{"id":"https://openalex.org/W2531839392","doi":"https://doi.org/10.1137/16m1082706","title":"A Root-Node--Based Algebraic Multigrid Method","display_name":"A Root-Node--Based Algebraic Multigrid Method","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2531839392","doi":"https://doi.org/10.1137/16m1082706","mag":"2531839392"},"language":"en","primary_location":{"id":"doi:10.1137/16m1082706","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1082706","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.03154","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008694561","display_name":"Thomas A. Manteuffel","orcid":"https://orcid.org/0000-0002-8897-4146"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas A. Manteuffel","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado at Boulder"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado at Boulder","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027808971","display_name":"Luke N. Olson","orcid":"https://orcid.org/0000-0002-5283-6104"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luke N. Olson","raw_affiliation_strings":["Center for Applied Scientific Computing, Lawrence Livermore National Laboratory","Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory","institution_ids":["https://openalex.org/I1282311441"]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038235793","display_name":"Jacob B. Schroder","orcid":"https://orcid.org/0000-0002-1076-9206"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jacob B. Schroder","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5013739420","display_name":"Ben S. Southworth","orcid":"https://orcid.org/0000-0002-0283-4928"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ben S. Southworth","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado at Boulder"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado at Boulder","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5607,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.92533388,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"39","issue":"5","first_page":"S723","last_page":"S756"},"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":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9944000244140625,"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/multigrid-method","display_name":"Multigrid method","score":0.8358824253082275},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.574089527130127},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5577530860900879},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5551245808601379},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5434373617172241},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47736024856567383},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46198660135269165},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.4357929527759552},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.42981240153312683},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4281570613384247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38791176676750183},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.24107596278190613},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10164415836334229}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8358824253082275},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.574089527130127},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5577530860900879},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5551245808601379},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5434373617172241},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47736024856567383},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46198660135269165},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.4357929527759552},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.42981240153312683},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4281570613384247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38791176676750183},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.24107596278190613},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10164415836334229},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1082706","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1082706","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"},{"id":"pmh:oai:arXiv.org:1610.03154","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1610.03154","pdf_url":"https://arxiv.org/pdf/1610.03154","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.03154","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1610.03154","pdf_url":"https://arxiv.org/pdf/1610.03154","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7900000214576721}],"awards":[{"id":"https://openalex.org/G1356433355","display_name":null,"funder_award_id":"DE\u2010AC5207NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G2038510818","display_name":null,"funder_award_id":"DE-NA0002376","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G205123881","display_name":null,"funder_award_id":"32 CFR 168a","funder_id":"https://openalex.org/F4320333566","funder_display_name":"National Defense Science and Engineering Graduate"},{"id":"https://openalex.org/G2145270357","display_name":null,"funder_award_id":"AC52\u201007NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3669113783","display_name":null,"funder_award_id":"07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G3973756402","display_name":null,"funder_award_id":"FA95501210478","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4286649103","display_name":null,"funder_award_id":"DE-FC02\u201303ER25574","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G4529606868","display_name":"CENTER FOR EXASCALE RADIATION TRANSPORT (CERT)","funder_award_id":"DENA0002376","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7791925507","display_name":null,"funder_award_id":"CFR 168a","funder_id":"https://openalex.org/F4320333566","funder_display_name":"National Defense Science and Engineering Graduate"},{"id":"https://openalex.org/G797722205","display_name":null,"funder_award_id":"B600360","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G8447223214","display_name":null,"funder_award_id":"B600360","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8563877469","display_name":null,"funder_award_id":"DE-NA0002376","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G991281326","display_name":null,"funder_award_id":"AC52-07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320333566","display_name":"National Defense Science and Engineering Graduate","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338286","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W26823901","https://openalex.org/W40652001","https://openalex.org/W168146100","https://openalex.org/W1519509134","https://openalex.org/W1522102036","https://openalex.org/W1525132831","https://openalex.org/W1533888979","https://openalex.org/W1806777346","https://openalex.org/W1819041639","https://openalex.org/W1885889690","https://openalex.org/W1967983557","https://openalex.org/W1992935956","https://openalex.org/W1997775923","https://openalex.org/W1999937686","https://openalex.org/W2005073368","https://openalex.org/W2013555402","https://openalex.org/W2016315720","https://openalex.org/W2022639074","https://openalex.org/W2025501795","https://openalex.org/W2031827243","https://openalex.org/W2031887218","https://openalex.org/W2032718616","https://openalex.org/W2039789965","https://openalex.org/W2040173915","https://openalex.org/W2042913171","https://openalex.org/W2070618263","https://openalex.org/W2078687549","https://openalex.org/W2095092117","https://openalex.org/W2095318027","https://openalex.org/W2100238837","https://openalex.org/W2112968403","https://openalex.org/W2128328239","https://openalex.org/W2133248904","https://openalex.org/W2142304406","https://openalex.org/W2142846929","https://openalex.org/W2143952613","https://openalex.org/W2148874397","https://openalex.org/W2167128668","https://openalex.org/W2167512083","https://openalex.org/W2217658382","https://openalex.org/W2243781021","https://openalex.org/W2252040419","https://openalex.org/W2266375104","https://openalex.org/W2342261098","https://openalex.org/W2473418259","https://openalex.org/W2912759508","https://openalex.org/W2945154147","https://openalex.org/W3185776723","https://openalex.org/W4247826031"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W2573021234","https://openalex.org/W2106610492","https://openalex.org/W2383355899","https://openalex.org/W1524119935","https://openalex.org/W3011358647","https://openalex.org/W2155760131","https://openalex.org/W2161759000"],"abstract_inverted_index":{"This":[0],"paper":[1,85],"provides":[2],"a":[3,15,76,96,111,180],"unified":[4],"and":[5,17,67,100,110,138,166,175,193],"detailed":[6,184],"presentation":[7],"of":[8,83,98,123,157,186,190],"root-node--style":[9],"algebraic":[10],"multigrid":[11],"(AMG).":[12],"AMG":[13,36,70,107,159,206],"is":[14,37,71,86,108,114,117,134],"popular":[16],"effective":[18],"iterative":[19],"method":[20],"for":[21,39,78,105,136,198,204],"solving":[22],"large,":[23],"sparse":[24],"linear":[25],"systems":[26],"that":[27],"arise":[28],"from":[29],"discretizing":[30],"partial":[31],"differential":[32],"equations.":[33],"However,":[34],"while":[35],"designed":[38],"symmetric":[40,143],"positive":[41],"definite":[42],"(SPD)":[43],"matrices,":[44],"certain":[45],"SPD":[46,168],"problems,":[47,163,165,169],"such":[48,79],"as":[49,75,95,140,144],"anisotropic":[50,172],"diffusion,":[51,173],"are":[52,150,196],"still":[53],"not":[54,73],"adequately":[55],"addressed":[56],"by":[57],"existing":[58],"methods.":[59,209],"Non-SPD":[60],"problems":[61],"pose":[62],"an":[63],"even":[64],"greater":[65],"challenge,":[66],"in":[68,179],"practice":[69],"often":[72],"considered":[74],"solver":[77],"problems.":[80,130],"The":[81],"focus":[82],"this":[84],"on":[87,128],"so-called":[88],"root-node":[89,106,125,137,158,205],"AMG,":[90,126],"which":[91,116],"can":[92],"be":[93],"viewed":[94],"combination":[97],"classical":[99],"aggregation-based":[101],"multigrid.":[102],"An":[103],"algorithm":[104],"outlined,":[109],"filtering":[112],"strategy":[113],"developed,":[115],"able":[118],"to":[119,142,160],"control":[120],"the":[121,154,187,191],"cost":[122,189],"using":[124],"particularly":[127],"difficult":[129,167],"New":[131,183],"theoretical":[132],"motivation":[133],"provided":[135],"energy-minimization":[139],"applied":[141],"well":[145],"nonsymmetric":[146,162],"systems.":[147],"Numerical":[148],"results":[149],"then":[151],"presented":[152],"demonstrating":[153],"robust":[155],"ability":[156],"solve":[161,194],"systems-based":[164],"including":[170],"strongly":[171],"convection-diffusion,":[174],"upwind":[176],"steady-state":[177],"transport,":[178],"scalable":[181],"manner.":[182],"estimates":[185],"computational":[188],"setup":[192],"phases":[195],"given":[197],"each":[199],"example,":[200],"providing":[201],"additional":[202],"support":[203],"over":[207],"alternative":[208]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}