{"id":"https://openalex.org/W2053040989","doi":"https://doi.org/10.1137/100818996","title":"IMF: An Incomplete Multifrontal $LU$-Factorization for Element-Structured Sparse Linear Systems","display_name":"IMF: An Incomplete Multifrontal $LU$-Factorization for Element-Structured Sparse Linear Systems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2053040989","doi":"https://doi.org/10.1137/100818996","mag":"2053040989"},"language":"en","primary_location":{"id":"doi:10.1137/100818996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100818996","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":true,"oa_status":"green","oa_url":"http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW581.abs.html","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047646325","display_name":"Nick Vannieuwenhoven","orcid":"https://orcid.org/0000-0001-5692-4163"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Nick Vannieuwenhoven","raw_affiliation_strings":[", KU Leuven"],"affiliations":[{"raw_affiliation_string":", KU Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079388991","display_name":"Karl Meerbergen","orcid":"https://orcid.org/0000-0002-1508-0248"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Karl Meerbergen","raw_affiliation_strings":["Numerical Approximation and Linear Algebra Group, Department of Computer Science, KU Leuven, B-3000 Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Numerical Approximation and Linear Algebra Group, Department of Computer Science, KU Leuven, B-3000 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047646325"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":2.2212,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.87894887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"35","issue":"1","first_page":"A270","last_page":"A293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9869999885559082,"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/preconditioner","display_name":"Preconditioner","score":0.9369089603424072},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.8277410268783569},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.6890196204185486},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6290347576141357},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5790526866912842},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.568221390247345},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.556673526763916},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5452951788902283},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5369666814804077},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.477290540933609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43509384989738464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3418644070625305},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.33457374572753906},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3020282983779907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16773805022239685},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1013856828212738},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.09948676824569702},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.060895711183547974}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9369089603424072},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8277410268783569},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.6890196204185486},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6290347576141357},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5790526866912842},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.568221390247345},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.556673526763916},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5452951788902283},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5369666814804077},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.477290540933609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43509384989738464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3418644070625305},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.33457374572753906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3020282983779907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16773805022239685},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1013856828212738},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09948676824569702},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.060895711183547974},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/100818996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100818996","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:10.1.1.188.4999","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.188.4999","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW581.pdf","raw_type":"text"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/289574","is_oa":true,"landing_page_url":"http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW581.abs.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"TW Reports, Report No. TW581","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/356528","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/356528","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol. 35 (1), Art.No. 1, (A270-A293)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/289574","is_oa":true,"landing_page_url":"http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW581.abs.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"TW Reports, Report No. TW581","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W23806513","https://openalex.org/W194487525","https://openalex.org/W1480928214","https://openalex.org/W1551404369","https://openalex.org/W1575701986","https://openalex.org/W1760551737","https://openalex.org/W1964031104","https://openalex.org/W1975442866","https://openalex.org/W1977631509","https://openalex.org/W1981220107","https://openalex.org/W1981885118","https://openalex.org/W1989316443","https://openalex.org/W1992208469","https://openalex.org/W1993274656","https://openalex.org/W1997596109","https://openalex.org/W2002032847","https://openalex.org/W2002257715","https://openalex.org/W2009250131","https://openalex.org/W2009441498","https://openalex.org/W2013336356","https://openalex.org/W2020064379","https://openalex.org/W2020804487","https://openalex.org/W2022819055","https://openalex.org/W2024615455","https://openalex.org/W2027162534","https://openalex.org/W2027485220","https://openalex.org/W2027851979","https://openalex.org/W2031990962","https://openalex.org/W2034722767","https://openalex.org/W2035080386","https://openalex.org/W2036603155","https://openalex.org/W2038516134","https://openalex.org/W2040003476","https://openalex.org/W2040639345","https://openalex.org/W2044724368","https://openalex.org/W2055987340","https://openalex.org/W2062233541","https://openalex.org/W2063675347","https://openalex.org/W2066610136","https://openalex.org/W2070299075","https://openalex.org/W2079724896","https://openalex.org/W2080090223","https://openalex.org/W2082599981","https://openalex.org/W2088160222","https://openalex.org/W2093750962","https://openalex.org/W2095420020","https://openalex.org/W2096559782","https://openalex.org/W2099643552","https://openalex.org/W2104120668","https://openalex.org/W2106088594","https://openalex.org/W2119395117","https://openalex.org/W2133248904","https://openalex.org/W2136722618","https://openalex.org/W2141870784","https://openalex.org/W2148147555","https://openalex.org/W2155216327","https://openalex.org/W2164374667","https://openalex.org/W2166271012","https://openalex.org/W3145128584","https://openalex.org/W3149604617","https://openalex.org/W4230183876","https://openalex.org/W4298442487"],"related_works":["https://openalex.org/W2781922386","https://openalex.org/W1525847273","https://openalex.org/W3121053933","https://openalex.org/W2597750221","https://openalex.org/W2910530623","https://openalex.org/W2166705945","https://openalex.org/W1997497072","https://openalex.org/W4300624904","https://openalex.org/W2521750236","https://openalex.org/W1649457768"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2,34],"incomplete":[3,14],"multifrontal":[4,11],"$LU$-factorization":[5],"(IMF)":[6],"preconditioner":[7,22],"that":[8,52,95,144],"extends":[9],"supernodal":[10],"methods":[12],"to":[13,27,60],"factorizations.":[15],"It":[16],"can":[17],"be":[18],"used":[19],"as":[20],"a":[21,24,41,46],"in":[23,105,123],"Krylov-subspace":[25],"method":[26],"solve":[28],"large-scale":[29],"sparse":[30],"linear":[31],"systems":[32],"with":[33,78,99,114],"element":[35,43,54],"structure,":[36],"e.g.,":[37],"those":[38],"arising":[39,104,117],"from":[40,118],"finite":[42],"discretization":[44],"of":[45,68,84,108,126,134,140,145],"partial":[47,73],"differential":[48],"equation.":[49,112],"The":[50],"fact":[51],"the":[53,62,66,69,79,82,88,106,109,124,132,137,146],"matrices":[55,116],"are":[56],"dense":[57],"is":[58,76,97],"exploited":[59],"increase":[61],"computational":[63,138],"performance":[64,139],"and":[65,87],"robustness":[67,133],"factorization":[70],"through":[71],"efficient":[72],"pivoting.":[74],"IMF":[75,96,141],"compared":[77],"multilevel":[80],"ARMS2,":[81],"level":[83],"fill-in":[85],"ILU,":[86],"threshold-based":[89],"ILUTP":[90],"preconditioners.":[91],"Our":[92],"experiments":[93],"indicate":[94],"competitive":[98],"ARMS2":[100,148],"on":[101],"saddle-point":[102],"problems":[103],"solution":[107],"steady-state":[110],"Navier--Stokes":[111],"Experiments":[113],"element-structured":[115],"structural":[119],"engineering":[120],"applications,":[121],"found":[122],"University":[125],"Florida":[127],"Sparse":[128],"Matrix":[129],"Collection,":[130],"illustrate":[131],"IMF.":[135],"Finally,":[136],"clearly":[142],"surpasses":[143],"related":[147],"preconditioner.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}