{"id":"https://openalex.org/W7134820280","doi":"https://doi.org/10.48550/arxiv.2603.07768","title":"Weak Scalability of time parallel Schwarz methods for parabolic optimal control problems","display_name":"Weak Scalability of time parallel Schwarz methods for parabolic optimal control problems","publication_year":2026,"publication_date":"2026-03-08","ids":{"openalex":"https://openalex.org/W7134820280","doi":"https://doi.org/10.48550/arxiv.2603.07768"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.07768","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128641232","display_name":"Liu-Di Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Liu-Di","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017622445","display_name":"Tommaso Vanzan","orcid":"https://orcid.org/0000-0001-7554-4692"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vanzan, Tommaso","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.37895812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.4196000099182129,"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":0.4196000099182129,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.32100000977516174,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.06120000034570694,"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/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.659500002861023},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6107000112533569},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.5978999733924866},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5293999910354614},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.47350001335144043},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.446399986743927},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4401000142097473},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4237000048160553},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.41019999980926514}],"concepts":[{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.659500002861023},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6107000112533569},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.5978999733924866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5351999998092651},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5293999910354614},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.47350001335144043},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45969998836517334},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.446399986743927},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4401000142097473},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4237000048160553},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4171999990940094},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.41019999980926514},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40799999237060547},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.375900000333786},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.37040001153945923},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.36079999804496765},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3562999963760376},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3386000096797943},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.30880001187324524},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.299699991941452},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.26809999346733093},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.260699987411499}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.07768","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.07768","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.07768","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":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.07768","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Parabolic":[0],"optimal":[1,63],"control":[2,64],"problems":[3],"arise":[4],"in":[5],"numerous":[6],"scientific":[7],"and":[8,27,71,109,127,150,178],"engineering":[9],"applications.":[10],"They":[11],"typically":[12],"lead":[13],"to":[14,31,38,61,141],"large-scale":[15,190],"coupled":[16],"forward-backward":[17],"systems":[18],"that":[19],"cannot":[20],"be":[21],"treated":[22],"with":[23],"classical":[24],"time-stepping":[25],"schemes":[26],"are":[28,36],"computationally":[29],"expensive":[30],"solve.":[32],"Therefore,":[33],"parallel":[34,57,158],"methods":[35],"essential":[37],"reduce":[39],"the":[40,55,68,74,82,90,94,102,110,124,132,135,152,156,164,170,184],"computational":[41],"time":[42,50,56,85,138,157,174],"required.":[43],"In":[44],"this":[45,79],"work,":[46],"we":[47,97],"investigate":[48],"a":[49,105],"domain":[51,175],"decomposition":[52,176],"approach,":[53],"namely":[54],"Schwarz":[58,159],"method,":[59],"applied":[60],"parabolic":[62],"problems.":[65],"We":[66],"analyze":[67],"convergence":[69],"behavior":[70],"focus":[72],"on":[73,123,183,192],"weak":[75,153,171],"scalability":[76,154,172],"property":[77],"of":[78,84,93,104,112,131,137,155,173,186],"method":[80],"as":[81,134],"number":[83,136],"intervals":[86,139],"increases.":[87],"To":[88],"characterize":[89],"spectral":[91,125],"radius":[92,126],"iteration":[95],"matrix,":[96],"present":[98],"two":[99],"analysis":[100],"techniques:":[101],"construction":[103],"tailored":[106],"matrix":[107,115],"norm":[108],"application":[111],"block":[113],"Toeplitz":[114],"theory.":[116],"Our":[117],"analyses":[118],"yield":[119],"both":[120],"nonasymptotic":[121],"bounds":[122],"an":[128],"asymptotic":[129],"characterization":[130],"eigenvalues":[133],"tends":[140],"infinity.":[142],"Numerical":[143],"experiments":[144],"further":[145],"confirm":[146],"our":[147,179,187],"theoretical":[148,166],"findings":[149],"demonstrate":[151],"method.":[160],"This":[161],"work":[162],"introduces":[163],"first":[165],"tool":[167],"for":[168,189],"analyzing":[169],"methods,":[177],"results":[180],"shed":[181],"light":[182],"suitability":[185],"algorithm":[188],"simulations":[191],"modern":[193],"high-performance":[194],"computing":[195],"architectures.":[196]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-03-11T00:00:00"}