{"id":"https://openalex.org/W2158351656","doi":"https://doi.org/10.1137/110861002","title":"Stable Parareal in Time Method for First- and Second-Order Hyperbolic Systems","display_name":"Stable Parareal in Time Method for First- and Second-Order Hyperbolic Systems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2158351656","doi":"https://doi.org/10.1137/110861002","mag":"2158351656"},"language":"en","primary_location":{"id":"doi:10.1137/110861002","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110861002","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/A5101001114","display_name":"Xiaoying Dai","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoying Dai","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing,","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089357934","display_name":"Yvon Maday","orcid":"https://orcid.org/0000-0002-0443-6544"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210098814","display_name":"UPMC Health System","ror":"https://ror.org/011htkb76","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210098814"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Yvon Maday","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI, USA","UPMC Univ Paris 06, UMR 7598,","CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France","Laboratoire Jacques-Louis Lions, F-75005, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]},{"raw_affiliation_string":"UPMC Univ Paris 06, UMR 7598,","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210098814"]},{"raw_affiliation_string":"CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, F-75005, Paris, France","institution_ids":["https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.9896,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.97846649,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"1","first_page":"A52","last_page":"A78"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9592999815940857,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9585000276565552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6518937349319458},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.565726637840271},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.56547611951828},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5291032195091248},{"id":"https://openalex.org/keywords/time-domain","display_name":"Time domain","score":0.497405081987381},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4807817339897156},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4591268002986908},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37041109800338745},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3471977114677429},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27292633056640625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20619213581085205}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6518937349319458},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.565726637840271},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.56547611951828},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5291032195091248},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.497405081987381},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4807817339897156},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4591268002986908},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37041109800338745},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3471977114677429},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27292633056640625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20619213581085205},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110861002","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110861002","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:10.1.1.763.392","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.392","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/1201.1064.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.7200000286102295,"display_name":"Life in Land"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W132831348","https://openalex.org/W1527509447","https://openalex.org/W1538356049","https://openalex.org/W1544770838","https://openalex.org/W1564178044","https://openalex.org/W1792961480","https://openalex.org/W1823531150","https://openalex.org/W1959309014","https://openalex.org/W1967633238","https://openalex.org/W1979475531","https://openalex.org/W2023344463","https://openalex.org/W2027491117","https://openalex.org/W2043402936","https://openalex.org/W2047951536","https://openalex.org/W2059262502","https://openalex.org/W2138150617","https://openalex.org/W2140489561","https://openalex.org/W2176149742","https://openalex.org/W2245867738","https://openalex.org/W2609883971","https://openalex.org/W2769879319"],"related_works":["https://openalex.org/W1995118522","https://openalex.org/W64916076","https://openalex.org/W2090020940","https://openalex.org/W4364366001","https://openalex.org/W1072895066","https://openalex.org/W2565229889","https://openalex.org/W4213003931","https://openalex.org/W2607078461","https://openalex.org/W2383959235","https://openalex.org/W2061359299"],"abstract_inverted_index":{"The":[0,146],"parareal":[1,41,69,118,156],"in":[2,42,70,119,157],"time":[3,43,71,120,158],"algorithm":[4,15,44,121],"allows":[5],"one":[6,32],"to":[7,33,47,58,127,135],"perform":[8],"parallel":[9],"simulations":[10,50],"of":[11,22,37,39,51,64,66,104,116,151,154],"time-dependent":[12,23],"problems.":[13],"This":[14,54],"has":[16,56],"been":[17],"implemented":[18],"on":[19],"many":[20],"types":[21],"problems":[24,85],"with":[25],"some":[26],"success.":[27],"Recent":[28],"contributions":[29],"have":[30],"allowed":[31],"extend":[34],"the":[35,40,60,67,87,95,99,112,117,132,149,155],"domain":[36],"application":[38],"so":[45],"as":[46,97],"handle":[48],"long-time":[49],"Hamiltonian":[52],"systems.":[53],"improvement":[55],"managed":[57],"avoid":[59],"fatally":[61],"large":[62],"lack":[63],"accuracy":[65],"plain":[68],"algorithm,":[72],"which":[73],"does":[74],"not":[75],"conserve":[76],"invariant":[77],"quantities.":[78],"A":[79],"somewhat":[80],"similar":[81],"difficulty":[82],"occurs":[83],"for":[84,101,114],"where":[86],"solution":[88],"lacks":[89],"regularity,":[90],"either":[91],"initially":[92],"or":[93],"during":[94],"evolution,":[96],"is":[98],"case":[100],"hyperbolic":[102],"systems":[103],"conservation":[105],"laws.":[106],"In":[107],"this":[108,152],"paper":[109],"we":[110],"identify":[111],"reasons":[113],"instabilities":[115],"and":[122,141],"propose":[123],"a":[124,137,142],"simple":[125],"way":[126],"cure":[128],"them.":[129],"We":[130],"use":[131],"new":[133],"method":[134],"solve":[136],"linear":[138],"wave":[139],"equation":[140],"nonlinear":[143],"Burgers'":[144],"equation.":[145],"results":[147],"illustrate":[148],"stability":[150],"variant":[153],"algorithm.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
