{"id":"https://openalex.org/W1993779177","doi":"https://doi.org/10.1137/s003614450342061","title":"A New Paradigm for Parallel Adaptive Meshing Algorithms","display_name":"A New Paradigm for Parallel Adaptive Meshing Algorithms","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1993779177","doi":"https://doi.org/10.1137/s003614450342061","mag":"1993779177"},"language":"en","primary_location":{"id":"doi:10.1137/s003614450342061","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614450342061","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073296480","display_name":"Randolph E. Bank","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Randolph E. Bank","raw_affiliation_strings":["Department of Mathematics, University of California at San Diego, La Jolla, CA 92093"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at San Diego, La Jolla, CA 92093","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080980271","display_name":"Michael Holst","orcid":"https://orcid.org/0000-0002-3064-4697"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Holst","raw_affiliation_strings":["Department of Mathematics, University of California at San Diego, La Jolla, CA 92093"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at San Diego, La Jolla, CA 92093","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073296480"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":2.7433,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.88794273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"2","first_page":"291","last_page":"323"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9984999895095825,"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/T10514","display_name":"Numerical methods in engineering","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/solver","display_name":"Solver","score":0.7624214887619019},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7035243511199951},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.579447329044342},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5709278583526611},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.5679918527603149},{"id":"https://openalex.org/keywords/load-balancing","display_name":"Load balancing (electrical power)","score":0.5293943285942078},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5241323113441467},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4853297770023346},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4618247151374817},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4339957535266876},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.4100351631641388},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39070239663124084},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.23615700006484985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20636498928070068},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09729298949241638}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7624214887619019},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7035243511199951},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.579447329044342},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5709278583526611},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.5679918527603149},{"id":"https://openalex.org/C138959212","wikidata":"https://www.wikidata.org/wiki/Q1806783","display_name":"Load balancing (electrical power)","level":3,"score":0.5293943285942078},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5241323113441467},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4853297770023346},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4618247151374817},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4339957535266876},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.4100351631641388},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39070239663124084},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.23615700006484985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20636498928070068},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09729298949241638},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s003614450342061","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614450342061","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[{"id":"https://openalex.org/G2809074984","display_name":"Scientific Computing Research Environments for the Mathematical Sciences (SCREMS)","funder_award_id":"0112413","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3282479228","display_name":"CAREER: Adaptive multilevel finite element methods with applications to biomolecules and gravitation","funder_award_id":"9875856","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G647264089","display_name":"Heirarchical Basis Multigrid/ILU Algorithms for Solving     Finite Element Equations","funder_award_id":"9706090","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6983923351","display_name":"Optimization with PDE Constraints","funder_award_id":"0208449","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452998910","display_name":null,"funder_award_id":"00000","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7836065595","display_name":"Scalable Parallel Multilevel Algorithms for the Solution and Optimization of Partial Differential Equations","funder_award_id":"9973276","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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/F4320332603","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1565479511","https://openalex.org/W1572617741","https://openalex.org/W1963512446","https://openalex.org/W1971758446","https://openalex.org/W1980455776","https://openalex.org/W1982856339","https://openalex.org/W1986604141","https://openalex.org/W1989331860","https://openalex.org/W1991647816","https://openalex.org/W2001012793","https://openalex.org/W2002731244","https://openalex.org/W2011531927","https://openalex.org/W2012229545","https://openalex.org/W2014383457","https://openalex.org/W2017085690","https://openalex.org/W2021144788","https://openalex.org/W2026707481","https://openalex.org/W2029582401","https://openalex.org/W2043577799","https://openalex.org/W2058525241","https://openalex.org/W2069961480","https://openalex.org/W2081861751","https://openalex.org/W2094281210","https://openalex.org/W2096159022","https://openalex.org/W2098990162","https://openalex.org/W2114030927","https://openalex.org/W2171819226","https://openalex.org/W2568342123","https://openalex.org/W2963652100","https://openalex.org/W4240023077","https://openalex.org/W4248482327","https://openalex.org/W4252219741"],"related_works":["https://openalex.org/W2383807498","https://openalex.org/W1978572805","https://openalex.org/W1997992934","https://openalex.org/W1987225439","https://openalex.org/W4238188170","https://openalex.org/W2125114371","https://openalex.org/W2019977573","https://openalex.org/W2149980199","https://openalex.org/W3125766170","https://openalex.org/W2040641410"],"abstract_inverted_index":{"We":[0,234],"present":[1,235],"a":[2,24,50,54,74,79,83,103,120,161,170,212,222,236,330,333],"new":[3,25,61],"approach":[4,17],"to":[5,47,69,91,101,107,186],"the":[6,19,63,70,92,113,126,132,146,157,173,179,183,187,201,209,217,227,244,252,260,264,340,359,364,370],"use":[7],"of":[8,73,125,131,156,172,182,211,238,246,251,262,339],"parallel":[9,51],"computers":[10],"with":[11,141],"adaptive":[12,39,85,149],"finite":[13],"element":[14,110],"methods.":[15],"This":[16,337],"addresses":[18],"load":[20,64],"balancing":[21,65],"problem":[22,66,77,98],"in":[23,49,57,112,119],"way,":[26],"requiring":[27,88,193],"far":[28],"less":[29],"communication":[30,196],"than":[31],"current":[32],"approaches.":[33],"It":[34],"also":[35],"allows":[36],"existing":[37],"sequential":[38,84,93,148],"PDE":[40],"codes":[41],"such":[42],"as":[43,169,230,257,259],"PLTMG":[44],"and":[45,160,275,284,291,304,317,332,346,362],"MC":[46],"run":[48],"environment":[52],"without":[53,87],"large":[55],"investment":[56],"recoding.":[58],"In":[59],"this":[60,247],"approach,":[62],"is":[67,99,166,268],"reduced":[68],"numerical":[71,240,360],"solution":[72],"small":[75,96],"elliptic":[76,97],"on":[78,138,328],"single":[80],"processor,":[81,140],"using":[82,144,226],"solver,":[86],"any":[89],"modifications":[90],"solver.":[94,150],"The":[95,129,249],"used":[100,118],"produce":[102],"posteriori":[104,334],"error":[105,335],"estimates":[106],"predict":[108],"future":[109],"densities":[111],"mesh,":[114],"which":[115],"are":[116],"then":[117,134],"weighted":[121,175],"recursive":[122],"spectral":[123,176],"bisection":[124],"initial":[127,174,180,232,253],"mesh.":[128],"bulk":[130],"calculation":[133],"takes":[135],"place":[136],"independently":[137],"each":[139],"no":[142],"communication,":[143],"possibly":[145],"same":[147],"Each":[151],"processor":[152],"adapts":[153],"its":[154],"region":[155],"mesh":[158,164,184,215],"independently,":[159],"nearly":[162],"load-balanced":[163],"distribution":[165],"usually":[167],"obtained":[168],"result":[171],"bisection.":[177],"Only":[178],"fan-out":[181],"decomposition":[185],"processors":[188,203],"requires":[189],"communication.":[190],"Twoadditional":[191],"steps":[192],"boundary":[194],"exchange":[195],"may":[197],"be":[198],"employed":[199],"after":[200],"individual":[202],"reach":[204],"an":[205,231],"adapted":[206],"solution,":[207],"namely,":[208],"construction":[210],"global":[213],"conforming":[214],"from":[216],"independent":[218],"subproblems,":[219],"followed":[220],"by":[221,270],"final":[223],"smoothing":[224],"phase":[225],"subdomain":[228],"solutions":[229],"guess.":[233],"series":[237],"convincing":[239],"experiments":[241,361],"that":[242],"illustrate":[243],"effectiveness":[245],"approach.":[248],"justification":[250,261],"refinement":[254],"prediction":[255],"step,":[256],"well":[258],"skipping":[263],"two":[265],"communication-intensive":[266],"steps,":[267],"supported":[269],"some":[271],"recent":[272,287],"[J.":[273,288],"Xu":[274],"A.":[276,289,292,301,314],"Zhou,":[277],"Math.":[278,295,308,321],"Comp.,":[279,296,309,322],"69":[280],"(2000),":[281,355],"pp.":[282,299,312,325,356],"881--909]":[283],"not":[285],"so":[286],"Nitsche":[290],"H.":[293,302,315],"Schatz,":[294],"28":[297],"(1974),":[298],"937--958;":[300],"Schatz":[303,316],"L.":[305,318],"B.":[306,319],"Wahlbin,":[307,320],"31":[310],"(1977),":[311],"414--442;":[313],"64":[323],"(1995),":[324],"907--928]":[326],"results":[327],"local":[329],"priori":[331],"estimation.":[336],"revision":[338],"original":[341,371],"article":[342],"[R.":[343],"E.":[344],"Bank":[345],"M.":[347],"J.":[348,351],"Holst,":[349],"SIAM":[350],"Sci.":[352],"Comput.,":[353],"22":[354],"1411--1443]":[357],"updates":[358],"reflects":[363],"knowledge":[365],"we":[366],"have":[367],"gained":[368],"since":[369],"paper":[372],"appeared.":[373]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
