{"id":"https://openalex.org/W2097286932","doi":"https://doi.org/10.1137/s0036142997323983","title":"Multiplicative Schwarz Algorithms for the Galerkin Boundary Element Method","display_name":"Multiplicative Schwarz Algorithms for the Galerkin Boundary Element Method","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2097286932","doi":"https://doi.org/10.1137/s0036142997323983","mag":"2097286932"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142997323983","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997323983","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/A5080507530","display_name":"Matthias Maischak","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Matthias Maischak.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080759662","display_name":"Ernst P. Stephan","orcid":"https://orcid.org/0000-0002-4069-6263"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ernst P. Stephan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052916984","display_name":"Thanh Tran","orcid":"https://orcid.org/0000-0001-6117-4811"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thanh Tran","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080507530"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6583,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.83681319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"38","issue":"4","first_page":"1243","last_page":"1268"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9997000098228455,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8875174522399902},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.8708956837654114},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.8461039662361145},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7629008293151855},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.721198558807373},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.6791795492172241},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.5990827679634094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49706724286079407},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.49346983432769775},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.47710758447647095},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4217478632926941},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4117470979690552},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.39960503578186035},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3575555086135864},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.29952502250671387}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8875174522399902},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.8708956837654114},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.8461039662361145},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7629008293151855},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.721198558807373},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.6791795492172241},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.5990827679634094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49706724286079407},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49346983432769775},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.47710758447647095},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4217478632926941},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4117470979690552},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.39960503578186035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3575555086135864},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.29952502250671387},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142997323983","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997323983","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.45.3586","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.3586","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.ifam.uni-hannover.de/pub/preprints/ifam29.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W151675190","https://openalex.org/W1521303164","https://openalex.org/W1973685600","https://openalex.org/W1994843419","https://openalex.org/W2015836100","https://openalex.org/W2017085690","https://openalex.org/W2019517543","https://openalex.org/W2043347951","https://openalex.org/W2049977563","https://openalex.org/W2071196586","https://openalex.org/W2073805195","https://openalex.org/W4238641148"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W2028890215","https://openalex.org/W2159100661","https://openalex.org/W2000290814","https://openalex.org/W3839471","https://openalex.org/W2339825459","https://openalex.org/W2138840323","https://openalex.org/W1994696552","https://openalex.org/W1515964003","https://openalex.org/W2367747968"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,7,10,26,36,40,50,53,57,62,67,85,88],"multiplicative":[3,41],"Schwarz":[4,42],"method":[5,15],"for":[6,16,49,52,61,83],"h-":[8],"and":[9,19,56,87],"p-version":[11,63,89],"Galerkin":[12],"boundary":[13],"element":[14],"a":[17,20],"hypersingular":[18],"weakly":[21],"singular":[22],"integral":[23,31],"equation":[24],"of":[25,39],"first":[27],"kind.":[28],"For":[29],"both":[30,84],"equations":[32],"we":[33,64],"prove":[34],"that":[35,66],"contraction":[37,68],"rate":[38,69],"operator":[43],"is":[44],"strictly":[45],"less":[46],"than":[47],"1":[48],"h-version":[51,86],"two":[54],"level":[55],"multilevel":[58],"methods,":[59],"whereas":[60],"show":[65],"approaches":[70],"one":[71],"only":[72],"logarithmically":[73],"in":[74],"p":[75],"forthe":[76],"2-level":[77],"method.":[78],"Computational":[79],"results":[80],"are":[81],"presented":[82],"which":[90],"support":[91],"our":[92],"theory.":[93]},"counts_by_year":[{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
