{"id":"https://openalex.org/W2009575526","doi":"https://doi.org/10.1137/030601090","title":"Overlapping Schwarz Waveform Relaxation for Convection-Dominated Nonlinear Conservation Laws","display_name":"Overlapping Schwarz Waveform Relaxation for Convection-Dominated Nonlinear Conservation Laws","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2009575526","doi":"https://doi.org/10.1137/030601090","mag":"2009575526"},"language":"en","primary_location":{"id":"doi:10.1137/030601090","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601090","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://archive-ouverte.unige.ch/unige:6276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089456729","display_name":"Martin J. Gander","orcid":"https://orcid.org/0000-0001-8450-9223"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Martin J. Gander","raw_affiliation_strings":["Section de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, CH-1211 Gen\u00e8ve"],"affiliations":[{"raw_affiliation_string":"Section de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, CH-1211 Gen\u00e8ve","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101833555","display_name":"Christian Rohde","orcid":"https://orcid.org/0000-0001-9183-5094"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Rohde","raw_affiliation_strings":["Fakult\u00e1t f\u00fcr Mathmatik, Universit\u00e4t Bielefeld, D-33615 Bielefeld, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e1t f\u00fcr Mathmatik, Universit\u00e4t Bielefeld, D-33615 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089456729"],"corresponding_institution_ids":["https://openalex.org/I114457229"],"apc_list":null,"apc_paid":null,"fwci":2.9678,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.8983682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"2","first_page":"415","last_page":"439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9962999820709229,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9962999820709229,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8320033550262451},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.6247477531433105},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5896041989326477},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5731178522109985},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5681546926498413},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5438556671142578},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5200386047363281},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.498903751373291},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.4359460771083832},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41831398010253906},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08175486326217651}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8320033550262451},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6247477531433105},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5896041989326477},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5731178522109985},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5681546926498413},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5438556671142578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5200386047363281},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.498903751373291},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.4359460771083832},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41831398010253906},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08175486326217651},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/030601090","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030601090","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:unige.ch:unige:6276","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:6276","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 1064-8275","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.9940","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.9940","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.unige.ch/~gander/Preprints/3-60109.pdf","raw_type":"text"},{"id":"pmh:oai:freidok.uni-freiburg.de:57190","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/57190","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Preprint Fakult\u00e4t f\u00fcr Mathematik und Physik, Universit\u00e4t Freiburg. - 03-13 (2003)","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:unige.ch:unige:6276","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:6276","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 1064-8275","raw_type":"Text"},"sustainable_development_goals":[{"score":0.699999988079071,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1480366635","https://openalex.org/W1502454266","https://openalex.org/W1532580938","https://openalex.org/W1535819777","https://openalex.org/W1556837715","https://openalex.org/W1571871558","https://openalex.org/W1602967628","https://openalex.org/W1994206948","https://openalex.org/W1997561648","https://openalex.org/W1998789711","https://openalex.org/W2008515687","https://openalex.org/W2032588038","https://openalex.org/W2036597275","https://openalex.org/W2046409434","https://openalex.org/W2077891170","https://openalex.org/W2140323003","https://openalex.org/W2164832539","https://openalex.org/W2334095483","https://openalex.org/W2369386221","https://openalex.org/W2503240363","https://openalex.org/W2616478045","https://openalex.org/W2809233767","https://openalex.org/W4229588332","https://openalex.org/W4255388216","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1995118522","https://openalex.org/W64916076","https://openalex.org/W2090020940","https://openalex.org/W4364366001","https://openalex.org/W1072895066","https://openalex.org/W2565229889","https://openalex.org/W4213003931","https://openalex.org/W2383959235","https://openalex.org/W2061359299","https://openalex.org/W2023378125"],"abstract_inverted_index":{"We":[0,176],"analyze":[1],"the":[2,5,34,37,49,57,59,62,65,75,83,91,94,104,116,132,141,144,147,152,156,160,174],"convergence":[3,32,41,53,134,149,157],"of":[4,33,46,64,74,77,82,93],"overlapping":[6],"Schwarz":[7],"waveform":[8],"relaxation":[9],"algorithm":[10,35,95,117,161],"applied":[11],"to":[12,85,103,113],"convection-dominated":[13],"nonlinear":[14],"conservation":[15],"laws":[16],"in":[17,36,42,48,146,173],"one":[18],"spatial":[19],"dimension.":[20],"For":[21],"two":[22],"subdomains":[23,87],"and":[24,40,61,107,159],"bounded":[25,137],"time":[26,66,122,138],"intervals":[27,139],"we":[28,100],"prove":[29,114],"superlinear":[30,133],"asymptotic":[31],"parabolic":[38],"case":[39],"a":[43,80,97,109,169],"finite":[44],"number":[45,76],"steps":[47],"hyperbolic":[50],"limit.":[51],"The":[52],"results":[54,84,180],"depend":[55],"on":[56,136],"overlap,":[58],"viscosity,":[60],"length":[63],"interval":[67],"under":[68],"consideration,":[69],"but":[70],"they":[71],"are":[72],"independent":[73],"subdomains,":[78],"as":[79],"generalization":[81],"many":[86],"shows.":[88],"To":[89],"investigate":[90],"behavior":[92],"for":[96,131],"long":[98,121],"time,":[99],"apply":[101],"it":[102],"Burgers":[105],"equation":[106],"use":[108],"steady":[110],"state":[111],"argument":[112],"that":[115],"converges":[118],"linearly":[119],"over":[120],"intervals.":[123],"This":[124],"result":[125],"reveals":[126],"an":[127],"interesting":[128],"paradox:":[129],"while":[130],"rate":[135,158],"decreasing":[140,151],"viscosity":[142,153],"improves":[143],"performance,":[145],"linear":[148],"regime":[150],"slows":[154],"down":[155],"can":[162],"converge":[163],"arbitrarily":[164],"slowly,":[165],"if":[166],"there":[167],"is":[168],"standing":[170],"shock":[171],"wave":[172],"overlap.":[175],"illustrate":[177],"our":[178],"theoretical":[179],"with":[181],"numerical":[182],"experiments.":[183]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}