{"id":"https://openalex.org/W3170785738","doi":"https://doi.org/10.1007/s00211-023-01347-x","title":"Asymptotic analysis of domain decomposition for optimal transport","display_name":"Asymptotic analysis of domain decomposition for optimal transport","publication_year":2023,"publication_date":"2023-02-28","ids":{"openalex":"https://openalex.org/W3170785738","doi":"https://doi.org/10.1007/s00211-023-01347-x","mag":"3170785738"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-023-01347-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00211-023-01347-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01347-x.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01347-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041021069","display_name":"Mauro Bonafini","orcid":null},"institutions":[{"id":"https://openalex.org/I119439378","display_name":"University of Verona","ror":"https://ror.org/039bp8j42","country_code":"IT","type":"education","lineage":["https://openalex.org/I119439378"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Mauro Bonafini","raw_affiliation_strings":["Department of Computer Science, University of Verona, Verona, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Verona, Verona, Italy","institution_ids":["https://openalex.org/I119439378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083547507","display_name":"Ismael Medina","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ismael Medina","raw_affiliation_strings":["Campus Institute Data Science, University of G\u00f6ttingen, G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"Campus Institute Data Science, University of G\u00f6ttingen, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059838227","display_name":"Bernhard Schmitzer","orcid":"https://orcid.org/0000-0002-6146-8833"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bernhard Schmitzer","raw_affiliation_strings":["Campus Institute Data Science, University of G\u00f6ttingen, G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"Campus Institute Data Science, University of G\u00f6ttingen, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041021069"],"corresponding_institution_ids":["https://openalex.org/I119439378"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.4017,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6105806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"153","issue":"2-3","first_page":"451","last_page":"492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"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":0.9980000257492065,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9975000023841858,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6852182149887085},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6623113751411438},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5721623301506042},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5596590638160706},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5166981220245361},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4170208275318146},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35277774930000305},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27576085925102234},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20867598056793213}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6852182149887085},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6623113751411438},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5721623301506042},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5596590638160706},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5166981220245361},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4170208275318146},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35277774930000305},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27576085925102234},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20867598056793213},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-023-01347-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00211-023-01347-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01347-x.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/124385","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/124385","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"yes"}],"best_oa_location":{"id":"doi:10.1007/s00211-023-01347-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00211-023-01347-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01347-x.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8928656450","display_name":null,"funder_award_id":"Projekt DEAL","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321870","display_name":"Georg-August-Universit\u00e4t G\u00f6ttingen","ror":"https://ror.org/01y9bpm73"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3170785738.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W39337161","https://openalex.org/W55464428","https://openalex.org/W98171807","https://openalex.org/W385466589","https://openalex.org/W1480714962","https://openalex.org/W1511358834","https://openalex.org/W1549932963","https://openalex.org/W1594563152","https://openalex.org/W1975896700","https://openalex.org/W1982143037","https://openalex.org/W1994521023","https://openalex.org/W2045361520","https://openalex.org/W2067193435","https://openalex.org/W2068013644","https://openalex.org/W2096413780","https://openalex.org/W2132883347","https://openalex.org/W2534420330","https://openalex.org/W2793477525","https://openalex.org/W2802739963","https://openalex.org/W2963035177","https://openalex.org/W2963160215","https://openalex.org/W2963334579","https://openalex.org/W2963651635","https://openalex.org/W2963830216","https://openalex.org/W3037862998","https://openalex.org/W3042387682","https://openalex.org/W3217527333","https://openalex.org/W4206471589","https://openalex.org/W4233762729","https://openalex.org/W4255839052"],"related_works":["https://openalex.org/W2018702098","https://openalex.org/W2597266923","https://openalex.org/W2156024331","https://openalex.org/W569408057","https://openalex.org/W2161243591","https://openalex.org/W30930551","https://openalex.org/W2153233687","https://openalex.org/W4211094555","https://openalex.org/W2003238696","https://openalex.org/W2392036275"],"abstract_inverted_index":{"Abstract":[0],"Large":[1],"optimal":[2],"transport":[3],"problems":[4,17],"can":[5],"be":[6],"approached":[7],"via":[8,73],"domain":[9,152],"decomposition,":[10],"i.e.":[11],"by":[12,71,100,116],"iteratively":[13],"solving":[14],"small":[15],"partial":[16],"independently":[18],"and":[19,36,40,114,158],"in":[20,33,56,85,159],"parallel.":[21],"Convergence":[22],"to":[23],"the":[24,34,83,86,105,109,117,120,126,148,151],"global":[25,136],"minimizers":[26],"under":[27],"suitable":[28],"assumptions":[29],"has":[30,44],"been":[31,45],"shown":[32],"unregularized":[35],"entropy":[37],"regularized":[38],"setting":[39],"its":[41,53],"computational":[42],"efficiency":[43,149],"demonstrated":[46],"experimentally.":[47],"An":[48],"accurate":[49],"theoretical":[50],"understanding":[51,70],"of":[52,82,88,96,119,125,150],"convergence":[54],"speed":[55],"geometric":[57],"settings":[58],"is":[59,98,111,138],"still":[60],"lacking.":[61],"In":[62],"this":[63],"article":[64],"we":[65],"work":[66],"towards":[67],"such":[68],"an":[69,79,130],"deriving,":[72],"$$\\varGamma":[74],"$$":[75],"<mml:math":[76],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u0393</mml:mi></mml:math>":[77],"-convergence,":[78],"asymptotic":[80],"description":[81],"algorithm":[84,154],"limit":[87,94,127],"infinitely":[89],"fine":[90],"partition":[91],"cells.":[92],"The":[93],"trajectory":[95],"couplings":[97],"described":[99],"a":[101],"continuity":[102],"equation":[103],"on":[104],"product":[106],"space":[107],"where":[108],"momentum":[110],"purely":[112],"horizontal":[113],"driven":[115],"gradient":[118],"cost":[121],"function.":[122],"Global":[123],"optimality":[124,137],"trajectories":[128],"remains":[129],"interesting":[131],"open":[132],"problem,":[133],"even":[134],"when":[135],"established":[139],"at":[140,155],"finite":[141,156],"scales.":[142],"Our":[143],"result":[144],"provides":[145],"insights":[146],"about":[147],"decomposition":[153],"resolutions":[157],"combination":[160],"with":[161],"coarse-to-fine":[162],"schemes.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}