{"id":"https://openalex.org/W1981142209","doi":"https://doi.org/10.1137/s106482750139892x","title":"Spectral AMGe ($\\rho$AMGe)","display_name":"Spectral AMGe ($\\rho$AMGe)","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1981142209","doi":"https://doi.org/10.1137/s106482750139892x","mag":"1981142209"},"language":"en","primary_location":{"id":"doi:10.1137/s106482750139892x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482750139892x","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/A5026148848","display_name":"Timothy P. Chartier","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"T. Chartier","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057085539","display_name":"Robert D. Falgout","orcid":"https://orcid.org/0000-0003-4884-0087"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. D. Falgout","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074054014","display_name":"Van Emden Henson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. E. Henson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067320421","display_name":"Jim E. Jones","orcid":"https://orcid.org/0000-0002-0144-6130"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Jones","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008694561","display_name":"Thomas A. Manteuffel","orcid":"https://orcid.org/0000-0002-8897-4146"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Manteuffel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111718934","display_name":"Steve McCormick","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. McCormick","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047719926","display_name":"J. Ruge","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Ruge","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. S. Vassilevski","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5026148848"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.4302,"has_fulltext":false,"cited_by_count":115,"citation_normalized_percentile":{"value":0.98862095,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"25","issue":"1","first_page":"1","last_page":"26"},"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":1.0,"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":1.0,"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":0.9986000061035156,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/multigrid-method","display_name":"Multigrid method","score":0.7866127490997314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7294881343841553},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5367822051048279},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.5243233442306519},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.521909236907959},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.49304673075675964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48724332451820374},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4460771083831787},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.4388331174850464},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2822416424751282},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1842324435710907}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.7866127490997314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7294881343841553},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5367822051048279},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.5243233442306519},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.521909236907959},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.49304673075675964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48724332451820374},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4460771083831787},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.4388331174850464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2822416424751282},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1842324435710907},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s106482750139892x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482750139892x","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:CiteSeerX.psu:10.1.1.15.3940","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.3940","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.llnl.gov/CASC/linear_solvers/pubs/UCRL_JC146369.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1495073934","https://openalex.org/W1972914248","https://openalex.org/W1974521166","https://openalex.org/W1995145527","https://openalex.org/W1997542937","https://openalex.org/W1997596109","https://openalex.org/W2031859223","https://openalex.org/W2072662440","https://openalex.org/W2075536798","https://openalex.org/W2097199462","https://openalex.org/W2106088594","https://openalex.org/W2125051291","https://openalex.org/W2498157954","https://openalex.org/W4248626901"],"related_works":["https://openalex.org/W2011091376","https://openalex.org/W2487261884","https://openalex.org/W1758121264","https://openalex.org/W2383355899","https://openalex.org/W1501940787","https://openalex.org/W1524119935","https://openalex.org/W2161759000","https://openalex.org/W3144246503","https://openalex.org/W2009858568","https://openalex.org/W4388406280"],"abstract_inverted_index":{"We":[0],"introduce":[1],"spectral":[2,131],"element-based":[3],"algebraic":[4,9,16,56],"multigrid":[5,10,57],"($\\rho$AMGe),":[6],"a":[7,151,166],"new":[8],"method":[11,30,111],"for":[12,73,153,159,169],"solving":[13],"systems":[14],"of":[15,25,42,67,87,99,106,124,133,136,144],"equations":[17],"that":[18,49,79],"arise":[19],"in":[20,61,84,93],"Ritz-type":[21],"finite":[22],"element":[23,35,137],"discretizations":[24],"partial":[26],"differential":[27],"equations.":[28],"The":[29],"requires":[31],"access":[32],"to":[33,102,108,140],"the":[34,85,94,104,110,122,125,130,155],"stiffness":[36,138],"matrices,":[37],"which":[38,109],"enables":[39],"accurate":[40],"approximation":[41],"algebraically":[43,145],"\"smooth\"":[44],"vectors":[45],"(i.e.,":[46],"error":[47,147],"components":[48],"relaxation":[50],"cannot":[51],"effectively":[52],"eliminate).":[53],"Most":[54],"other":[55],"methods":[58],"are":[59,75],"based":[60],"some":[62],"manner":[63],"on":[64],"predefined":[65],"concepts":[66],"smoothness.":[68],"Coarse-grid":[69],"selection":[70],"and":[71,158],"prolongation,":[72],"example,":[74],"often":[76],"defined":[77],"assuming":[78],"smooth":[80,126,146],"errors":[81],"vary":[82],"slowly":[83],"direction":[86],"\"strong\"":[88],"connections":[89],"(relatively":[90],"large":[91],"coefficients":[92],"operator":[95],"matrix).":[96],"One":[97],"aim":[98],"$\\rho$AMGe":[100,128,170],"is":[101],"broaden":[103],"range":[105],"problems":[107],"can":[112],"be":[113],"successfully":[114],"applied":[115],"by":[116],"avoiding":[117],"any":[118],"implicit":[119],"premise":[120],"about":[121],"nature":[123],"error.":[127],"uses":[129],"decomposition":[132],"small":[134],"collections":[135],"matrices":[139],"determine":[141],"local":[142],"representations":[143],"components.":[148],"This":[149,163],"provides":[150],"foundation":[152,168],"generating":[154],"coarse":[156],"level":[157],"defining":[160],"effective":[161],"interpolation.":[162],"paper":[164],"presents":[165],"theoretical":[167],"along":[171],"with":[172],"numerical":[173],"experiments":[174],"demonstrating":[175],"its":[176],"robustness.":[177]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
