{"id":"https://openalex.org/W2033505935","doi":"https://doi.org/10.1137/070686135","title":"Multigrid Optimization Schemes for Solving Bose\u2013Einstein Condensate Control Problems","display_name":"Multigrid Optimization Schemes for Solving Bose\u2013Einstein Condensate Control Problems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2033505935","doi":"https://doi.org/10.1137/070686135","mag":"2033505935"},"language":"en","primary_location":{"id":"doi:10.1137/070686135","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070686135","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/A5027648225","display_name":"Alfio Borz\u0131\u0300","orcid":"https://orcid.org/0000-0002-8050-1336"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Borz\u00ec","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045357961","display_name":"Ulrich Hohenester","orcid":"https://orcid.org/0000-0001-8929-2086"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"U. Hohenester","raw_affiliation_strings":["Institut f\u00fcr Physik, Karl-Franzens-Universit\u00e4t Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Physik, Karl-Franzens-Universit\u00e4t Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045357961"],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":null,"apc_paid":null,"fwci":1.62,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.82663024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"1","first_page":"441","last_page":"462"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11993","display_name":"Atomic and Subatomic Physics Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/multigrid-method","display_name":"Multigrid method","score":0.8312346935272217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5962758660316467},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5525550246238708},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5224860310554504},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5051694512367249},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4708060026168823},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4674525856971741},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.455446720123291},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3915720283985138},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31471556425094604},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.281340628862381},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22061845660209656},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10461249947547913}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8312346935272217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5962758660316467},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5525550246238708},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5224860310554504},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5051694512367249},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4708060026168823},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4674525856971741},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.455446720123291},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3915720283985138},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31471556425094604},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.281340628862381},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22061845660209656},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10461249947547913},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070686135","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070686135","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:unipub.uni-graz.at:1834680","is_oa":false,"landing_page_url":"http://resolver.obvsg.at/urn:nbn:at:at-ubg:3-3785","pdf_url":null,"source":{"id":"https://openalex.org/S4306400359","display_name":"Unipub UB Graz (Universit\u00e4t Graz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766117","host_organization_name":"University of Graz","host_organization_lineage":["https://openalex.org/I15766117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1971920652","https://openalex.org/W1976792725","https://openalex.org/W1980845667","https://openalex.org/W2006461985","https://openalex.org/W2013529907","https://openalex.org/W2013946933","https://openalex.org/W2018526877","https://openalex.org/W2020279670","https://openalex.org/W2020924923","https://openalex.org/W2023819779","https://openalex.org/W2034012235","https://openalex.org/W2036795049","https://openalex.org/W2039625138","https://openalex.org/W2041696736","https://openalex.org/W2044625188","https://openalex.org/W2048357515","https://openalex.org/W2048775851","https://openalex.org/W2049974290","https://openalex.org/W2052023085","https://openalex.org/W2065361411","https://openalex.org/W2071438440","https://openalex.org/W2079166741","https://openalex.org/W2083494341","https://openalex.org/W2083561837","https://openalex.org/W2085160061","https://openalex.org/W2091549324","https://openalex.org/W2108560279","https://openalex.org/W2122565324","https://openalex.org/W2151317657","https://openalex.org/W2168899295"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W84272617","https://openalex.org/W613282331","https://openalex.org/W2155025153","https://openalex.org/W4253880741","https://openalex.org/W2361205607","https://openalex.org/W4235544854","https://openalex.org/W2047206873"],"abstract_inverted_index":{"The":[0,26,80,134],"control":[1,18,60,101],"of":[2,5,16,29,33,48,85,137,153],"the":[3,14,30,39,73,77,100,118,159],"transport":[4],"Bose\u2013Einstein":[6,34],"condensates":[7,35],"in":[8],"magnetic":[9,51],"microtraps":[10],"is":[11,36,66,148],"formulated":[12],"within":[13],"framework":[15],"optimal":[17,59],"theory":[19],"and":[20,42,113,127,144],"solved":[21],"by":[22,38,76,107],"multigrid":[23,129,160],"optimization":[24,130,161,166],"schemes.":[25],"time":[27,92],"evolution":[28],"wave":[31],"function":[32],"governed":[37],"Gross\u2013Pitaevskii":[40],"equation":[41,98],"can":[43],"be":[44,70],"manipulated":[45],"through":[46],"variation":[47],"a":[49,109,121,128,164],"controllable":[50],"confinement":[52],"potential.":[53],"In":[54],"order":[55],"to":[56],"define":[57],"an":[58,62,96],"strategy,":[61],"appropriate":[63],"cost":[64],"functional":[65],"introduced":[67],"that":[68,158],"must":[69],"minimized":[71],"under":[72],"constraint":[74],"given":[75],"dynamic":[78],"equation.":[79],"resulting":[81,119],"optimality":[82],"system":[83],"consists":[84],"two":[86,139],"nonlinear":[87,123],"Schr\u00f6dinger-type":[88],"equations":[89,104],"with":[90,95],"opposite":[91],"orientation":[93],"coupled":[94],"elliptic":[97],"for":[99],"function.":[102],"These":[103],"are":[105,132,141],"approximated":[106],"using":[108],"time-splitting":[110],"pseudospectral":[111],"method":[112],"finite":[114],"differences.":[115],"To":[116],"solve":[117],"problem":[120],"cascadic":[122],"conjugate":[124],"gradient":[125],"scheme":[126,131,162],"considered.":[133],"convergence":[135],"properties":[136],"these":[138],"schemes":[140],"investigated":[142],"theoretically,":[143],"their":[145],"computational":[146],"performance":[147],"discussed":[149],"based":[150],"on":[151],"results":[152],"numerical":[154],"experiments.":[155],"It":[156],"appears":[157],"provides":[163],"robust":[165],"strategy.":[167]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}