{"id":"https://openalex.org/W2971127317","doi":"https://doi.org/10.1515/cmam-2018-0188","title":"Quasi-overlapping Semi-discrete Schwarz Waveform Relaxation Algorithms: The Hyperbolic Problem","display_name":"Quasi-overlapping Semi-discrete Schwarz Waveform Relaxation Algorithms: The Hyperbolic Problem","publication_year":2019,"publication_date":"2019-08-28","ids":{"openalex":"https://openalex.org/W2971127317","doi":"https://doi.org/10.1515/cmam-2018-0188","mag":"2971127317"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0188","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0188","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5033641370","display_name":"Mohammad Al-Khaleel","orcid":"https://orcid.org/0000-0001-6266-373X"},"institutions":[{"id":"https://openalex.org/I176601375","display_name":"Khalifa University of Science and Technology","ror":"https://ror.org/05hffr360","country_code":"AE","type":"education","lineage":["https://openalex.org/I176601375"]},{"id":"https://openalex.org/I85507684","display_name":"Yarmouk University","ror":"https://ror.org/004mbaj56","country_code":"JO","type":"education","lineage":["https://openalex.org/I85507684"]}],"countries":["AE","JO"],"is_corresponding":true,"raw_author_name":"Mohammad Al-Khaleel","raw_affiliation_strings":["Department of Applied Mathematics , Khalifa University , Abu Dhabi , United Arab Emirates ; and Department of Mathematics, Yarmouk University, Irbid, Jordan","Department of Mathematics, Yarmouk University, Irbid, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-6266-373X","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , Khalifa University , Abu Dhabi , United Arab Emirates ; and Department of Mathematics, Yarmouk University, Irbid, Jordan","institution_ids":["https://openalex.org/I176601375","https://openalex.org/I85507684"]},{"raw_affiliation_string":"Department of Mathematics, Yarmouk University, Irbid, Jordan","institution_ids":["https://openalex.org/I85507684"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102838305","display_name":"Shu\u2010Lin Wu","orcid":"https://orcid.org/0000-0002-4301-3018"},"institutions":[{"id":"https://openalex.org/I64852412","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23","country_code":"CN","type":"education","lineage":["https://openalex.org/I64852412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shu-Lin Wu","raw_affiliation_strings":["School of Science , Sichuan University of Science and Engineering , Zigong , Sichuan 643000 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science , Sichuan University of Science and Engineering , Zigong , Sichuan 643000 , P. R. China","institution_ids":["https://openalex.org/I64852412"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033641370"],"corresponding_institution_ids":["https://openalex.org/I176601375","https://openalex.org/I85507684"],"apc_list":null,"apc_paid":null,"fwci":0.7765,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70027133,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"3","first_page":"397","last_page":"417"},"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":0.9991999864578247,"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":0.9986000061035156,"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/discretization","display_name":"Discretization","score":0.8080361485481262},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6980356574058533},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6680967807769775},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5366244912147522},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48460066318511963},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.47669097781181335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43468159437179565},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4147988557815552},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3681112825870514},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1052914559841156}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8080361485481262},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6980356574058533},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6680967807769775},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5366244912147522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48460066318511963},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.47669097781181335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43468159437179565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4147988557815552},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3681112825870514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1052914559841156},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0188","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0188","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1589236075","https://openalex.org/W1602827292","https://openalex.org/W1843800166","https://openalex.org/W1971325652","https://openalex.org/W1975919514","https://openalex.org/W1984480729","https://openalex.org/W1987152170","https://openalex.org/W2007510482","https://openalex.org/W2025377524","https://openalex.org/W2044062963","https://openalex.org/W2055459591","https://openalex.org/W2089342568","https://openalex.org/W2098954480","https://openalex.org/W2129851503","https://openalex.org/W2130254387","https://openalex.org/W2137236532","https://openalex.org/W2321725241","https://openalex.org/W2896767755","https://openalex.org/W4235228724","https://openalex.org/W4241134520"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W1507702947","https://openalex.org/W2370926798"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Schwarz":[2],"waveform":[3],"relaxation":[4],"(SWR)":[5],"algorithms":[6,47,97,120,135,152,210],"have":[7],"many":[8],"favorable":[9],"properties":[10,84],"and":[11,15,36,102,114,176,196,211,218],"are":[12,71,198],"extensively":[13],"studied":[14],"investigated":[16],"for":[17],"solving":[18],"time":[19],"dependent":[20],"problems":[21,64,69],"mainly":[22],"at":[23,153],"a":[24,32,138,191],"continuous":[25,56],"level.":[26,156],"In":[27,157],"this":[28],"paper,":[29],"we":[30,37,163],"consider":[31],"semi-discrete":[33,45,95,118,155,160],"level":[34,161],"analysis":[35],"investigate":[38],"the":[39,55,62,67,77,83,86,92,133,149,154,158,166,170,173,177,183,204,208],"convergence":[40,141,184],"behavior":[41],"of":[42,54,76,85,207,215],"what":[43],"so-called":[44],"SWR":[46,87,96,119,151],"combined":[48],"with":[49,98,126,148],"discrete":[50,144],"transmission":[51,123,145],"conditions":[52,124,146],"instead":[53],"ones.":[57],"We":[58,89,109,130],"shall":[59],"target":[60],"here":[61],"hyperbolic":[63],"but":[65],"not":[66],"parabolic":[68],"that":[70,104,132,168],"usually":[72],"considered":[73],"by":[74],"most":[75],"researchers":[78],"in":[79,190,200],"general":[80],"when":[81],"investigating":[82],"methods.":[88],"first":[90],"present":[91],"classical":[93],"overlapping":[94,117],"different":[99,127],"partitioning":[100,128],"choices":[101],"show":[103,131],"they":[105],"converge":[106],"very":[107],"slow.":[108],"then":[110],"introduce":[111],"optimal,":[112],"optimized,":[113],"quasi":[115],"optimized":[116,150],"using":[121,143],"new":[122,134],"also":[125,164],"choices.":[129],"lead":[136],"to":[137,202],"much":[139],"better":[140,192],"through":[142],"associated":[147],"performed":[159],"analysis,":[162],"demonstrate":[165],"fact":[167],"as":[169],"ratio":[171],"between":[172],"overlap":[174],"size":[175,180],"spatial":[178],"discretization":[179],"gets":[181,186],"bigger,":[182],"factor":[185],"smaller":[187],"which":[188],"results":[189,195],"convergence.":[193],"Numerical":[194],"experiments":[197],"presented":[199],"order":[201],"confirm":[203],"theoretical":[205],"aspects":[206],"proposed":[209],"providing":[212],"an":[213],"evidence":[214],"their":[216,219],"usefulness":[217],"accuracy.":[220]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
