{"id":"https://openalex.org/W3012795662","doi":"https://doi.org/10.1007/s10915-021-01631-8","title":"Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems","display_name":"Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems","publication_year":2020,"publication_date":"2020-03-20","ids":{"openalex":"https://openalex.org/W3012795662","doi":"https://doi.org/10.1007/s10915-021-01631-8","mag":"3012795662"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2003.09251","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.09251","pdf_url":"https://arxiv.org/pdf/2003.09251","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.09251","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010218507","display_name":"Marcella Bonazzoli","orcid":"https://orcid.org/0000-0002-0284-5643"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bonazzoli, Marcella","raw_affiliation_strings":["Inversion of Differential Equations For Imaging and physiX","Shape reconstruction and identification"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inversion of Differential Equations For Imaging and physiX","institution_ids":[]},{"raw_affiliation_string":"Shape reconstruction and identification","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002742743","display_name":"Xavier Claeys","orcid":"https://orcid.org/0000-0003-0826-6244"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Claeys, Xavier","raw_affiliation_strings":["Algorithms and parallel tools for integrated numerical simulations","Laboratoire Jacques-Louis Lions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms and parallel tools for integrated numerical simulations","institution_ids":[]},{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Nataf, Fr\u00e9d\u00e9ric","orcid":null},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nataf, Fr\u00e9d\u00e9ric","raw_affiliation_strings":["Algorithms and parallel tools for integrated numerical simulations","Laboratoire Jacques-Louis Lions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms and parallel tools for integrated numerical simulations","institution_ids":[]},{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072648642","display_name":"Pierre-Henri Tournier","orcid":"https://orcid.org/0000-0002-7406-108X"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tournier, Pierre-Henri","raw_affiliation_strings":["Algorithms and parallel tools for integrated numerical simulations","Laboratoire Jacques-Louis Lions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithms and parallel tools for integrated numerical simulations","institution_ids":[]},{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8636000156402588,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8636000156402588,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.08959999680519104,"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":0.00989999994635582,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8890800476074219},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6896877884864807},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6605710983276367},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.557020902633667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5377545356750488},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4924648702144623},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.43124639987945557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3735243082046509},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3180564045906067},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19608688354492188},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14677393436431885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1412125825881958},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07970026135444641},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.05615738034248352},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.03859594464302063}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8890800476074219},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6896877884864807},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6605710983276367},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.557020902633667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5377545356750488},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4924648702144623},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.43124639987945557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3735243082046509},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3180564045906067},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19608688354492188},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14677393436431885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1412125825881958},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07970026135444641},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.05615738034248352},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.03859594464302063},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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":"pmh:oai:arXiv.org:2003.09251","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.09251","pdf_url":"https://arxiv.org/pdf/2003.09251","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-02513123v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02513123","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":"https://hal.archives-ouvertes.fr/hal-02513123","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.09251","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.09251","pdf_url":"https://arxiv.org/pdf/2003.09251","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W149522324","https://openalex.org/W1503942291","https://openalex.org/W1550543785","https://openalex.org/W1586623601","https://openalex.org/W1673309917","https://openalex.org/W1780245888","https://openalex.org/W1932034027","https://openalex.org/W1969745760","https://openalex.org/W1977061454","https://openalex.org/W1980584261","https://openalex.org/W2008215882","https://openalex.org/W2024949119","https://openalex.org/W2031804122","https://openalex.org/W2031887218","https://openalex.org/W2033447735","https://openalex.org/W2041523977","https://openalex.org/W2062246266","https://openalex.org/W2063228755","https://openalex.org/W2068395392","https://openalex.org/W2070232376","https://openalex.org/W2070299075","https://openalex.org/W2093672390","https://openalex.org/W2140323003","https://openalex.org/W2161243591","https://openalex.org/W2767278683","https://openalex.org/W2806526478","https://openalex.org/W2963726548","https://openalex.org/W3087680391","https://openalex.org/W3111536438"],"related_works":["https://openalex.org/W4229577910","https://openalex.org/W2800324324","https://openalex.org/W2640255794","https://openalex.org/W2026707481","https://openalex.org/W2743060302","https://openalex.org/W2054089597","https://openalex.org/W2117656216","https://openalex.org/W2626358056","https://openalex.org/W3047336714","https://openalex.org/W1480631731"],"abstract_inverted_index":{"We":[0,90],"analyze":[1],"the":[2,5,34,37,69,72,80,88,98,145,151,159],"convergence":[3],"of":[4,56,71,82,85,128,161],"one-level":[6],"overlapping":[7,136],"domain":[8,137],"decomposition":[9,138],"preconditioner":[10],"SORAS":[11],"(Symmetrized":[12],"Optimized":[13],"Restricted":[14],"Additive":[15],"Schwarz)":[16],"applied":[17],"to":[18,63,105],"a":[19,54,76,117,162],"generic":[20],"linear":[21],"system":[22],"whose":[23,120],"matrix":[24],"is":[25,95,102,167],"not":[26,103,114],"necessarily":[27],"symmetric/self-adjoint":[28],"nor":[29],"positive":[30],"definite.":[31],"By":[32],"generalizing":[33],"theory":[35,94],"for":[36,135,144,154],"Helmholtz":[38],"equation":[39,148,156],"developed":[40],"in":[41,97],"[I.G.":[42],"Graham,":[43],"E.A.":[44],"Spence,":[45],"and":[46,58,75],"J.":[47],"Zou,":[48],"SIAM":[49],"J.Numer.Anal.,":[50],"2020],":[51],"we":[52,131,157],"identify":[53],"list":[55],"assumptions":[57],"estimates":[59,134],"that":[60,92,100],"are":[61,122],"sufficient":[62],"obtain":[64],"an":[65,126],"upper":[66],"bound":[67,78],"on":[68,79,116],"norm":[70],"preconditioned":[73],"matrix,":[74],"lower":[77],"distance":[81],"its":[83],"field":[84],"values":[86],"from":[87],"origin.":[89],"stress":[91],"our":[93],"general":[96],"sense":[99],"it":[101,112],"specific":[104],"one":[106],"particular":[107],"boundary":[108],"value":[109],"problem.":[110],"Moreover,":[111],"does":[113],"rely":[115],"coarse":[118],"mesh":[119],"elements":[121],"sufficiently":[123],"small.":[124],"As":[125],"illustration":[127],"this":[129,155],"framework,":[130],"prove":[132,150],"new":[133],"methods":[139],"with":[140],"Robin-type":[141],"transmission":[142],"conditions":[143],"heterogeneous":[146],"reaction-convection-diffusion":[147],"(to":[149],"stability":[152],"assumption":[153],"consider":[158],"case":[160],"coercive":[163],"bilinear":[164],"form,":[165],"which":[166],"non-symmetric,":[168],"though).":[169]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}