{"id":"https://openalex.org/W2903259461","doi":"https://doi.org/10.1137/18m1230463","title":"Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency","display_name":"Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2903259461","doi":"https://doi.org/10.1137/18m1230463","mag":"2903259461"},"language":"en","primary_location":{"id":"doi:10.1137/18m1230463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1230463","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1812.00835","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061248986","display_name":"Patrick Henning","orcid":"https://orcid.org/0000-0002-6432-5504"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Patrick Henning","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014228488","display_name":"Daniel Peterseim","orcid":"https://orcid.org/0000-0001-7213-556X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Peterseim","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061248986"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2779,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.53934837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"58","issue":"3","first_page":"1744","last_page":"1772"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11804","display_name":"Quantum many-body systems","score":0.998199999332428,"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/eigenfunction","display_name":"Eigenfunction","score":0.7727298736572266},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7371635437011719},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7072055339813232},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6944455504417419},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.6508641839027405},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5481985211372375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5241209268569946},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5195584297180176},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4999809265136719},{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.4594583809375763},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41188547015190125},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16153106093406677},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1594884991645813},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0885729193687439}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7727298736572266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7371635437011719},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7072055339813232},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6944455504417419},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.6508641839027405},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5481985211372375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5241209268569946},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5195584297180176},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4999809265136719},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.4594583809375763},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41188547015190125},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16153106093406677},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1594884991645813},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0885729193687439},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1230463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1230463","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1812.00835","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.00835","pdf_url":"https://arxiv.org/pdf/1812.00835","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":"mag:2903259461","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1812.00835.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:78594","is_oa":false,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-785948","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"doi:10.48550/arxiv.1812.00835","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1812.00835","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1812.00835","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.00835","pdf_url":"https://arxiv.org/pdf/1812.00835","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":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6600000262260437}],"awards":[{"id":"https://openalex.org/G4636375529","display_name":null,"funder_award_id":"PE2143/2-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5714321922","display_name":null,"funder_award_id":"2016-03339","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320316588","display_name":"G\u00f6ran Gustafssons Stiftelser","ror":"https://ror.org/05s5h0e62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2903259461.pdf"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W1547403762","https://openalex.org/W1551152500","https://openalex.org/W1678736689","https://openalex.org/W1971447654","https://openalex.org/W1972945824","https://openalex.org/W2002704696","https://openalex.org/W2017049754","https://openalex.org/W2025470258","https://openalex.org/W2028803634","https://openalex.org/W2032875116","https://openalex.org/W2034012235","https://openalex.org/W2036920827","https://openalex.org/W2038249383","https://openalex.org/W2050338742","https://openalex.org/W2064853335","https://openalex.org/W2071438440","https://openalex.org/W2080739875","https://openalex.org/W2083561837","https://openalex.org/W2085565258","https://openalex.org/W2097804575","https://openalex.org/W2108533466","https://openalex.org/W2116323997","https://openalex.org/W2122716160","https://openalex.org/W2124673426","https://openalex.org/W2135044443","https://openalex.org/W2147014517","https://openalex.org/W2153532220","https://openalex.org/W2176364383","https://openalex.org/W2264002775","https://openalex.org/W2550808303","https://openalex.org/W2562972486","https://openalex.org/W2590927644","https://openalex.org/W2593060510","https://openalex.org/W2609070549","https://openalex.org/W2761881704","https://openalex.org/W2801701048","https://openalex.org/W2953165259","https://openalex.org/W2963073920","https://openalex.org/W2963808375","https://openalex.org/W2964345672","https://openalex.org/W3007093339","https://openalex.org/W3102111330","https://openalex.org/W3103711849","https://openalex.org/W3104355068","https://openalex.org/W3123992157","https://openalex.org/W3184099360"],"related_works":["https://openalex.org/W2964954239","https://openalex.org/W2950832211","https://openalex.org/W2949303259","https://openalex.org/W3161684200","https://openalex.org/W2319073748","https://openalex.org/W2296159450","https://openalex.org/W2056903616","https://openalex.org/W2962845679","https://openalex.org/W3017316809","https://openalex.org/W1503761432","https://openalex.org/W1967112126","https://openalex.org/W2998053691","https://openalex.org/W2022314932","https://openalex.org/W3022261466","https://openalex.org/W2948928428","https://openalex.org/W1607165029","https://openalex.org/W2092380438","https://openalex.org/W2083154033","https://openalex.org/W3212741025","https://openalex.org/W2146266711"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,60,72],"new":[3],"normalized":[4],"Sobolev":[5],"gradient":[6,31,139],"flow":[7,28,32,70],"for":[8,80,108,141],"the":[9,24,27,46,53,69,77,81,90,93,113,124,128],"Gross--Pitaevskii":[10],"eigenvalue":[11,83],"problem":[12],"based":[13],"on":[14,21,56],"an":[15,38,104],"energy":[16,94],"inner":[17],"product":[18],"that":[19],"depends":[20,55],"time":[22,66,88],"through":[23],"density":[25],"of":[26,59,68,120,127],"itself.":[29],"The":[30,63],"is":[33,116],"well-defined":[34],"and":[35,98,130],"converges":[36,99],"to":[37,103],"eigenfunction.":[39,105],"For":[40,85],"ground":[41,114],"states":[42],"we":[43],"can":[44],"quantify":[45],"convergence":[47],"speed":[48],"as":[49],"exponentially":[50],"fast":[51],"where":[52],"rate":[54],"spectral":[57],"gaps":[58],"linearized":[61],"operator.":[62],"forward":[64],"Euler":[65],"discretization":[67],"yields":[71],"numerical":[73,121],"method":[74,91,129],"which":[75],"generalizes":[76],"inverse":[78],"iteration":[79],"nonlinear":[82],"problem.":[84,143],"sufficiently":[86],"small":[87],"steps,":[89],"reduces":[92],"in":[95,101],"every":[96],"step":[97],"globally":[100],"$H^1$":[102],"In":[106],"particular,":[107],"any":[109],"nonnegative":[110],"starting":[111],"value,":[112],"state":[115],"obtained.":[117],"A":[118],"series":[119],"experiments":[122],"demonstrates":[123],"computational":[125],"efficiency":[126],"its":[131],"competitiveness":[132],"with":[133],"established":[134],"discretizations":[135],"arising":[136],"from":[137],"other":[138],"flows":[140],"this":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}