{"id":"https://openalex.org/W2022146461","doi":"https://doi.org/10.1137/s1064827596311591","title":"Dynamically Relaxed Block Incomplete Factorizations for Solving Two- and Three-Dimensional Problems","display_name":"Dynamically Relaxed Block Incomplete Factorizations for Solving Two- and Three-Dimensional Problems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2022146461","doi":"https://doi.org/10.1137/s1064827596311591","mag":"2022146461"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827596311591","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596311591","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/A5030298904","display_name":"Mardoch\u00e9e Magolu Monga-Made","orcid":null},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Mardoch\u00e9e Magolu Monga-Made","raw_affiliation_strings":["Universit\u00e9 libre de Bruxelles"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 libre de Bruxelles","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057146535","display_name":"Yvan Notay","orcid":"https://orcid.org/0000-0001-7176-4890"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Yvan Notay","raw_affiliation_strings":["Universit\u00e9 libre de Bruxelles"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 libre de Bruxelles","institution_ids":["https://openalex.org/I132053463"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030298904"],"corresponding_institution_ids":["https://openalex.org/I132053463"],"apc_list":null,"apc_paid":null,"fwci":0.9369,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75701625,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"6","first_page":"2008","last_page":"2028"},"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":0.9995999932289124,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.8301964998245239},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.691645622253418},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6045240759849548},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.525968074798584},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5214197635650635},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.4941852390766144},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47435152530670166},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4338090717792511},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.42883360385894775},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35198336839675903},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33602607250213623},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2299647331237793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12001702189445496}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8301964998245239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.691645622253418},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6045240759849548},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.525968074798584},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5214197635650635},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.4941852390766144},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47435152530670166},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4338090717792511},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.42883360385894775},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35198336839675903},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33602607250213623},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2299647331237793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12001702189445496},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827596311591","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596311591","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:10.1.1.48.7589","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.7589","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://mnserver.ulb.ac.be/pub/reports/drbilu.ps.gz","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":36,"referenced_works":["https://openalex.org/W28710127","https://openalex.org/W1500921805","https://openalex.org/W1538878357","https://openalex.org/W1546004968","https://openalex.org/W1559203263","https://openalex.org/W1575701986","https://openalex.org/W1967802773","https://openalex.org/W1981745143","https://openalex.org/W1983649071","https://openalex.org/W2000374859","https://openalex.org/W2000916326","https://openalex.org/W2009334753","https://openalex.org/W2010298350","https://openalex.org/W2027764906","https://openalex.org/W2032354159","https://openalex.org/W2038925070","https://openalex.org/W2045244586","https://openalex.org/W2049352126","https://openalex.org/W2050875433","https://openalex.org/W2061813658","https://openalex.org/W2064616889","https://openalex.org/W2065090106","https://openalex.org/W2066399015","https://openalex.org/W2067010774","https://openalex.org/W2072347611","https://openalex.org/W2074190947","https://openalex.org/W2078816762","https://openalex.org/W2085194351","https://openalex.org/W2093247664","https://openalex.org/W2107010019","https://openalex.org/W2148591729","https://openalex.org/W2476631907","https://openalex.org/W2742886347","https://openalex.org/W2798484686","https://openalex.org/W3150437274","https://openalex.org/W4249588109"],"related_works":["https://openalex.org/W2136512912","https://openalex.org/W2127267268","https://openalex.org/W2156446763","https://openalex.org/W2067910792","https://openalex.org/W2150194458","https://openalex.org/W2143461633","https://openalex.org/W2889071233","https://openalex.org/W4321471459","https://openalex.org/W4221156924","https://openalex.org/W2059970075"],"abstract_inverted_index":{"To":[0],"efficiently":[1],"solve":[2],"second-order":[3],"discrete":[4],"elliptic":[5],"PDEs":[6],"by":[7],"Krylov":[8],"subspace-like":[9],"methods,":[10,94],"one":[11,53],"needs":[12],"to":[13,46,55,100],"use":[14],"some":[15,137],"robust":[16,97],"preconditioning":[17,147],"techniques.":[18],"Relaxed":[19],"incomplete":[20],"factorizations":[21],"(RILU)":[22],"are":[23,150],"powerful":[24],"candidates.\\":[25],"Unfortunately,":[26],"their":[27],"efficiency":[28],"critically":[29],"depends":[30],"on":[31],"the":[32,35,61,70,111,144],"choice":[33],"of":[34,76,107,113,118],"relaxation":[36],"parameter":[37],"$\\omega$":[38],"whose":[39],"\"optimal\"":[40],"value":[41],"is":[42,96,123],"not":[43],"only":[44],"hard":[45],"estimate":[47],"but":[48],"also":[49],"strongly":[50],"varies":[51],"from":[52],"problem":[54],"another.":[56],"These":[57],"methods":[58,132],"interpolate":[59],"between":[60],"popular":[62],"ILU":[63],"and":[64,91,103,125,130],"its":[65,88],"modified":[66],"variant":[67,75],"(MILU).":[68],"Concerning":[69],"pointwise":[71,129],"schemes,":[72],"a":[73],"new":[74,145],"RILU":[77,90],"that":[78,142],"dynamically":[79,120],"computes":[80],"variable":[81],"$\\omega=\\omega_i$":[82],"has":[83],"been":[84],"introduced":[85],"recently.":[86],"Like":[87],"ancestor":[89],"unlike":[92],"standard":[93],"it":[95,109],"with":[98,127,136,143],"respect":[99],"both":[101],"existence":[102],"performance.":[104],"On":[105],"top":[106],"that,":[108],"breaks":[110],"problem-dependence":[112],"``$\\omega_{opt}$.\"\\":[114],"A":[115],"block":[116],"version":[117],"this":[119],"relaxed":[121],"method":[122],"proposed":[124],"compared":[126],"classical":[128],"blockwise":[131,146],"as":[133,135],"well":[134],"existing":[138],"\"dynamic\"":[139],"variants,":[140],"showing":[141],"technique,":[148],"anisotropies":[149],"handled":[151],"more":[152],"effectively.":[153]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
