{"id":"https://openalex.org/W3037002849","doi":"https://doi.org/10.1137/20m1344913","title":"Combining Machine Learning and Adaptive Coarse Spaces---A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions","display_name":"Combining Machine Learning and Adaptive Coarse Spaces---A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3037002849","doi":"https://doi.org/10.1137/20m1344913","mag":"3037002849"},"language":"en","primary_location":{"id":"doi:10.1137/20m1344913","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1344913","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081654668","display_name":"Alexander Heinlein","orcid":"https://orcid.org/0000-0003-1578-8104"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Heinlein","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041978201","display_name":"Axel Klawonn","orcid":"https://orcid.org/0000-0003-4765-7387"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Axel Klawonn","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4765-7387","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033189715","display_name":"Martin Lanser","orcid":"https://orcid.org/0000-0002-4232-9395"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Lanser","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069751100","display_name":"Janine Weber","orcid":"https://orcid.org/0000-0002-6692-2230"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Janine Weber","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":1.7259,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.81297052,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"43","issue":"5","first_page":"S816","last_page":"S838"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9962999820709229,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/feti","display_name":"FETI","score":0.7114859223365784},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6372966766357422},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36058205366134644},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3386416435241699},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3209838271141052},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.3201419711112976}],"concepts":[{"id":"https://openalex.org/C171609451","wikidata":"https://www.wikidata.org/wiki/Q5425382","display_name":"FETI","level":4,"score":0.7114859223365784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6372966766357422},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36058205366134644},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3386416435241699},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3209838271141052},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.3201419711112976},{"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":3,"locations":[{"id":"doi:10.1137/20m1344913","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1344913","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:USBKOELN.ub.uni-koeln.de:56637","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400371","display_name":"K\u00f6lner Universit\u00e4ts PublikationsServer (Universit\u00e4t zu K\u00f6ln)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210115942","host_organization_name":"Rhenish Institute for Environmental Research","host_organization_lineage":["https://openalex.org/I4210115942"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"doc-type:article"},{"id":"pmh:oai:USBKOELN.ub.uni-koeln.de:11285","is_oa":false,"landing_page_url":"https://orcid.org/0000-0003-1578-8104>,","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Monograph"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1416659525","https://openalex.org/W1971812145","https://openalex.org/W1978592052","https://openalex.org/W1985085190","https://openalex.org/W2000867371","https://openalex.org/W2018655045","https://openalex.org/W2019221864","https://openalex.org/W2024179839","https://openalex.org/W2062446082","https://openalex.org/W2073527121","https://openalex.org/W2124087857","https://openalex.org/W2520892807","https://openalex.org/W2904048988","https://openalex.org/W2941348163","https://openalex.org/W2991451110","https://openalex.org/W3138259231"],"related_works":["https://openalex.org/W2091647599","https://openalex.org/W2008273138","https://openalex.org/W2063806054","https://openalex.org/W2019221864","https://openalex.org/W1798387320","https://openalex.org/W2092836554","https://openalex.org/W2409928099","https://openalex.org/W1553775038","https://openalex.org/W2404765580","https://openalex.org/W2070319852"],"abstract_inverted_index":{"The":[0,60],"hybrid":[1],"ML-FETI-DP":[2,63,111],"algorithm":[3,112],"combines":[4],"the":[5,46,67,92,107,110,132,150,179,183,190],"advantages":[6],"of":[7,26,50,62,91,149,172,182,189],"adaptive":[8,93],"coarse":[9,22],"spa-ces":[10],"in":[11,178],"domain":[12,29],"decomposition":[13,30],"methods":[14],"and":[15,48,73,141,159,199],"certain":[16],"supervised":[17],"machine":[18,151],"learning":[19,152],"techniques.":[20],"Adaptive":[21],"spaces":[23],"ensure":[24,146],"robustness":[25,90],"highly":[27,34],"scalable":[28],"solvers,":[31],"even":[32],"for":[33,131,156],"heterogeneous":[35],"coefficient":[36,40,68,165],"distributions":[37,166],"with":[38,163],"arbitrary":[39],"jumps.":[41],"However,":[42],"their":[43],"construction":[44],"requires":[45,119],"setup":[47],"solution":[49],"local":[51],"generalized":[52],"eigenvalue":[53,77,173,191],"problems,":[54],"which":[55,118],"is":[56,64,113],"typically":[57],"compu-tationally":[58],"expensive.":[59],"idea":[61],"to":[65,80,115,126,145],"interpret":[66],"distribution":[69],"as":[70,103,135,137],"image":[71,104],"data":[72,123,130,143],"predict":[74],"whether":[75],"an":[76],"problem":[78],"has":[79],"be":[81,85,176,194],"solved":[82],"or":[83],"can":[84,175,193],"neglected":[86],"while":[87],"still":[88],"maintaining":[89],"FETI-DP":[94],"method.":[95],"For":[96],"this":[97],"purpose,":[98],"neural":[99,133],"networks":[100],"are":[101],"used":[102],"classifiers.":[105],"In":[106],"present":[108],"work,":[109],"extended":[114],"three":[116],"di-mensions,":[117],"both":[120],"a":[121,138,169],"complex":[122],"preprocessing":[124],"procedure":[125],"construct":[127],"consistent":[128],"input":[129],"network":[134],"well":[136],"representative":[139],"training":[140],"validation":[142],"set":[144,197],"generalization":[147],"properties":[148],"model.":[153],"Numerical":[154],"experiments":[155],"stationary":[157],"dif-fusion":[158],"linear":[160],"elasticity":[161],"problems":[162,174,192],"realistic":[164],"show":[167],"that":[168],"large":[170],"number":[171],"saved;":[177],"best":[180],"case":[181],"numerical":[184],"results":[185],"presented":[186],"here,":[187],"97\\\\%":[188],"avoided":[195],"being":[196],"up":[198],"solved.":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
