{"id":"https://openalex.org/W2004288382","doi":"https://doi.org/10.1137/120899017","title":"An Asymptotic Preserving Scheme Based on a New Formulation for NLS in the Semiclassical Limit","display_name":"An Asymptotic Preserving Scheme Based on a New Formulation for NLS in the Semiclassical Limit","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2004288382","doi":"https://doi.org/10.1137/120899017","mag":"2004288382"},"language":"en","primary_location":{"id":"doi:10.1137/120899017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120899017","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1211.3391","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Christophe Besse","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christophe Besse","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"R\u00e9mi Carles","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R\u00e9mi Carles","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Florian M\u00e9hats","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Florian M\u00e9hats","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4383,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.58930308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"1228","last_page":"1260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.4372999966144562,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.4372999966144562,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.12449999898672104,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.0835999995470047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semiclassical-physics","display_name":"Semiclassical physics","score":0.7696999907493591},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5455999970436096},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5083000063896179},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5047000050544739},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49000000953674316},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.48399999737739563},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45489999651908875},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.3968999981880188},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.390500009059906}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.7696999907493591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.580299973487854},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5455999970436096},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5083000063896179},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49000000953674316},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.48399999737739563},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45489999651908875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4399000108242035},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.3968999981880188},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.390500009059906},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37779998779296875},{"id":"https://openalex.org/C197111296","wikidata":"https://www.wikidata.org/wiki/Q122894","display_name":"Planck constant","level":3,"score":0.37529999017715454},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.35659998655319214},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2752000093460083},{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.26899999380111694},{"id":"https://openalex.org/C166126730","wikidata":"https://www.wikidata.org/wiki/Q725309","display_name":"Planck","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/120899017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120899017","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1211.3391","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1211.3391","pdf_url":"https://arxiv.org/pdf/1211.3391","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":"pmh:oai:HAL:hal-00752011v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00752011","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2013, 11 (4), pp.1228-1260. &#x27E8;10.1137/120899017&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1211.3391","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1211.3391","pdf_url":"https://arxiv.org/pdf/1211.3391","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/G1374601543","display_name":null,"funder_award_id":"ANR-11-IS01-0003","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4024226679","display_name":"Schr\u00f6dinger equations and applications","funder_award_id":"ANR-12-JS01-0005","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4448336722","display_name":"Centre Europ\u00e9en pour les Math\u00e9matiques, la Physique et leurs Interactions","funder_award_id":"ANR-11-LABX-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5875353992","display_name":null,"funder_award_id":"NT09_460489","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6445655660","display_name":null,"funder_award_id":"ANR-08-JCJC-0124-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7474824671","display_name":"R\u00e9gimes Asymptotiques pour l'\u00e9quation de Schr\u00f6dinger","funder_award_id":"ANR-08-JCJC-0124","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7556566064","display_name":"modeling and simulation of Low DImensional QUAntum Systems","funder_award_id":"ANR-11-IS01-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8081701703","display_name":"Bose-Einstein Condensates: Advanced SIMulation Deterministic and Stochastic Computational Models, HPC Implementation, Simulation of Experiments","funder_award_id":"ANR-12-MONU-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8684267442","display_name":null,"funder_award_id":"MicroWave NT09_460489","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"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1521469263","https://openalex.org/W1663802614","https://openalex.org/W1968106586","https://openalex.org/W1972140872","https://openalex.org/W1973279410","https://openalex.org/W1978434425","https://openalex.org/W1981588909","https://openalex.org/W1983797262","https://openalex.org/W1994545070","https://openalex.org/W2001032670","https://openalex.org/W2012220122","https://openalex.org/W2013529907","https://openalex.org/W2016870785","https://openalex.org/W2019056380","https://openalex.org/W2020728557","https://openalex.org/W2023969416","https://openalex.org/W2024329825","https://openalex.org/W2025751738","https://openalex.org/W2029191767","https://openalex.org/W2032827682","https://openalex.org/W2033099995","https://openalex.org/W2046913111","https://openalex.org/W2050873954","https://openalex.org/W2051952162","https://openalex.org/W2055048779","https://openalex.org/W2056092599","https://openalex.org/W2056971052","https://openalex.org/W2056979287","https://openalex.org/W2057432996","https://openalex.org/W2060005168","https://openalex.org/W2063702850","https://openalex.org/W2067196967","https://openalex.org/W2068731834","https://openalex.org/W2073339836","https://openalex.org/W2074306248","https://openalex.org/W2079706362","https://openalex.org/W2083916485","https://openalex.org/W2085927003","https://openalex.org/W2108160059","https://openalex.org/W2123055717","https://openalex.org/W2155073557","https://openalex.org/W2162097938","https://openalex.org/W2165588672","https://openalex.org/W2169867102","https://openalex.org/W2173139136","https://openalex.org/W2359425119","https://openalex.org/W3098235107","https://openalex.org/W4253117495"],"related_works":[],"abstract_inverted_index":{"We":[0,10,33,61],"consider":[1],"the":[2,6,21,36,58,76,82,89,100,110],"semiclassical":[3],"limit":[4],"for":[5,51],"nonlinear":[7],"Schr\u00f6dinger":[8,112],"equation.":[9,113],"introduce":[11],"a":[12,17,43,52,63],"phase/amplitude":[13],"representation":[14],"given":[15],"by":[16],"system":[18,37],"similar":[19],"to":[20,109],"hydrodynamical":[22],"formulation,":[23],"whose":[24],"novelty":[25],"consists":[26],"of":[27,45,99],"including":[28],"some":[29],"asymptotically":[30],"vanishing":[31],"viscosity.":[32],"prove":[34],"that":[35],"is":[38,69,105],"always":[39],"locally":[40],"well-posed":[41,50],"in":[42,57,75],"class":[44],"Sobolev":[46],"spaces,":[47],"and":[48,95],"globally":[49],"fixed":[53],"positive":[54],"Planck":[55,101],"constant":[56],"one-dimensional":[59],"case.":[60],"propose":[62],"second":[64],"order":[65],"numerical":[66],"scheme":[67],"which":[68],"asymptotic":[70],"preserving.":[71],"Before":[72],"singularities":[73],"appear":[74],"limiting":[77],"Euler":[78],"equation,":[79],"we":[80],"recover":[81],"quadratic":[83],"physical":[84],"observables":[85],"as":[86,88],"well":[87,107],"wave":[90],"function":[91],"with":[92],"mesh":[93],"size":[94],"time":[96],"step":[97],"independent":[98],"constant.":[102],"This":[103],"approach":[104],"also":[106],"suited":[108],"linear":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2016-06-24T00:00:00"}
