{"id":"https://openalex.org/W4382628829","doi":"https://doi.org/10.1007/s11075-023-01548-3","title":"A low-rank update for relaxed Schur complement preconditioners in fluid flow problems","display_name":"A low-rank update for relaxed Schur complement preconditioners in fluid flow problems","publication_year":2023,"publication_date":"2023-05-10","ids":{"openalex":"https://openalex.org/W4382628829","doi":"https://doi.org/10.1007/s11075-023-01548-3"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-023-01548-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-023-01548-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01548-3.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01548-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012338004","display_name":"Rebekka S. Beddig","orcid":"https://orcid.org/0000-0002-3773-8530"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rebekka S. Beddig","raw_affiliation_strings":["Hamburg University of Technology, Institute of Mathematics, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hamburg University of Technology, Institute of Mathematics, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043502670","display_name":"J\u00f6rn Behrens","orcid":"https://orcid.org/0000-0001-9836-8716"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J\u00f6rn Behrens","raw_affiliation_strings":["Department of Mathematics, University of Hamburg, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hamburg, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014285191","display_name":"Sabine Le Borne","orcid":"https://orcid.org/0000-0002-4399-4442"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sabine Le\u00a0Borne","raw_affiliation_strings":["Hamburg University of Technology, Institute of Mathematics, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hamburg University of Technology, Institute of Mathematics, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014285191"],"corresponding_institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13385328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"94","issue":"4","first_page":"1597","last_page":"1618"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9983999729156494,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/schur-complement","display_name":"Schur complement","score":0.9364063143730164},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.9103640913963318},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7238393425941467},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5850342512130737},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5706537961959839},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5149653553962708},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4796657860279083},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.4577021598815918},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.44513049721717834},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43781623244285583},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.41853490471839905},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.41696658730506897},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3792773485183716},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.33725470304489136},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21175026893615723},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.15456834435462952},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.14371711015701294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13547039031982422},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.11500683426856995},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07879596948623657}],"concepts":[{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.9364063143730164},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9103640913963318},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7238393425941467},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5850342512130737},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5706537961959839},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5149653553962708},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4796657860279083},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.4577021598815918},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.44513049721717834},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43781623244285583},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.41853490471839905},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.41696658730506897},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3792773485183716},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.33725470304489136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21175026893615723},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.15456834435462952},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.14371711015701294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13547039031982422},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.11500683426856995},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07879596948623657},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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":1,"locations":[{"id":"doi:10.1007/s11075-023-01548-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-023-01548-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01548-3.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-023-01548-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-023-01548-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01548-3.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5252384289","display_name":null,"funder_award_id":"GRK 2583","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4382628829.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W2022643988","https://openalex.org/W2022916138","https://openalex.org/W2029782978","https://openalex.org/W2037666071","https://openalex.org/W2050206349","https://openalex.org/W2051490992","https://openalex.org/W2080622320","https://openalex.org/W2082606496","https://openalex.org/W2093225505","https://openalex.org/W2093753671","https://openalex.org/W2117756735","https://openalex.org/W2141870784","https://openalex.org/W2606658789","https://openalex.org/W2775518998","https://openalex.org/W3000936750","https://openalex.org/W3005312226","https://openalex.org/W3019424027","https://openalex.org/W3049219233","https://openalex.org/W3108353645","https://openalex.org/W3157285840","https://openalex.org/W3212687756","https://openalex.org/W4220707365","https://openalex.org/W4231405723","https://openalex.org/W4285586698"],"related_works":["https://openalex.org/W2401310550","https://openalex.org/W4389317411","https://openalex.org/W1492522302","https://openalex.org/W2381322109","https://openalex.org/W1189497506","https://openalex.org/W2096454229","https://openalex.org/W3031624508","https://openalex.org/W2604862712","https://openalex.org/W2062832849","https://openalex.org/W2053994227"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"simulation":[2],"of":[3,51,116,125],"fluid":[4],"dynamic":[5],"problems":[6],"often":[7],"involves":[8],"solving":[9],"large-scale":[10],"saddle-point":[11],"systems.":[12],"Their":[13],"numerical":[14],"solution":[15],"with":[16,129],"iterative":[17],"solvers":[18],"requires":[19],"efficient":[20],"preconditioners.":[21],"Low-rank":[22],"updates":[23],"can":[24,75],"adapt":[25],"standard":[26],"preconditioners":[27,42],"to":[28,131],"accelerate":[29],"their":[30,132],"convergence.":[31],"We":[32,62,86,120],"consider":[33],"a":[34,47,65,104],"multiplicative":[35],"low-rank":[36,49,127],"correction":[37],"for":[38,91,98,106],"pressure":[39],"Schur":[40,60],"complement":[41],"that":[43,68],"is":[44],"based":[45],"on":[46,109,134],"(randomized)":[48],"approximation":[50],"the":[52,55,58,70,77,83,92,99,114,117,126],"error":[53,89],"between":[54],"identity":[56],"and":[57,136],"preconditioned":[59],"complement.":[61],"further":[63],"introduce":[64],"relaxation":[66],"parameter":[67,74],"scales":[69],"initial":[71,78],"preconditioner.":[72],"This":[73],"improve":[76],"preconditioner":[79],"as":[80,82],"well":[81],"update":[84,94,118,128],"scheme.":[85,119],"provide":[87],"an":[88],"analysis":[90],"described":[93],"method.":[95],"Numerical":[96],"results":[97],"linearized":[100],"Navier\u2013Stokes":[101],"equations":[102],"in":[103],"model":[105],"atmospheric":[107],"dynamics":[108],"two":[110],"different":[111],"geometries":[112],"illustrate":[113],"action":[115],"numerically":[121],"analyze":[122],"various":[123],"parameters":[124],"respect":[130],"influence":[133],"convergence":[135],"computational":[137],"time.":[138]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
