{"id":"https://openalex.org/W2083005122","doi":"https://doi.org/10.1137/110838868","title":"An Overlapping Schwarz Algorithm for Raviart--Thomas Vector Fields with Discontinuous Coefficients","display_name":"An Overlapping Schwarz Algorithm for Raviart--Thomas Vector Fields with Discontinuous Coefficients","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2083005122","doi":"https://doi.org/10.1137/110838868","mag":"2083005122"},"language":"en","primary_location":{"id":"doi:10.1137/110838868","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110838868","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/A5053538103","display_name":"Duk\u2010Soon Oh","orcid":"https://orcid.org/0000-0002-6583-0967"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Duk-Soon Oh","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053538103"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3666128,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.81645944,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"51","issue":"1","first_page":"297","last_page":"321"},"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":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8435423970222473},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.824228048324585},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7820590734481812},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.6974406838417053},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.67710942029953},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5100660920143127},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.47690367698669434},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46388110518455505},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.45475897192955017},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4515650272369385},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.45150506496429443},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4385569393634796},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.41185176372528076},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3579404950141907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.357311487197876},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3514421284198761},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27380242943763733},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.18488043546676636},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13497766852378845}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8435423970222473},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.824228048324585},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7820590734481812},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.6974406838417053},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.67710942029953},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5100660920143127},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.47690367698669434},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46388110518455505},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.45475897192955017},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4515650272369385},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.45150506496429443},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4385569393634796},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.41185176372528076},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3579404950141907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.357311487197876},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3514421284198761},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27380242943763733},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.18488043546676636},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13497766852378845},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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":1,"locations":[{"id":"doi:10.1137/110838868","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110838868","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8199999928474426,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W591292934","https://openalex.org/W1548589512","https://openalex.org/W1595782612","https://openalex.org/W1967011851","https://openalex.org/W1973656429","https://openalex.org/W1985506636","https://openalex.org/W1986442363","https://openalex.org/W1987095255","https://openalex.org/W1987132801","https://openalex.org/W1991556834","https://openalex.org/W1994934002","https://openalex.org/W2001104413","https://openalex.org/W2006000772","https://openalex.org/W2006895912","https://openalex.org/W2009985306","https://openalex.org/W2010804587","https://openalex.org/W2030879142","https://openalex.org/W2030947573","https://openalex.org/W2033986961","https://openalex.org/W2049754743","https://openalex.org/W2060349229","https://openalex.org/W2062618977","https://openalex.org/W2066886152","https://openalex.org/W2071704402","https://openalex.org/W2072816215","https://openalex.org/W2078783107","https://openalex.org/W2132292023","https://openalex.org/W2516406740","https://openalex.org/W2523642991","https://openalex.org/W3042562017"],"related_works":["https://openalex.org/W1986812736","https://openalex.org/W2963172443","https://openalex.org/W2471168230","https://openalex.org/W2773710110","https://openalex.org/W1968940950","https://openalex.org/W3010792445","https://openalex.org/W4301963091","https://openalex.org/W2963172444","https://openalex.org/W3083441863","https://openalex.org/W2077463666"],"abstract_inverted_index":{"Overlapping":[0],"Schwarz":[1,19],"methods":[2],"form":[3],"one":[4],"of":[5,9,32,43,66,72,91,98,122,132,143,149,154],"two":[6],"major":[7],"families":[8],"domain":[10],"decomposition":[11],"methods.":[12],"In":[13],"this":[14],"paper,":[15],"a":[16,67,81],"two-level":[17],"overlapping":[18,56],"method":[20,100],"for":[21],"Raviart--Thomas":[22],"vector":[23],"fields":[24],"is":[25,35,101,119,147],"developed":[26],"and":[27,47,125,127,135,152],"analyzed.":[28],"The":[29,58,95,141],"global":[30],"component":[31],"the":[33,48,73,89,92,120,123,130,133,136,144,150,155,158,161,167],"preconditioner":[34],"based":[36],"on":[37,55,88],"local":[38,49,52,93],"energy-minimizing":[39],"discrete":[40],"harmonic":[41],"extensions":[42],"coarse":[44],"interface":[45,159],"values,":[46],"components":[50],"use":[51],"direct":[53],"solvers":[54],"subdomains.":[57,162],"algorithm":[59],"can":[60],"be":[61,104],"implemented":[62],"algebraically":[63],"using":[64],"submatrices":[65],"fully":[68],"assembled":[69],"stiffness":[70],"matrix":[71],"entire":[74],"finite":[75],"element":[76],"problem.":[77],"Moreover,":[78],"it":[79],"gives":[80],"condition":[82,96,145],"number":[83,97,146],"bound":[84,142],"which":[85,165],"depends":[86],"only":[87],"size":[90],"subproblems.":[94],"our":[99],"shown":[102],"to":[103],"bounded":[105],"by":[106],"$C":[107],"(":[108,113],"1":[109,114],"+":[110,115],"\\log":[111],"(H/h))":[112],"H/\\delta)$,":[116],"where":[117],"$H$":[118],"diameter":[121],"subdomain":[124],"$h$":[126],"$\\delta$":[128],"are":[129,169],"sizes":[131],"elements":[134],"overlap":[137],"between":[138,160],"subdomains,":[139],"respectively.":[140],"independent":[148],"values":[151],"jumps":[153],"coefficients":[156],"across":[157],"Numerical":[163],"results,":[164],"support":[166],"theory,":[168],"also":[170],"presented.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"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"}