{"id":"https://openalex.org/W2785206729","doi":"https://doi.org/10.1137/16m1088302","title":"A Two-Level Overlapping Hybrid Domain Decomposition Method for Eigenvalue Problems","display_name":"A Two-Level Overlapping Hybrid Domain Decomposition Method for Eigenvalue Problems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2785206729","doi":"https://doi.org/10.1137/16m1088302","mag":"2785206729"},"language":"en","primary_location":{"id":"doi:10.1137/16m1088302","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1088302","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5048097042","display_name":"Wei Wang","orcid":"https://orcid.org/0000-0002-7483-4310"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wei Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100742189","display_name":"Xuejun Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuejun Xu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048097042"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8107,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.67868422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"1","first_page":"344","last_page":"368"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983000159263611,"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/preconditioner","display_name":"Preconditioner","score":0.8660433888435364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8571704626083374},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7601463794708252},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6944022178649902},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5708038210868835},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5230863094329834},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46584829688072205},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45415323972702026},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37772852182388306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37127333879470825},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3293308615684509},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1591169536113739},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.1244732141494751},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06692144274711609}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8660433888435364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8571704626083374},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7601463794708252},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6944022178649902},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5708038210868835},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5230863094329834},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46584829688072205},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45415323972702026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37772852182388306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37127333879470825},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3293308615684509},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1591169536113739},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.1244732141494751},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06692144274711609},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1088302","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1088302","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5803754804","display_name":null,"funder_award_id":"11671302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1977937121","https://openalex.org/W1981792545","https://openalex.org/W2041568728","https://openalex.org/W2049096219","https://openalex.org/W2051389949","https://openalex.org/W2072267808","https://openalex.org/W2083177745","https://openalex.org/W2084073638","https://openalex.org/W2104715457","https://openalex.org/W2140581820","https://openalex.org/W2146553400","https://openalex.org/W2151718183","https://openalex.org/W4211134967"],"related_works":["https://openalex.org/W4229577910","https://openalex.org/W2800324324","https://openalex.org/W2640255794","https://openalex.org/W2791597622","https://openalex.org/W2743060302","https://openalex.org/W2054089597","https://openalex.org/W2117656216","https://openalex.org/W2026707481","https://openalex.org/W2626358056","https://openalex.org/W1480631731"],"abstract_inverted_index":{"In":[0,21],"this":[1],"paper,":[2],"we":[3,35,55,113],"present":[4],"a":[5,37,65],"two-level":[6],"overlapping":[7,82],"hybrid":[8],"domain":[9],"decomposition":[10],"method":[11],"for":[12,40],"solving":[13],"the":[14,25,28,33,41,57,69,74,81,85,94,96,100,102,111],"large":[15],"scale":[16],"discrete":[17],"elliptic":[18],"eigenvalue":[19,42],"problems.":[20],"order":[22],"to":[23],"eliminate":[24],"components":[26],"in":[27,44,52,110],"orthogonal":[29],"complement":[30],"space":[31,50],"of":[32,68,76,98],"eigenspace,":[34],"construct":[36],"parallel":[38],"preconditioner":[39],"problem":[43],"fine":[45],"space.":[46],"After":[47],"one":[48],"coarse":[49],"correction":[51],"each":[53],"iteration,":[54],"get":[56],"error":[58],"reduction":[59],"as":[60,90],"$\\gamma=c(1-C\\frac{\\delta}{H})$,":[61],"where":[62],"$C$":[63],"is":[64,80],"constant":[66],"independent":[67],"mesh":[70],"size":[71,83],"$h$":[72],"and":[73,87,121],"diameter":[75],"subdomains":[77],"$H$,":[78],"$\\delta$":[79],"among":[84],"subdomains,":[86,99],"$c\\rightarrow1$":[88],"decreasingly":[89],"$H\\rightarrow0$,":[91],"which":[92],"means":[93],"greater":[95],"number":[97],"better":[101],"convergence":[103],"rate.":[104],"Different":[105],"from":[106],"other":[107],"numerical":[108],"algorithms":[109],"literature,":[112],"do":[114],"not":[115],"need":[116],"any":[117],"assumptions":[118],"between":[119],"$H$":[120],"$h$.":[122],"Numerical":[123],"results":[124],"supporting":[125],"our":[126],"theory":[127],"are":[128],"given.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
