{"id":"https://openalex.org/W7204241386","doi":"https://doi.org/10.48550/arxiv.2608.23595","title":"Tensor-Train Isogeometric Analysis for Large-Scale Three-Dimensional Linear Elasticity","display_name":"Tensor-Train Isogeometric Analysis for Large-Scale Three-Dimensional Linear Elasticity","publication_year":2026,"publication_date":"2026-08-17","ids":{"openalex":"https://openalex.org/W7204241386","doi":"https://doi.org/10.48550/arxiv.2608.23595"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.23595","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23595","pdf_url":"https://arxiv.org/pdf/2608.23595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.23595","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135281298","display_name":"Quoc Thai Tran","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tran, Quoc Thai","raw_affiliation_strings":["Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006188151","display_name":"Duc P. Truong","orcid":"https://orcid.org/0000-0002-9806-3274","observed_orcids":["https://orcid.org/0000-0002-9806-3274"]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Truong, Duc P.","raw_affiliation_strings":["Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135183067","display_name":"William Dai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dai, William","raw_affiliation_strings":["Computational Physics Division , Los Alamos National Laboratory , Los Alamos , NM , USA","X"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Physics Division , Los Alamos National Laboratory , Los Alamos , NM , USA","institution_ids":["https://openalex.org/I1343871089"]},{"raw_affiliation_string":"X","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126148700","display_name":"Kim \u00d8 Rasmussen","orcid":"https://orcid.org/0000-0002-4029-4723","observed_orcids":["https://orcid.org/0000-0002-4029-4723"]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rasmussen, Kim \u00d8.","raw_affiliation_strings":["Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM , USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T12303","display_name":"Tensor decomposition and applications","score":0.649399995803833,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.649399995803833,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.2542000114917755,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.016899999231100082,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tensor-train-format","display_name":"tensor train format","score":0.7480000257492065},{"id":"https://openalex.org/keywords/isogeometric-analysis","display_name":"isogeometric analysis","score":0.9940000176429749},{"id":"https://openalex.org/keywords/three-dimensional-linear-elasticity","display_name":"three-dimensional linear elasticity","score":0.8669999837875366},{"id":"https://openalex.org/keywords/amen","display_name":"Amen","score":0.8349999785423279}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7353000044822693},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6449999809265137},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.6202999949455261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5440999865531921},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4993000030517578},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.4869999885559082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4555000066757202},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4343999922275543},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.40310001373291016},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.350600004196167},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34380000829696655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3433000147342682},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.31949999928474426},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.25529998540878296}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.23595","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23595","pdf_url":"https://arxiv.org/pdf/2608.23595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2608.23595","doi":"https://doi.org/10.48550/arxiv.2608.23595","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.23595","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.23595","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23595","pdf_url":"https://arxiv.org/pdf/2608.23595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1017065088","display_name":null,"funder_award_id":"#89233218CNA000001","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1279347439","display_name":null,"funder_award_id":"89233218CNA 000001","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G2356915424","display_name":null,"funder_award_id":"89233218CNA000001","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G6410514744","display_name":null,"funder_award_id":"89233218C-NA000001","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G6563880843","display_name":null,"funder_award_id":"No.  89233218CNA000001","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204241386.pdf","grobid_xml":"https://content.openalex.org/works/W7204241386.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2077817396","https://openalex.org/W7116062684","https://openalex.org/W7127433900","https://openalex.org/W7168146332"],"related_works":["https://openalex.org/W7129069470","https://openalex.org/W4414274442","https://openalex.org/W4406448981","https://openalex.org/W4387311093","https://openalex.org/W7136094934","https://openalex.org/W4390000416","https://openalex.org/W2025571216","https://openalex.org/W7097730412","https://openalex.org/W7162218374","https://openalex.org/W3135061116"],"abstract_inverted_index":{"This":[0],"work":[1],"develops":[2],"tensor-train":[3],"(TT)":[4],"formulations":[5,125],"for":[6,94,102,132],"solving":[7],"large-scale":[8,133],"three-dimensional":[9,134],"linear":[10],"elasticity":[11,61,135],"problems":[12],"discretized":[13],"by":[14],"isogeometric":[15],"analysis.":[16],"By":[17],"exploiting":[18],"the":[19,23,27,34,59,75,95,103],"tensor-product":[20],"structure":[21,29],"of":[22,30,111],"basis":[24],"functions":[25],"and":[26,41,69,114,129],"low-rank":[28],"geometry-dependent":[31],"coefficient":[32],"fields,":[33],"stiffness":[35],"operator,":[36,38],"mass":[37],"force":[39],"vector,":[40],"displacement":[42],"solution":[43,50],"are":[44,52],"represented":[45],"in":[46,57,73],"TT":[47,67,84,89],"format.":[48],"Two":[49],"strategies":[51],"investigated:":[53],"a":[54,70],"block-operator":[55],"formulation,":[56,72,97],"which":[58,74],"coupled":[60,77],"operator":[62],"is":[63,79,92,100],"stored":[64,80],"as":[65,81],"separated":[66],"blocks,":[68],"single-operator":[71,104],"full":[76],"system":[78],"one":[82],"monolithic":[83],"operator.":[85],"A":[86],"matrix-free":[87],"three-field":[88],"conjugate-gradient":[90],"solver":[91],"introduced":[93],"block":[96],"while":[98],"AMEn":[99],"used":[101],"formulation.":[105],"Numerical":[106],"examples":[107],"demonstrate":[108],"substantial":[109],"compression":[110],"both":[112],"operators":[113],"solutions":[115],"compared":[116],"with":[117],"conventional":[118],"sparse":[119],"full-grid":[120],"representations,":[121],"showing":[122],"that":[123],"TT-based":[124],"provide":[126],"an":[127],"efficient":[128],"scalable":[130],"approach":[131],"simulations.":[136]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-27T00:00:00"}
