{"id":"https://openalex.org/W3125964941","doi":"https://doi.org/10.1137/21m1390773","title":"Space-Time Block Preconditioning for Incompressible Flow","display_name":"Space-Time Block Preconditioning for Incompressible Flow","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W3125964941","doi":"https://doi.org/10.1137/21m1390773","mag":"3125964941"},"language":"en","primary_location":{"id":"doi:10.1137/21m1390773","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1390773","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2101.07003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035740107","display_name":"Federico Danieli","orcid":"https://orcid.org/0000-0002-0866-2485"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Federico Danieli","raw_affiliation_strings":["University of Oxford"],"raw_orcid":"https://orcid.org/0000-0002-0866-2485","affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013739420","display_name":"Ben S. Southworth","orcid":"https://orcid.org/0000-0002-0283-4928"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ben S. Southworth","raw_affiliation_strings":["University of Oxford"],"raw_orcid":"https://orcid.org/0000-0002-0283-4928","affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110146377","display_name":"Andrew J. Wathen","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew J. Wathen","raw_affiliation_strings":["Los Alamos national Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos national Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035740107"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.3323,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.47240846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"44","issue":"1","first_page":"A337","last_page":"A363"},"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":0.9995999932289124,"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"}},"topics":[{"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/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/T11416","display_name":"Numerical methods for differential equations","score":0.9993000030517578,"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":0.9002671241760254},{"id":"https://openalex.org/keywords/space-time","display_name":"Space time","score":0.634607195854187},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5268296599388123},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.510258674621582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5079575181007385},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.4884142279624939},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45542967319488525},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4313802123069763},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.42793476581573486},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4250867962837219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4227690100669861},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.41296035051345825},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4005524218082428},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.380453884601593},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35690250992774963},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3133789300918579},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15185710787773132},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13100561499595642}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9002671241760254},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.634607195854187},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5268296599388123},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.510258674621582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5079575181007385},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.4884142279624939},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45542967319488525},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4313802123069763},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.42793476581573486},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4250867962837219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4227690100669861},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.41296035051345825},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4005524218082428},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.380453884601593},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35690250992774963},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3133789300918579},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15185710787773132},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13100561499595642},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical 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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/21m1390773","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1390773","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:arXiv.org:2101.07003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.07003","pdf_url":"https://arxiv.org/pdf/2101.07003","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3125964941","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2101.07003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:osti.gov:1864996","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1864996","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"doi:10.48550/arxiv.2101.07003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2101.07003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:3215283038","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2101.07003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2101.07003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.07003","pdf_url":"https://arxiv.org/pdf/2101.07003","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G667190850","display_name":"EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling","funder_award_id":"EP/L015803/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320332695","display_name":"Culham Centre for Fusion Energy","ror":"https://ror.org/05nmyph15"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1527509447","https://openalex.org/W1530661923","https://openalex.org/W1914698198","https://openalex.org/W1965741417","https://openalex.org/W1972197364","https://openalex.org/W1977061454","https://openalex.org/W1997305590","https://openalex.org/W2012630580","https://openalex.org/W2013813162","https://openalex.org/W2018850201","https://openalex.org/W2025778540","https://openalex.org/W2027491117","https://openalex.org/W2041876368","https://openalex.org/W2065884217","https://openalex.org/W2082529066","https://openalex.org/W2082606496","https://openalex.org/W2105970221","https://openalex.org/W2115291951","https://openalex.org/W2116621195","https://openalex.org/W2121613024","https://openalex.org/W2126042051","https://openalex.org/W2130214873","https://openalex.org/W2133248904","https://openalex.org/W2140153041","https://openalex.org/W2461259506","https://openalex.org/W2498157954","https://openalex.org/W2522121349","https://openalex.org/W2524221349","https://openalex.org/W2596342056","https://openalex.org/W2795471203","https://openalex.org/W2797996434","https://openalex.org/W2816245330","https://openalex.org/W2894547671","https://openalex.org/W2963524234","https://openalex.org/W2982352474","https://openalex.org/W3035682179","https://openalex.org/W3093624614","https://openalex.org/W3101004960","https://openalex.org/W3111546103","https://openalex.org/W3202687683"],"related_works":["https://openalex.org/W2318157895","https://openalex.org/W2289930808","https://openalex.org/W2219976283","https://openalex.org/W3205061873","https://openalex.org/W2811261340","https://openalex.org/W2627081135","https://openalex.org/W352093355","https://openalex.org/W2923657103","https://openalex.org/W3103047057","https://openalex.org/W2804747736","https://openalex.org/W2072104102","https://openalex.org/W3138143599","https://openalex.org/W2313021364","https://openalex.org/W100619804","https://openalex.org/W2887357428","https://openalex.org/W1724900401","https://openalex.org/W1136510834","https://openalex.org/W2989841117","https://openalex.org/W2064798389","https://openalex.org/W1599048370"],"abstract_inverted_index":{"Parallel-in-time":[0],"methods":[1,27,41,57,87],"have":[2],"become":[3],"increasingly":[4],"popular":[5],"in":[6,33,139,172,179,189,204],"the":[7,15,29,43,81,99,106,121,132,140],"simulation":[8],"of":[9,18,61,66,83,101,109,116,134,151,181,206,208],"time-dependent":[10,93],"numerical":[11],"PDEs,":[12],"allowing":[13],"for":[14,105],"efficient":[16],"use":[17],"additional":[19],"MPI":[20],"processes":[21],"when":[22,194],"spatial":[23,54,117,153,182],"parallelism":[24,32,74],"saturates.":[25],"Most":[26],"treat":[28],"solution":[30,108,133],"and":[31,35,68,75,158,183,201],"space":[34,67],"time":[36,50],"separately.":[37],"In":[38],"contrast,":[39],"all-at-once":[40,86,107],"solve":[42],"full":[44],"space-time":[45,102,122,136,160],"system":[46],"directly,":[47],"largely":[48,89],"treating":[49],"as":[51],"simply":[52],"another":[53],"dimension.":[55],"All-at-once":[56],"offer":[58],"a":[59,126,135,145,159,197],"number":[60,207],"benefits":[62],"over":[63],"separate":[64],"treatment":[65],"time,":[69],"most":[70],"notably":[71],"significantly":[72],"increased":[73],"faster":[76],"time-to-solution":[77],"(when":[78],"applicable).":[79],"However,":[80],"development":[82],"fast,":[84],"scalable":[85],"has":[88],"been":[90],"limited":[91],"to":[92,120,196],"(advection-)diffusion":[94,137],"problems.":[95],"This":[96],"paper":[97],"introduces":[98],"concept":[100],"block":[103,118,127],"preconditioning":[104,119],"incompressible":[110,173],"flow.":[111,174],"By":[112],"extending":[113],"well-known":[114],"concepts":[115],"setting,":[123],"we":[124],"develop":[125],"preconditioner":[128,209],"whose":[129],"application":[130],"requires":[131],"equation":[138],"velocity":[141],"block,":[142],"coupled":[143],"with":[144,212],"pressure":[146],"Schur":[147],"complement":[148],"approximation":[149],"consisting":[150],"independent":[152],"solves":[154],"at":[155],"each":[156],"time-step,":[157],"matrix-vector":[161],"multiplication.":[162],"The":[163],"new":[164],"method":[165],"is":[166],"tested":[167],"on":[168],"four":[169],"classical":[170],"models":[171],"Results":[175],"indicate":[176],"perfect":[177,187],"scalability":[178,188],"refinement":[180],"temporal":[184],"mesh":[185],"spacing,":[186],"nonlinear":[190,198],"Picard":[191],"iterations":[192],"count":[193],"applied":[195],"Navier-Stokes":[199],"problem,":[200],"minimal":[202],"overhead":[203],"terms":[205],"applications":[210],"compared":[211],"sequential":[213],"time-stepping.":[214]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}