{"id":"https://openalex.org/W1587829729","doi":"https://doi.org/10.1186/s40323-015-0021-0","title":"Component-based reduced basis for parametrized symmetric eigenproblems","display_name":"Component-based reduced basis for parametrized symmetric eigenproblems","publication_year":2015,"publication_date":"2015-05-22","ids":{"openalex":"https://openalex.org/W1587829729","doi":"https://doi.org/10.1186/s40323-015-0021-0","mag":"1587829729"},"language":"en","primary_location":{"id":"doi:10.1186/s40323-015-0021-0","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-015-0021-0","pdf_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-015-0021-0","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-015-0021-0","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048020076","display_name":"Sylvain Vallagh\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["CH","US"],"is_corresponding":true,"raw_author_name":"Sylvain Vallagh\u00e9","raw_affiliation_strings":["Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","Swiss Federal Institute of Technology in Lausanne, Station 8, 1015, Lausanne, Switzerland","Swiss Federal Institute of Technology in Lausanne, Lausanne, Switzerland","Massachusetts Institute of Technology, Cambridge MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Swiss Federal Institute of Technology in Lausanne, Station 8, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Swiss Federal Institute of Technology in Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007711406","display_name":"Phuong Huynh","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["CH","US"],"is_corresponding":false,"raw_author_name":"Phuong Huynh","raw_affiliation_strings":["Akselos, EPFL Innovation Park, 1015, Lausanne, Switzerland","Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","Massachusetts Institute of Technology, Cambridge MA, USA","Akselos, EPFL Innovation Park, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Akselos, EPFL Innovation Park, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Akselos, EPFL Innovation Park, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016607094","display_name":"David J. Knezevic","orcid":null},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["CH","US"],"is_corresponding":false,"raw_author_name":"David J Knezevic","raw_affiliation_strings":["Akselos, EPFL Innovation Park, 1015, Lausanne, Switzerland","Harvard University, 29 Oxford Street, 02138, Cambridge MA, USA","Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","Harvard University, Cambridge MA, USA","Akselos, EPFL Innovation Park, Lausanne, Switzerland","Massachusetts Institute of Technology, Cambridge MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Akselos, EPFL Innovation Park, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Harvard University, 29 Oxford Street, 02138, Cambridge MA, USA","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Harvard University, Cambridge MA, USA","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"Akselos, EPFL Innovation Park, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027774064","display_name":"Nguy\u1ec5n Kim L\u1ee3i","orcid":"https://orcid.org/0000-0002-3063-6910"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Loi Nguyen","raw_affiliation_strings":["Akselos, EPFL Innovation Park, 1015, Lausanne, Switzerland","Akselos, EPFL Innovation Park, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Akselos, EPFL Innovation Park, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Akselos, EPFL Innovation Park, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063350067","display_name":"Anthony T. Patera","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony T Patera","raw_affiliation_strings":["Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","Massachusetts Institute of Technology; ,; Cambridge MA USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, 77 Mass Ave, 02139, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology; ,; Cambridge MA USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048020076"],"corresponding_institution_ids":["https://openalex.org/I5124864","https://openalex.org/I63966007"],"apc_list":{"value":990,"currency":"GBP","value_usd":1214},"apc_paid":{"value":990,"currency":"GBP","value_usd":1214},"fwci":1.3598,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.78737334,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994000196456909,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7060593962669373},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6234749555587769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5870695114135742},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5819969177246094},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5646705627441406},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5304868817329407},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4659463167190552},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.42702215909957886},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.41070643067359924},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39059433341026306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3610791563987732},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14476656913757324},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14435958862304688},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07567217946052551}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7060593962669373},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6234749555587769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5870695114135742},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5819969177246094},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5646705627441406},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5304868817329407},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4659463167190552},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.42702215909957886},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.41070643067359924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39059433341026306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3610791563987732},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14476656913757324},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14435958862304688},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07567217946052551},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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:10.1186/s40323-015-0021-0","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-015-0021-0","pdf_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-015-0021-0","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04514213v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04514213","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://link.springer.com/article/10.1186/s40323-015-0021-0/fulltext.html","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1186/s40323-015-0021-0","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40323-015-0021-0","pdf_url":"https://amses-journal.springeropen.com/counter/pdf/10.1186/s40323-015-0021-0","source":{"id":"https://openalex.org/S3034486266","display_name":"Advanced Modeling and Simulation in Engineering Sciences","issn_l":"2213-7467","issn":["2213-7467"],"is_oa":true,"is_in_doaj":true,"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":"Advanced Modeling and Simulation in Engineering Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6098521345","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7123870309","display_name":null,"funder_award_id":"N00014-11-1-0713","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7836042352","display_name":null,"funder_award_id":"FA9550-09-1-0613","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320320998","display_name":"Kommission f\u00fcr Technologie und Innovation","ror":"https://ror.org/012y9zp98"},{"id":"https://openalex.org/F4320332423","display_name":"Deshpande Center for Technological Innovation, Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1587829729.pdf","grobid_xml":"https://content.openalex.org/works/W1587829729.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1505358753","https://openalex.org/W1554655007","https://openalex.org/W1597544196","https://openalex.org/W1642453465","https://openalex.org/W1680579736","https://openalex.org/W1863321137","https://openalex.org/W1973166496","https://openalex.org/W1976653974","https://openalex.org/W2011121645","https://openalex.org/W2011655084","https://openalex.org/W2017745440","https://openalex.org/W2026734498","https://openalex.org/W2031841233","https://openalex.org/W2052690618","https://openalex.org/W2078950386","https://openalex.org/W2088232737","https://openalex.org/W2102333097","https://openalex.org/W2102753028","https://openalex.org/W2116237003","https://openalex.org/W2118357359","https://openalex.org/W2126028850","https://openalex.org/W2126087872","https://openalex.org/W2130712370","https://openalex.org/W2138543857","https://openalex.org/W2165347921","https://openalex.org/W2333269921","https://openalex.org/W2467346979","https://openalex.org/W2568618671","https://openalex.org/W3196541678","https://openalex.org/W6811789344"],"related_works":["https://openalex.org/W2146459776","https://openalex.org/W1975201729","https://openalex.org/W1980119950","https://openalex.org/W3092306907","https://openalex.org/W2089558316","https://openalex.org/W2055747065","https://openalex.org/W1990997111","https://openalex.org/W3099980414","https://openalex.org/W2364148186","https://openalex.org/W2046859099"],"abstract_inverted_index":{"A":[0],"component-based":[1],"approach":[2,98],"is":[3],"introduced":[4],"for":[5,121,131,171,246],"fast":[6],"and":[7,21,46,148,161,206,217,230],"flexible":[8],"solution":[9,75],"of":[10,64,76,124,134,185,195,220],"parameter-dependent":[11],"symmetric":[12,19],"eigenproblems.":[13],"Considering":[14],"a":[15,28,47,77,95,110,122,132,178,202,235],"generalized":[16],"eigenproblem":[17,31,71,170],"with":[18,51,99],"stiffness":[20,44,146],"mass":[22,49,151],"operators,":[23],"we":[24,84,127,157,207],"start":[25],"by":[26],"introducing":[27],"\u201c":[29,168],"\u03c3-shifted\u201d":[30,169],"where":[32],"the":[33,43,59,65,69,74,87,105,114,118,145,149,154,167,172,183,193,196,214],"left":[34],"hand":[35],"side":[36],"operator":[37,45,147],"corresponds":[38],"to":[39,73,108,141,165,181,192,212,226,234],"an":[40,252],"equilibrium":[41],"between":[42,144],"weighted":[48,150],"operator,":[50],"weight-parameter":[52],"\u03c3>0.":[53],"Assuming":[54],"that":[55,187],"\u03c3=\u03bb":[56],"n":[57],">0,":[58],"nth":[60],"real":[61],"positive":[62],"eigenvalue":[63,201],"original":[66,197],"eigenproblem,":[67],"then":[68,176],"shifted":[70],"reduces":[72],"homogeneous":[78],"linear":[79,135,138],"problem.":[80],"In":[81,117,153],"this":[82],"context,":[83],"can":[85],"apply":[86],"static":[88,163],"condensation":[89,164],"reduced":[90,100],"basis":[91,101],"element":[92],"(SCRBE)":[93],"method,":[94],"domain":[96],"synthesis":[97],"(RB)":[102],"approximation":[103],"at":[104,113],"intradomain":[106],"level":[107],"populate":[109],"Schur":[111],"complement":[112],"interdomain":[115],"level.":[116],"Offline":[119],"stage,":[120],"library":[123],"archetype":[125],"subdomains":[126,160],"train":[128],"RB":[129],"spaces":[130],"family":[133],"problems;":[136],"these":[137],"problems":[139],"correspond":[140],"various":[142,209],"equilibriums":[143],"operator.":[152],"Online":[155],"stage":[156],"assemble":[158],"instantiated":[159],"perform":[162,177],"obtain":[166,227],"full":[173],"system.":[174],"We":[175,199,223],"direct":[179],"search":[180],"find":[182],"values":[184],"\u03c3":[186],"yield":[188],"singular":[189],"systems,":[190],"corresponding":[191],"eigenvalues":[194],"eigenproblem.":[198],"provide":[200],"posteriori":[203],"error":[204],"estimators":[205],"present":[208],"numerical":[210],"results":[211],"demonstrate":[213],"accuracy,":[215],"flexibility":[216],"computational":[218],"efficiency":[219],"our":[221,242],"approach.":[222],"are":[224],"able":[225],"large":[228,247],"speed":[229],"memory":[231],"improvements":[232],"compared":[233],"classical":[236],"Finite":[237],"Element":[238],"Method":[239],"(FEM),":[240],"making":[241],"method":[243],"very":[244],"suitable":[245],"models":[248],"commonly":[249],"considered":[250],"in":[251],"engineering":[253],"context.":[254]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}