{"id":"https://openalex.org/W2036777068","doi":"https://doi.org/10.1137/090770059","title":"Optimized Schwarz Waveform Relaxation for the Primitive Equations of the Ocean","display_name":"Optimized Schwarz Waveform Relaxation for the Primitive Equations of the Ocean","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2036777068","doi":"https://doi.org/10.1137/090770059","mag":"2036777068"},"language":"en","primary_location":{"id":"doi:10.1137/090770059","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090770059","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0905.3624","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111544662","display_name":"Emmanuel Audusse","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. Audusse","raw_affiliation_strings":["audusse@math.univ-paris13.fr and merlet@math.univ-paris13.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"audusse@math.univ-paris13.fr and merlet@math.univ-paris13.fr#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109419620","display_name":"Pierre Dreyfuss","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Dreyfuss","raw_affiliation_strings":["dreyfuss@unice.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"dreyfuss@unice.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089057640","display_name":"Beno\u00eet Merlet","orcid":"https://orcid.org/0000-0002-6334-9037"},"institutions":[{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"B. Merlet","raw_affiliation_strings":["Laboratoire Analyse, G\u00e9om\u00e9trie et Applications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","institution_ids":["https://openalex.org/I4210102686"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.11408906,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"32","issue":"5","first_page":"2908","last_page":"2936"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976000189781189,"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/primitive-equations","display_name":"Primitive equations","score":0.7107967138290405},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.6836593747138977},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6195933222770691},{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.5717437267303467},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5631100535392761},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5586672425270081},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5111103653907776},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4918947219848633},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.4832109212875366},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4138324558734894},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.41279780864715576},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34840089082717896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24443256855010986},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.23937642574310303},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23588702082633972},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11243370175361633},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.10289660096168518}],"concepts":[{"id":"https://openalex.org/C182692853","wikidata":"https://www.wikidata.org/wiki/Q2386647","display_name":"Primitive equations","level":4,"score":0.7107967138290405},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6836593747138977},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6195933222770691},{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.5717437267303467},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5631100535392761},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5586672425270081},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5111103653907776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4918947219848633},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.4832109212875366},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4138324558734894},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.41279780864715576},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34840089082717896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24443256855010986},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.23937642574310303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23588702082633972},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11243370175361633},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.10289660096168518},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/090770059","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090770059","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:0905.3624","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0905.3624","pdf_url":"https://arxiv.org/pdf/0905.3624","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:CiteSeerX.psu:10.1.1.531.8030","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.531.8030","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.unice.fr/~dreyfuss/P3.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00386817v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00386817","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2009","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0905.3624","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0905.3624","pdf_url":"https://arxiv.org/pdf/0905.3624","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"score":0.8500000238418579,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2036777068.pdf","grobid_xml":"https://content.openalex.org/works/W2036777068.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W185391259","https://openalex.org/W1489222793","https://openalex.org/W1498725771","https://openalex.org/W1514740718","https://openalex.org/W1548589512","https://openalex.org/W1570976541","https://openalex.org/W1977924110","https://openalex.org/W1985692215","https://openalex.org/W1998789711","https://openalex.org/W2001819970","https://openalex.org/W2007510482","https://openalex.org/W2020633626","https://openalex.org/W2025377524","https://openalex.org/W2029827147","https://openalex.org/W2031474171","https://openalex.org/W2036597275","https://openalex.org/W2040211481","https://openalex.org/W2046409434","https://openalex.org/W2064643401","https://openalex.org/W2069384562","https://openalex.org/W2088967627","https://openalex.org/W2089342568","https://openalex.org/W2129427228","https://openalex.org/W2141501543","https://openalex.org/W2142578979","https://openalex.org/W2148947997","https://openalex.org/W2171622994","https://openalex.org/W2281327298","https://openalex.org/W4254519656"],"related_works":["https://openalex.org/W1647103664","https://openalex.org/W2286395548","https://openalex.org/W1994696552","https://openalex.org/W2504287632","https://openalex.org/W2069946149","https://openalex.org/W3046643187","https://openalex.org/W1515964003","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2233890230"],"abstract_inverted_index":{"In":[0],"this":[1],"article":[2],"we":[3,48],"are":[4],"interested":[5],"in":[6,41],"the":[7,15,20,24,39,42,67,77,80],"derivation":[8],"of":[9,19,38,44,76,79],"efficient":[10],"domain":[11],"decomposition":[12],"methods":[13],"for":[14],"viscous":[16],"primitive":[17],"equations":[18,30],"ocean.":[21],"We":[22,64],"consider":[23],"rotating":[25],"three-dimensional":[26],"incompressible":[27],"hydrostatic":[28],"Navier\u2013Stokes":[29],"with":[31],"free":[32],"surface.":[33],"Performing":[34],"an":[35,50,58],"asymptotic":[36],"analysis":[37],"system":[40],"regime":[43],"small":[45],"Rossby":[46],"numbers,":[47],"compute":[49],"approximate":[51],"Dirichlet":[52],"to":[53],"Neumann":[54],"operator":[55],"and":[56,72],"build":[57],"optimized":[59],"Schwarz":[60],"waveform":[61],"relaxation":[62],"algorithm.":[63],"establish":[65],"that":[66],"algorithm":[68],"is":[69],"well":[70],"defined":[71],"provide":[73],"numerical":[74],"evidence":[75],"convergence":[78],"method.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}