{"id":"https://openalex.org/W3104748804","doi":"https://doi.org/10.1137/19m1276479","title":"Multilevel BDDC for Incompressible Navier--Stokes Equations","display_name":"Multilevel BDDC for Incompressible Navier--Stokes Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3104748804","doi":"https://doi.org/10.1137/19m1276479","mag":"3104748804"},"language":"en","primary_location":{"id":"doi:10.1137/19m1276479","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1276479","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276479","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276479","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010672834","display_name":"Martin Hanek","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Hanek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057184591","display_name":"Jakub \u0160\u00edstek","orcid":"https://orcid.org/0000-0002-5231-7830"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jakub \u0160\u00edstek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001153131","display_name":"Pavel Burda","orcid":"https://orcid.org/0000-0002-2841-792X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pavel Burda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010672834"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2667,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.54328299,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"42","issue":"6","first_page":"C359","last_page":"C383"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9993000030517578,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9926999807357788,"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/mathematics","display_name":"Mathematics","score":0.708405077457428},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6664859652519226},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6622898578643799},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5936853885650635},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5905869007110596},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5207569599151611},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5045443773269653},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.43236202001571655},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4303584694862366},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.4155259132385254},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.36248111724853516},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3229520916938782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3089367747306824},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1403578519821167}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.708405077457428},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6664859652519226},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6622898578643799},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5936853885650635},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5905869007110596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5207569599151611},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5045443773269653},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.43236202001571655},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4303584694862366},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.4155259132385254},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.36248111724853516},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3229520916938782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3089367747306824},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1403578519821167},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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},{"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:10.1137/19m1276479","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1276479","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276479","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/19m1276479","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1276479","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1276479","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2030938766","display_name":null,"funder_award_id":"18-096285","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G7808351090","display_name":null,"funder_award_id":"ROV:67985840","funder_id":"https://openalex.org/F4320322482","funder_display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320322482","display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky","ror":"https://ror.org/053avzc18"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3104748804.pdf","grobid_xml":"https://content.openalex.org/works/W3104748804.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1026399362","https://openalex.org/W1274527493","https://openalex.org/W1673742782","https://openalex.org/W1877845209","https://openalex.org/W1976561044","https://openalex.org/W1979794255","https://openalex.org/W1980584261","https://openalex.org/W1990431915","https://openalex.org/W1991532854","https://openalex.org/W2000867371","https://openalex.org/W2022107873","https://openalex.org/W2024179839","https://openalex.org/W2036019258","https://openalex.org/W2070232376","https://openalex.org/W2080164618","https://openalex.org/W2089861738","https://openalex.org/W2103486983","https://openalex.org/W2106619956","https://openalex.org/W2112311198","https://openalex.org/W2114471476","https://openalex.org/W2155216327","https://openalex.org/W2157071675","https://openalex.org/W2160906325","https://openalex.org/W2270752444"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W1572705989","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W4240399920"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"approach":[3],"to":[4,20,35,60,97],"the":[5,14,30,50,67,76,85,89],"numerical":[6],"solution":[7],"of":[8,38,52,79,84,93,100],"steady":[9],"Navier--Stokes":[10],"equations.":[11],"Approximation":[12],"by":[13,29],"finite":[15],"element":[16],"method":[17,70],"(FEM)":[18],"leads":[19,34],"a":[21,36],"nonlinear":[22],"saddle-point":[23,40],"system.":[24],"The":[25],"system":[26],"is":[27,87],"linearized":[28],"Picard":[31],"iteration,":[32],"which":[33],"sequence":[37],"linear":[39],"systems":[41],"with":[42],"nonsymmetric":[43],"matrices.":[44],"In":[45,63],"this":[46],"paper,":[47],"we":[48,65],"study":[49],"application":[51,92],"Balancing":[53],"Domain":[54],"Decomposition":[55],"based":[56],"on":[57],"Constraints":[58],"(BDDC)":[59],"these":[61],"systems.":[62],"particular,":[64],"formulate":[66],"multilevel":[68],"BDDC":[69,95],"and":[71,91],"explore":[72],"its":[73],"applicability":[74],"for":[75],"benchmark":[77],"problem":[78],"lid-driven":[80],"cavity.":[81],"Another":[82],"contribution":[83],"paper":[86],"describing":[88],"development":[90],"our":[94],"solver":[96],"real-world":[98],"problems":[99],"oil":[101],"flow":[102],"in":[103],"hydrostatic":[104],"bearings.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2025-10-10T00:00:00"}
