{"id":"https://openalex.org/W1966394094","doi":"https://doi.org/10.1137/120872681","title":"A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations","display_name":"A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1966394094","doi":"https://doi.org/10.1137/120872681","mag":"1966394094"},"language":"en","primary_location":{"id":"doi:10.1137/120872681","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120872681","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/1204.5926","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108100026","display_name":"Fr\u00e9d\u00e9ric Legoll","orcid":"https://orcid.org/0000-0002-2334-5058"},"institutions":[{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Legoll","raw_affiliation_strings":["multi-\u00e9chelle - Mod\u00e9lisation et exp\u00e9rimentation multi-\u00e9chelle pour les solides h\u00e9t\u00e9rog\u00e8nes (\u00c9cole des Ponts ParisTech\r\n6-8 avenue Blaise Pascal- Cit\u00e9 Descartes\r\nChamps-sur-Marne\r\nF-77455 Marne-la-Vall\u00e9e cedex 2 - France)","MICMAC - Methods and engineering of multiscale computing from atom to continuum (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"multi-\u00e9chelle - Mod\u00e9lisation et exp\u00e9rimentation multi-\u00e9chelle pour les solides h\u00e9t\u00e9rog\u00e8nes (\u00c9cole des Ponts ParisTech\r\n6-8 avenue Blaise Pascal- Cit\u00e9 Descartes\r\nChamps-sur-Marne\r\nF-77455 Marne-la-Vall\u00e9e cedex 2 - France)","institution_ids":["https://openalex.org/I142631665"]},{"raw_affiliation_string":"MICMAC - Methods and engineering of multiscale computing from atom to continuum (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048560398","display_name":"Tony Leli\u00e8vre","orcid":"https://orcid.org/0000-0002-3412-113X"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tony Leli\u00e8vre","raw_affiliation_strings":["CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","MICMAC - Methods and engineering of multiscale computing from atom to continuum (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]},{"raw_affiliation_string":"MICMAC - Methods and engineering of multiscale computing from atom to continuum (France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007947181","display_name":"Giovanni Samaey","orcid":"https://orcid.org/0000-0001-8433-4523"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Giovanni Samaey","raw_affiliation_strings":["KU Leuven - CS - Department of Computer Science (Departement Computerwetenschappen\r\nCelestijnenlaan 200A B-3001 Leuven - Belgium)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven - CS - Department of Computer Science (Departement Computerwetenschappen\r\nCelestijnenlaan 200A B-3001 Leuven - Belgium)","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0971,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.93707047,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"35","issue":"4","first_page":"A1951","last_page":"A1986"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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":0.9995999932289124,"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/propagator","display_name":"Propagator","score":0.6987411379814148},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6554540395736694},{"id":"https://openalex.org/keywords/macro","display_name":"Macro","score":0.5577977895736694},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5324407815933228},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5210713148117065},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46244269609451294},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4458671808242798},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4419049024581909},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.43893715739250183},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.4344249963760376},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43196019530296326},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4118036925792694},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4080129861831665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2689628005027771},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19350296258926392},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09475356340408325}],"concepts":[{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.6987411379814148},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6554540395736694},{"id":"https://openalex.org/C166955791","wikidata":"https://www.wikidata.org/wiki/Q629579","display_name":"Macro","level":2,"score":0.5577977895736694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5324407815933228},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5210713148117065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46244269609451294},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4458671808242798},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4419049024581909},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.43893715739250183},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.4344249963760376},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43196019530296326},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4118036925792694},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4080129861831665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2689628005027771},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19350296258926392},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09475356340408325},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/120872681","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120872681","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:1204.5926","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1204.5926","pdf_url":"https://arxiv.org/pdf/1204.5926","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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:10.1.1.747.9719","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.747.9719","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1204.5926.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00691939v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00691939","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":"SIAM Journal on Scientific Computing, 2013, 35 (4), pp.A1951-A1986. &#x27E8;10.1137/120872681&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1204.5926","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1204.5926","pdf_url":"https://arxiv.org/pdf/1204.5926","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/G553579311","display_name":"MEthodes G\u00e9om\u00e9triques et \u00e9chantillonnage: Application \u00e0 la Simulation mol\u00e9culaire","funder_award_id":"ANR-09-BLAN-0216","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"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/W1966394094.pdf","grobid_xml":"https://content.openalex.org/works/W1966394094.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1823531150","https://openalex.org/W1979475531","https://openalex.org/W1987455271","https://openalex.org/W1989707864","https://openalex.org/W1990157709","https://openalex.org/W2027358578","https://openalex.org/W2027491117","https://openalex.org/W2029778460","https://openalex.org/W2032227660","https://openalex.org/W2047951536","https://openalex.org/W2059262502","https://openalex.org/W2068180086","https://openalex.org/W2069870748","https://openalex.org/W2070460788","https://openalex.org/W2105970221","https://openalex.org/W2137867316","https://openalex.org/W2139158220","https://openalex.org/W2140489561","https://openalex.org/W2148717806","https://openalex.org/W2151084831","https://openalex.org/W2153935579","https://openalex.org/W2156603435","https://openalex.org/W2950756295","https://openalex.org/W3098558891"],"related_works":["https://openalex.org/W2747757380","https://openalex.org/W4249951934","https://openalex.org/W2336717475","https://openalex.org/W3028230607","https://openalex.org/W2019645717","https://openalex.org/W1522315692","https://openalex.org/W2143620155","https://openalex.org/W2024607757","https://openalex.org/W2052499411","https://openalex.org/W2016113450"],"abstract_inverted_index":{"We":[0,79,101,148],"introduce":[1],"a":[2,17,23,37,81,88,92],"micro-macro":[3,93],"parareal":[4,115],"algorithm":[5,14,86],"for":[6,87],"the":[7,42,57,63,67,70,75,85,104,109,114,125,128,140,144],"time-parallel":[8],"integration":[9,68],"of":[10,69,84,91,127,133,143],"multiscale-in-time":[11],"systems.":[12],"The":[13,135],"first":[15],"computes":[16],"cheap,":[18],"but":[19],"inaccurate,":[20],"solution":[21,106,112],"using":[22,36],"coarse":[24],"propagator":[25,39],"(simulating":[26],"an":[27],"approximate":[28,145],"slow":[29],"macroscopic":[30,131,146],"model),":[31],"which":[32],"is":[33,48,122],"iteratively":[34],"corrected":[35],"fine-scale":[38],"(accurately":[40],"simulating":[41],"full":[43,71,110],"microscopic":[44,72,111,129],"dynamics).":[45],"This":[46],"correction":[47],"done":[49],"in":[50],"parallel":[51],"over":[52,74],"many":[53],"subintervals,":[54],"thereby":[55],"reducing":[56],"wall-clock":[58],"time":[59,77],"needed":[60],"to":[61,66,108],"obtain":[62],"solution,":[64],"compared":[65],"model":[73],"complete":[76],"interval.":[78],"provide":[80],"numerical":[82,153],"analysis":[83],"prototypical":[89],"example":[90],"model,":[94],"namely,":[95],"singularly":[96],"perturbed":[97],"ordinary":[98],"differential":[99],"equations.":[100],"show":[102],"that":[103],"computed":[105],"converges":[107],"(when":[113],"iterations":[116],"proceed)":[117],"only":[118],"if":[119],"special":[120],"care":[121],"taken":[123],"during":[124],"coupling":[126],"and":[130],"levels":[132],"description.":[134],"error":[136,142],"bound":[137],"depends":[138],"on":[139],"modeling":[141],"model.":[147],"illustrate":[149],"these":[150],"results":[151],"with":[152],"experiments.":[154]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}
