{"id":"https://openalex.org/W1968658458","doi":"https://doi.org/10.1137/s1064827595285299","title":"A Fast Poisson Solver for the Finite Difference Solution of the Incompressible Navier--Stokes Equations","display_name":"A Fast Poisson Solver for the Finite Difference Solution of the Incompressible Navier--Stokes Equations","publication_year":1998,"publication_date":"1998-09-01","ids":{"openalex":"https://openalex.org/W1968658458","doi":"https://doi.org/10.1137/s1064827595285299","mag":"1968658458"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827595285299","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827595285299","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/A5110003399","display_name":"Gene H. Golub","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gene H. Golub","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015182129","display_name":"Lan Chieh Huang","orcid":"https://orcid.org/0009-0006-5579-1913"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lan Chieh Huang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066426676","display_name":"Horst D. Simon","orcid":"https://orcid.org/0000-0003-0832-3720"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Horst Simon","raw_affiliation_strings":["(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087309882","display_name":"Wei-Pai Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wei-Pai Tang","raw_affiliation_strings":["(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5110003399"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5972,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.79936237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"5","first_page":"1606","last_page":"1624"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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":0.9961000084877014,"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/solver","display_name":"Solver","score":0.7894618511199951},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.773067831993103},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.7388153672218323},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6132779121398926},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5721247792243958},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.571808397769928},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5509896278381348},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5032002329826355},{"id":"https://openalex.org/keywords/discrete-poisson-equation","display_name":"Discrete Poisson equation","score":0.5029677748680115},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5005440711975098},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.475157231092453},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4705510437488556},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4326986074447632},{"id":"https://openalex.org/keywords/pressure-correction-method","display_name":"Pressure-correction method","score":0.41152238845825195},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.28630954027175903},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2665981352329254},{"id":"https://openalex.org/keywords/laplaces-equation","display_name":"Laplace's equation","score":0.18221226334571838},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13859641551971436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08166173100471497},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07943269610404968}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7894618511199951},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.773067831993103},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.7388153672218323},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6132779121398926},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5721247792243958},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.571808397769928},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5509896278381348},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5032002329826355},{"id":"https://openalex.org/C3062749","wikidata":"https://www.wikidata.org/wiki/Q5282040","display_name":"Discrete Poisson equation","level":4,"score":0.5029677748680115},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5005440711975098},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.475157231092453},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4705510437488556},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4326986074447632},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.41152238845825195},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.28630954027175903},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2665981352329254},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.18221226334571838},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13859641551971436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08166173100471497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07943269610404968},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827595285299","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827595285299","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:10.1.1.43.2786","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.2786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.scicom.uwaterloo.ca/wptang/fast.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W99016522","https://openalex.org/W1826216474","https://openalex.org/W1965134668","https://openalex.org/W1984938247","https://openalex.org/W1988703624","https://openalex.org/W1990238127","https://openalex.org/W1991835897","https://openalex.org/W1997027646","https://openalex.org/W2006850990","https://openalex.org/W2014912142","https://openalex.org/W2021041911","https://openalex.org/W2023782398","https://openalex.org/W2034071825","https://openalex.org/W2042255949","https://openalex.org/W2054629935","https://openalex.org/W2076077791","https://openalex.org/W2076582418","https://openalex.org/W2077332343","https://openalex.org/W2083860858","https://openalex.org/W2131778920","https://openalex.org/W2145425533","https://openalex.org/W2295428826","https://openalex.org/W2477040106","https://openalex.org/W2798909945","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W1975357829","https://openalex.org/W2912163380","https://openalex.org/W2146838233","https://openalex.org/W2187387748","https://openalex.org/W2047933493","https://openalex.org/W2313597186","https://openalex.org/W1991751407","https://openalex.org/W4308131392","https://openalex.org/W1469108320","https://openalex.org/W1966298146"],"abstract_inverted_index":{"In":[0],"this":[1,66],"paper,":[2],"a":[3,43],"fast":[4,49],"direct":[5],"solver":[6,50],"for":[7,41],"the":[8,12,22,26,31,56],"Poisson":[9,18],"equation":[10,19],"on":[11],"half-staggered":[13,67],"grid":[14,68],"is":[15],"presented.":[16],"The":[17,48,59],"results":[20],"from":[21],"projection":[23],"method":[24],"of":[25,30],"finite":[27],"difference":[28],"solution":[29],"incompressible":[32],"Navier--Stokes":[33],"equations.":[34],"To":[35],"achieve":[36],"our":[37],"goal,":[38],"new":[39],"algorithms":[40],"diagonalizing":[42],"semidefinite":[44],"pair":[45],"are":[46,69],"developed.":[47],"can":[51],"also":[52,70],"be":[53],"extended":[54],"to":[55],"three-dimensional":[57],"case.":[58],"motivation":[60],"and":[61],"related":[62],"issues":[63],"in":[64],"using":[65],"discussed.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}