{"id":"https://openalex.org/W2070264798","doi":"https://doi.org/10.1137/040617455","title":"An Improved Convergence Bound for Aggregation-Based Domain Decomposition Preconditioners","display_name":"An Improved Convergence Bound for Aggregation-Based Domain Decomposition Preconditioners","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2070264798","doi":"https://doi.org/10.1137/040617455","mag":"2070264798"},"language":"en","primary_location":{"id":"doi:10.1137/040617455","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040617455","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5009201599","display_name":"Marzio Sala","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marzio Sala","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018004800","display_name":"John N. Shadid","orcid":"https://orcid.org/0009-0001-9804-1649"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John N. Shadid","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5106787959","display_name":"Ray Tuminaro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ray S. Tuminaro","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009201599"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0626,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.85986724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"27","issue":"3","first_page":"744","last_page":"756"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10514","display_name":"Numerical methods in engineering","score":0.9968000054359436,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9886000156402588,"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/preconditioner","display_name":"Preconditioner","score":0.9184784889221191},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.8940421342849731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7177273035049438},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6195816397666931},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5910664200782776},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5820683836936951},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4699521064758301},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.4418618679046631},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.37325406074523926},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3674735426902771},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3159381151199341},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2800901532173157},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.1976904571056366},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.14544916152954102}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9184784889221191},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.8940421342849731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7177273035049438},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6195816397666931},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5910664200782776},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5820683836936951},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4699521064758301},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.4418618679046631},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.37325406074523926},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3674735426902771},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3159381151199341},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2800901532173157},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.1976904571056366},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.14544916152954102},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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":1,"locations":[{"id":"doi:10.1137/040617455","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040617455","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1977828053","https://openalex.org/W1992988661","https://openalex.org/W1997542937","https://openalex.org/W2002284134","https://openalex.org/W2036869265","https://openalex.org/W2040011362","https://openalex.org/W2094534199","https://openalex.org/W2243781021","https://openalex.org/W2316564661","https://openalex.org/W2509362106","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W2159515580","https://openalex.org/W4229577910","https://openalex.org/W2081820376","https://openalex.org/W2800324324","https://openalex.org/W2640255794","https://openalex.org/W2791597622","https://openalex.org/W2091325992","https://openalex.org/W2743060302","https://openalex.org/W2026707481","https://openalex.org/W2901959480"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"present":[4],"a":[5,32,54,59,219],"two-level":[6,99,146],"overlapping":[7,29,147],"domain":[8,25,148],"decomposition":[9,149],"preconditioner":[10,102],"for":[11],"the":[12,45,51,64,70,74,86,89,94,98,112,115,118,124,127,130,134,190,226,229],"finite-element":[13],"discretization":[14],"of":[15,44,53,61,73,114,144,228],"elliptic":[16],"problems":[17],"in":[18,137,156,159,165],"two":[19],"and":[20,31,88,109,117,121,129,140,172],"three":[21],"dimensions.":[22],"The":[23],"computational":[24],"is":[26,40,103,123],"partitioned":[27],"into":[28],"subdomains,":[30],"coarse":[33,46,55,65,154],"space":[34,47],"correction,":[35],"based":[36],"on":[37,63,218],"aggregation":[38,153],"techniques,":[39],"added.":[41],"Our":[42],"definition":[43],"does":[48],"not":[49],"require":[50],"introduction":[52],"grid.":[56],"We":[57,91],"consider":[58],"set":[60],"assumptions":[62,79],"basis":[66],"functions":[67],"to":[68,189,224],"bound":[69],"condition":[71,95],"number":[72,96],"resulting":[75],"preconditioned":[76],"system.":[77],"These":[78],"involve":[80],"only":[81],"geometrical":[82],"quantities":[83],"associated":[84],"with":[85,151],"aggregates":[87],"subdomains.":[90],"prove":[92],"that":[93],"using":[97],"additive":[100],"Schwarz":[101],"$\\mathcal{O}(H/\\delta":[104],"+":[105],"H_0/\\delta)$,":[106],"where":[107],"H":[108],"$H_0$":[110],"are":[111,222],"diameters":[113],"subdomains":[116,128],"aggregates,":[119],"respectively,":[120],"$\\delta$":[122],"overlap":[125],"among":[126],"aggregates.":[131],"This":[132],"extends":[133],"bounds":[135],"presented":[136],"[C.":[138],"Lasser":[139],"A.":[141,173],"Toselli,":[142,174],"Convergence":[143],"some":[145],"preconditioners":[150],"smoothed":[152],"spaces,":[155],"Recent":[157],"Developments":[158],"Domain":[160,183],"Decomposition":[161,184],"Methods,":[162],"Lecture":[163],"Notes":[164],"Comput.":[166],"Sci.":[167],"Engrg.":[168],"23,":[169],"L.":[170],"Pavarino":[171],"eds.,":[175],"Springer-Verlag,":[176],"Berlin,":[177],"2002,":[178],"pp.":[179,214],"95--117;":[180],"M.":[181,206],"Sala,":[182,207],"Preconditioners:":[185],"Theoretical":[186],"Properties,":[187],"Application":[188],"Compressible":[191],"Euler":[192],"Equations,":[193],"Parallel":[194],"Aspects,":[195],"Ph.D.":[196],"thesis,":[197],"Ecole":[198],"Polytechnique":[199],"F\u00e9d\u00e9rale":[200],"de":[201],"Lausanne,":[202,203],"Switzerland,":[204],"2003;":[205],"Math.":[208],"Model.":[209],"Numer.":[210],"Anal.,":[211],"38":[212],"(2004),":[213],"765--780].":[215],"Numerical":[216],"experiments":[217],"model":[220],"problem":[221],"reported":[223],"illustrate":[225],"performance":[227],"proposed":[230],"preconditioner.":[231]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}