{"id":"https://openalex.org/W1980588520","doi":"https://doi.org/10.1137/0914014","title":"An Optimal Two-Level Overlapping Domain Decomposition Method for Elliptic Problems in Two and Three Dimensions","display_name":"An Optimal Two-Level Overlapping Domain Decomposition Method for Elliptic Problems in Two and Three Dimensions","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W1980588520","doi":"https://doi.org/10.1137/0914014","mag":"1980588520"},"language":"en","primary_location":{"id":"doi:10.1137/0914014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914014","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/A5006367748","display_name":"Xiao\u2010Chuan Cai","orcid":"https://orcid.org/0000-0003-0296-8640"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiao-Chuan Cai","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006367748"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0426,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.83947705,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"1","first_page":"239","last_page":"247"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.9145957231521606},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.9109700918197632},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8659968376159668},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7852752804756165},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.7022985816001892},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6193323135375977},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5453604459762573},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5433545708656311},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.47909122705459595},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4779229760169983},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.461811900138855},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.46112722158432007},{"id":"https://openalex.org/keywords/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.4122428894042969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2907102406024933},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24228808283805847},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21229103207588196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07446125149726868}],"concepts":[{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.9145957231521606},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.9109700918197632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8659968376159668},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7852752804756165},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.7022985816001892},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6193323135375977},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5453604459762573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5433545708656311},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.47909122705459595},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4779229760169983},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.461811900138855},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.46112722158432007},{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.4122428894042969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2907102406024933},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24228808283805847},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21229103207588196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07446125149726868},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0914014","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914014","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1973685600","https://openalex.org/W1985117360","https://openalex.org/W1994696552","https://openalex.org/W2024949119","https://openalex.org/W2033653234","https://openalex.org/W2068395392","https://openalex.org/W2075609158","https://openalex.org/W2140153041"],"related_works":["https://openalex.org/W1986812736","https://openalex.org/W2963172443","https://openalex.org/W1623009832","https://openalex.org/W2471168230","https://openalex.org/W2773710110","https://openalex.org/W4301963091","https://openalex.org/W2050028993","https://openalex.org/W1968940950","https://openalex.org/W3010792445","https://openalex.org/W2963172444"],"abstract_inverted_index":{"The":[0,76],"solution":[1],"of":[2,5,30,44,88,105,109,116],"linear":[3,86],"systems":[4],"algebraic":[6],"equations":[7,89],"that":[8,23,94,102],"arise":[9],"from":[10],"elliptic":[11,74],"finite":[12],"element":[13],"problems":[14],"is":[15,37,57,79,92,97,107,136],"considered.":[16],"A":[17,125],"two-level":[18],"overlapping":[19],"domain":[20],"decomposition":[21],"method":[22,40,78],"can":[24],"be":[25],"viewed":[26],"as":[27],"a":[28],"combination":[29],"the":[31,42,45,52,61,83,95,100,103,110,114,129],"additive":[32,53,130],"and":[33,56,65,90,113,122,131],"multiplicative":[34,62,132],"Schwarz":[35,54,63,133],"methods":[36],"studied.":[38],"This":[39],"combines":[41],"advantages":[43],"two":[46],"methods.":[47],"It":[48],"converges":[49],"faster":[50],"than":[51,60],"algorithm":[55,96],"more":[58],"parallelizable":[59],"algorithm,":[64],"works":[66],"for":[67],"general,":[68],"not":[69],"necessarily":[70],"self-adjoint,":[71],"linear,":[72],"second-order,":[73],"equations.":[75],"GMRES":[77,135],"used":[80],"to":[81],"solve":[82],"resulting":[84],"preconditioned":[85,134],"system":[87],"it":[91],"shown":[93],"optimal":[98],"in":[99,118],"sense":[101],"rate":[104],"convergence":[106],"independent":[108],"mesh":[111],"size":[112],"number":[115],"subregions":[117],"both":[119],"$R^2":[120],"$":[121],"$R^3":[123],"$.":[124],"numerical":[126],"comparison":[127],"with":[128],"reported.":[137]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}