{"id":"https://openalex.org/W2007510482","doi":"https://doi.org/10.1137/050642137","title":"Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems","display_name":"Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2007510482","doi":"https://doi.org/10.1137/050642137","mag":"2007510482"},"language":"en","primary_location":{"id":"doi:10.1137/050642137","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050642137","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":true,"oa_status":"green","oa_url":"https://archive-ouverte.unige.ch/unige:6273","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. J. Gander","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113857548","display_name":"Laurence Halpern","orcid":"https://orcid.org/0000-0002-7877-7130"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Halpern","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089456729"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.5938,"has_fulltext":false,"cited_by_count":186,"citation_normalized_percentile":{"value":0.99026579,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"45","issue":"2","first_page":"666","last_page":"697"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.7929221987724304},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.7368735074996948},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6887686252593994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6712551116943359},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.6201054453849792},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5944308042526245},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5900688767433167},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5437676906585693},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.45061081647872925},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4467158019542694},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4373369812965393},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38316810131073},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3726104497909546},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3224124312400818},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31922727823257446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25406718254089355}],"concepts":[{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.7929221987724304},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.7368735074996948},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6887686252593994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6712551116943359},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.6201054453849792},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5944308042526245},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5900688767433167},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5437676906585693},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45061081647872925},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4467158019542694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4373369812965393},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38316810131073},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3726104497909546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3224124312400818},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31922727823257446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25406718254089355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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":"doi:10.1137/050642137","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050642137","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:unige.ch:aou:unige:6273","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:6273","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: 0036-1429","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:unige.ch:aou:unige:6273","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:6273","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: 0036-1429","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1501940787","https://openalex.org/W1532580938","https://openalex.org/W1589236075","https://openalex.org/W1594563152","https://openalex.org/W1964039844","https://openalex.org/W1965273420","https://openalex.org/W1970955975","https://openalex.org/W1985576945","https://openalex.org/W1987455271","https://openalex.org/W1994206948","https://openalex.org/W1998789711","https://openalex.org/W2001819970","https://openalex.org/W2009949889","https://openalex.org/W2020633626","https://openalex.org/W2023344463","https://openalex.org/W2025377524","https://openalex.org/W2026688642","https://openalex.org/W2033447735","https://openalex.org/W2036597275","https://openalex.org/W2064643401","https://openalex.org/W2078641415","https://openalex.org/W2096847169","https://openalex.org/W2099857391","https://openalex.org/W2112930934","https://openalex.org/W2140323003","https://openalex.org/W2142578979","https://openalex.org/W2171622994","https://openalex.org/W2503240363","https://openalex.org/W2886312243","https://openalex.org/W4254519656"],"related_works":["https://openalex.org/W1974895211","https://openalex.org/W2176409448","https://openalex.org/W2129841057","https://openalex.org/W3040712279","https://openalex.org/W2364769705","https://openalex.org/W4367555392","https://openalex.org/W2374664672","https://openalex.org/W2056136368","https://openalex.org/W2999616507","https://openalex.org/W4226416379"],"abstract_inverted_index":{"We":[0,31,99,117,134],"study":[1],"in":[2,104],"this":[3,105],"paper":[4],"a":[5,41,72],"new":[6,121],"class":[7,73,106],"of":[8,15,22,26,48,74,78,111],"waveform":[9,50,114],"relaxation":[10,51,115],"algorithms":[11],"for":[12],"large":[13],"systems":[14],"ordinary":[16],"differential":[17,24],"equations":[18,25],"arising":[19],"from":[20],"discretizations":[21],"partial":[23],"advection":[27],"reaction":[28],"diffusion":[29],"type.":[30],"show":[32,118],"that":[33,119],"the":[34,38,45,49,83,91,95,101,108,112,120,131],"transmission":[35,56,64,76,97,102],"conditions":[36,57,65,77,103],"between":[37],"subsystems":[39],"have":[40],"tremendous":[42],"influence":[43],"on":[44],"convergence":[46],"speed":[47],"algorithms,":[52],"and":[53,86,126],"we":[54,70],"identify":[55],"with":[58,107,138],"optimal":[59,63,84],"performance.":[60],"Since":[61],"these":[62],"are":[66],"expensive":[67],"to":[68],"use,":[69],"introduce":[71],"local":[75],"Robin":[79],"type,":[80],"which":[81],"approximate":[82],"ones":[85],"can":[87],"be":[88],"used":[89],"at":[90],"same":[92],"cost":[93],"as":[94],"classical":[96,132],"conditions.":[98],"determine":[100],"best":[109],"performance":[110],"associated":[113],"algorithm.":[116],"algorithm":[122],"is":[123],"well":[124],"posed":[125],"converges":[127],"much":[128],"faster":[129],"than":[130],"one.":[133],"illustrate":[135],"our":[136],"analysis":[137],"numerical":[139],"experiments.":[140]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":6}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}