],"increased":[86],"pursuit":[88],"steady-state":[91],"solution,":[92],"candidate":[97],"solvers":[99],"spreads":[100],"domain":[103],"convergence":[105],"Newton\u2019s":[107],"approached.":[110],"In":[111],"numerical":[112],"experiments":[113],"over":[114],"course":[116],"full":[119],"trajectory,":[122],"short":[123],"recurrence":[124],"or":[125],"optimal":[126],"Krylov":[127],"combined":[129],"with":[130,139,212],"Gauss\u2013Seidel":[132],"(GS)":[133],"preconditioning":[134,191],"yield":[135],"better":[136],"execution":[137],"times":[138],"respect":[140],"block-line":[144],"SOR":[145,148,177],"techniques,":[146],"but":[147],"performs":[149],"competitively":[150],"at":[151,216],"smaller":[153],"storage":[154,175],"cost":[155],"until":[156],"final":[158],"stages.":[159,186],"Block-incomplete":[160],"factorization":[161],"methods,":[163],"other":[166],"hand,":[167],"require":[168],"nearly":[169],"factor":[171],"two":[173],"more":[174],"than":[176],"uniformly":[180],"less":[181],"effective":[182],"during":[183],"advantage":[188],"GS":[190,211],"partly":[193],"attributable":[194],"exploitation":[197],"dominant":[200],"convection":[201],"direction":[202],"examples;":[205],"nevertheless,":[206],"multidomain":[208],"version":[209],"streamwise":[213],"coupling":[214],"lagged":[215],"rows":[217],"between":[218],"adjacent":[219],"subdomains":[220],"incurs":[221],"only":[222],"modest":[224],"penalty.":[225]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
