{"id":"https://openalex.org/W1877902382","doi":"https://doi.org/10.1007/978-3-642-35275-1_8","title":"A Two-Level Schwarz Preconditioner for Heterogeneous Problems","display_name":"A Two-Level Schwarz Preconditioner for Heterogeneous Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1877902382","doi":"https://doi.org/10.1007/978-3-642-35275-1_8","mag":"1877902382"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-35275-1_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-35275-1_8","pdf_url":null,"source":{"id":"https://openalex.org/S4210192791","display_name":"Lecture notes in computational science and engineering","issn_l":"1439-7358","issn":["1439-7358","2197-7100"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computational Science and Engineering","raw_type":"book-chapter"},"type":"book-chapter","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/A5024462955","display_name":"Victorita Dolean","orcid":"https://orcid.org/0000-0002-5885-1903"},"institutions":[{"id":"https://openalex.org/I4210112930","display_name":"Laboratoire Jean-Alexandre Dieudonn\u00e9","ror":"https://ror.org/0274zdr66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210112930","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"V. Dolean","raw_affiliation_strings":["Laboratoire J.A. Dieudonn\u00e9, CNRS UMR 6621, 06108, Nice Cedex 02, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire J.A. Dieudonn\u00e9, CNRS UMR 6621, 06108, Nice Cedex 02, France","institution_ids":["https://openalex.org/I4210112930","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107748698","display_name":"Fr\u00e9d\u00e9ric Nataf","orcid":"https://orcid.org/0000-0003-2813-3481"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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":"F. Nataf","raw_affiliation_strings":["Laboratoire J.L. Lions, CNRS UMR 7598, Universit\u00e9 Pierre et Marie Curie, 75005, Paris, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire J.L. Lions, CNRS UMR 7598, Universit\u00e9 Pierre et Marie Curie, 75005, Paris, France","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050544926","display_name":"Robert Scheichl","orcid":"https://orcid.org/0000-0001-8493-4393"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R. Scheichl","raw_affiliation_strings":["Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076520272","display_name":"Nicole Spillane","orcid":"https://orcid.org/0000-0001-5067-946X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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":"N. Spillane","raw_affiliation_strings":["Laboratoire J.L. Lions, CNRS UMR 7598, Universit\u00e9 Pierre et Marie Curie, 75005, Paris, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire J.L. Lions, CNRS UMR 7598, Universit\u00e9 Pierre et Marie Curie, 75005, Paris, France","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024462955"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210112930"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06445149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"87","last_page":"94"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9973000288009644,"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":0.9934999942779541,"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":0.9576088190078735},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.9516773223876953},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.8682250380516052},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7056868076324463},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.5918996930122375},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5824604034423828},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4941006004810333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4920598864555359},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4880448877811432},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42666682600975037},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41728144884109497},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4114757180213928},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.4041061997413635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3710974454879761},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35107967257499695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17540806531906128},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.09709426760673523},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08741745352745056},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.06386879086494446}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9576088190078735},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.9516773223876953},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.8682250380516052},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7056868076324463},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.5918996930122375},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5824604034423828},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4941006004810333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4920598864555359},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4880448877811432},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42666682600975037},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41728144884109497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4114757180213928},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4041061997413635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3710974454879761},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35107967257499695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17540806531906128},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.09709426760673523},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08741745352745056},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.06386879086494446},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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":4,"locations":[{"id":"doi:10.1007/978-3-642-35275-1_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-35275-1_8","pdf_url":null,"source":{"id":"https://openalex.org/S4210192791","display_name":"Lecture notes in computational science and engineering","issn_l":"1439-7358","issn":["1439-7358","2197-7100"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computational Science and Engineering","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.368.6750","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.368.6750","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.bath.ac.uk/~masrs/nataf_mini_1.pdf","raw_type":"text"},{"id":"pmh:oai:opus.bath.ac.uk:36482","is_oa":false,"landing_page_url":"http://opus.bath.ac.uk/36482/1/ScheichlLNCS2013_91c.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401631","display_name":"The University of Bath Online Publications Store (The University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Items"},{"id":"pmh:oai:purehost.bath.ac.uk:publications/05f085b5-2a79-4cb8-94ed-332fe609891f","is_oa":false,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/05f085b5-2a79-4cb8-94ed-332fe609891f","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1548589512","https://openalex.org/W1844813672","https://openalex.org/W1970588051","https://openalex.org/W1973633019","https://openalex.org/W1981142209","https://openalex.org/W2028989647","https://openalex.org/W2030373618","https://openalex.org/W2043368701","https://openalex.org/W2058751009","https://openalex.org/W2063829621","https://openalex.org/W2082804737","https://openalex.org/W2123816848","https://openalex.org/W2146683922","https://openalex.org/W2557433803"],"related_works":["https://openalex.org/W1986812736","https://openalex.org/W2902154408","https://openalex.org/W2963172443","https://openalex.org/W1623009832","https://openalex.org/W2471168230","https://openalex.org/W2773710110","https://openalex.org/W4229577910","https://openalex.org/W1554397852","https://openalex.org/W1877902382","https://openalex.org/W2940255121"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}