{"id":"https://openalex.org/W3086608294","doi":"https://doi.org/10.1080/00207160.2020.1822995","title":"Parallel multiplicative Schwarz preconditioner for solving nonselfadjoint elliptic problems","display_name":"Parallel multiplicative Schwarz preconditioner for solving nonselfadjoint elliptic problems","publication_year":2020,"publication_date":"2020-09-14","ids":{"openalex":"https://openalex.org/W3086608294","doi":"https://doi.org/10.1080/00207160.2020.1822995","mag":"3086608294"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2020.1822995","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1822995","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5065128034","display_name":"Ruyi Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166499","display_name":"Henan Polytechnic University","ror":"https://ror.org/05vr1c885","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruyi Zhang","raw_affiliation_strings":["School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, People's Republic of China","institution_ids":["https://openalex.org/I4210166499"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021044782","display_name":"Shishun Li","orcid":"https://orcid.org/0000-0003-2163-9949"},"institutions":[{"id":"https://openalex.org/I4210166499","display_name":"Henan Polytechnic University","ror":"https://ror.org/05vr1c885","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166499"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shishun Li","raw_affiliation_strings":["School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, People's Republic of China","institution_ids":["https://openalex.org/I4210166499"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021044782"],"corresponding_institution_ids":["https://openalex.org/I4210166499"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11180963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"98","issue":"7","first_page":"1438","last_page":"1456"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9987000226974487,"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/preconditioner","display_name":"Preconditioner","score":0.908581018447876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.853904664516449},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.7993590831756592},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.6073354482650757},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.5808311104774475},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5806818008422852},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.56195467710495},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.517512321472168},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5097240805625916},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.4569237232208252},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.45302316546440125},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4374582767486572},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.40391790866851807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3098786473274231},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2562773823738098},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.18728244304656982}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.908581018447876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.853904664516449},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.7993590831756592},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.6073354482650757},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.5808311104774475},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5806818008422852},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.56195467710495},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.517512321472168},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5097240805625916},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.4569237232208252},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.45302316546440125},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4374582767486572},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.40391790866851807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3098786473274231},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2562773823738098},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.18728244304656982},{"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":1,"locations":[{"id":"doi:10.1080/00207160.2020.1822995","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1822995","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3494512700","display_name":null,"funder_award_id":"11701133,11726636","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1540854488","https://openalex.org/W1542243431","https://openalex.org/W1548589512","https://openalex.org/W1663177495","https://openalex.org/W1972644818","https://openalex.org/W1973685600","https://openalex.org/W1976057809","https://openalex.org/W1982701660","https://openalex.org/W1987132801","https://openalex.org/W1990671420","https://openalex.org/W1994206948","https://openalex.org/W1994696552","https://openalex.org/W1996147937","https://openalex.org/W2000290814","https://openalex.org/W2002102128","https://openalex.org/W2008322386","https://openalex.org/W2017085690","https://openalex.org/W2024949119","https://openalex.org/W2038619333","https://openalex.org/W2042771459","https://openalex.org/W2068395392","https://openalex.org/W2069087527","https://openalex.org/W2075229508","https://openalex.org/W2102136117","https://openalex.org/W2134819391","https://openalex.org/W2144616338","https://openalex.org/W2145968530","https://openalex.org/W2153455611","https://openalex.org/W2200436481","https://openalex.org/W2268965494","https://openalex.org/W2275142897","https://openalex.org/W2327425776","https://openalex.org/W2398367109","https://openalex.org/W2741486118","https://openalex.org/W2792401343","https://openalex.org/W2890215791","https://openalex.org/W3099120071","https://openalex.org/W4241481980"],"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":{"In":[0,23],"this":[1],"paper,":[2],"a":[3,12,33,48,53,58],"new":[4,59],"multiplicative":[5,135],"Schwarz":[6,30,73,90,136],"method":[7,31,129],"is":[8,39,130],"presented":[9],"for":[10,84,138],"solving":[11,139],"system":[13],"arising":[14],"from":[15],"the":[16,19,24,28,42,63,69,72,79,85,88,96,100,114,127,133,140],"discretization":[17],"of":[18,87,95,102,118],"nonselfadjoint":[20],"elliptic":[21],"equations.":[22,142],"implementation,":[25],"we":[26,61],"apply":[27],"proposed":[29,128],"as":[32],"Field-of-Value":[34],"(FOV)":[35],"equivalent":[36],"preconditioner":[37],"which":[38],"accelerated":[40],"with":[41,132],"GMRES":[43],"iterative":[44],"solver.":[45],"By":[46],"employing":[47],"strengthened":[49],"Cauchy\u2013Schwarz":[50],"inequality":[51],"and":[52,81,104,120],"stable":[54],"multilevel":[55],"decomposition":[56],"under":[57],"norm,":[60],"obtain":[62],"optimal":[64],"convergence":[65],"theory":[66,115],"by":[67],"choosing":[68],"parameters":[70],"in":[71,116],"operator":[74,91],"appropriately.":[75],"It":[76],"shows":[77],"that":[78,126],"lower":[80],"upper":[82],"bounds":[83],"spectrum":[86],"preconditioned":[89],"are":[92,110],"bounded":[93],"independently":[94],"fine":[97],"mesh":[98,105],"size,":[99],"number":[101],"subdomains":[103],"levels.":[106],"Some":[107],"numerical":[108,123],"results":[109],"reported":[111],"to":[112],"verify":[113],"terms":[117],"optimality":[119],"scalability.":[121],"Moreover,":[122],"comparisons":[124],"show":[125],"competitive":[131],"classical":[134],"algorithm":[137],"convection\u2013diffusion":[141]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
