{"id":"https://openalex.org/W4231207954","doi":"https://doi.org/10.1137/17m1115885","title":"Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-sized Subdomains: Part II","display_name":"Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-sized Subdomains: Part II","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W4231207954","doi":"https://doi.org/10.1137/17m1115885"},"language":"en","primary_location":{"id":"doi:10.1137/17m1115885","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1115885","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/A5000105184","display_name":"Gabriele Ciaramella","orcid":"https://orcid.org/0000-0002-5877-4426"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. Ciaramella","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089456729","display_name":"Martin J. Gander","orcid":"https://orcid.org/0000-0001-8450-9223"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. J. Gander","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000105184"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7098,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.87028443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"56","issue":"3","first_page":"1498","last_page":"1524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994999766349792,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5991631150245667},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.49875783920288086},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.4737456738948822},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.4447230398654938},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4132130742073059},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.412461519241333},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3840141296386719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26231926679611206},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25499817728996277},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.19510582089424133},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.10621169209480286}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5991631150245667},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.49875783920288086},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.4737456738948822},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.4447230398654938},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4132130742073059},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.412461519241333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3840141296386719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26231926679611206},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25499817728996277},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.19510582089424133},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.10621169209480286}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1115885","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1115885","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:re.public.polimi.it:11311/1193306","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/1193306","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2870170964","display_name":null,"funder_award_id":"PASC-DIAPHANE","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7961577459","display_name":null,"funder_award_id":"20020_149107/1","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W303519302","https://openalex.org/W1977909180","https://openalex.org/W1989589317","https://openalex.org/W2005662217","https://openalex.org/W2028355475","https://openalex.org/W2054769800","https://openalex.org/W2055563809","https://openalex.org/W2058848030","https://openalex.org/W2083715576","https://openalex.org/W2095237903","https://openalex.org/W2130098961","https://openalex.org/W2171622994","https://openalex.org/W2398729377","https://openalex.org/W2619687587","https://openalex.org/W3098328051"],"related_works":["https://openalex.org/W1647103664","https://openalex.org/W2286395548","https://openalex.org/W2504287632","https://openalex.org/W2069946149","https://openalex.org/W3046643187","https://openalex.org/W1515964003","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2233890230","https://openalex.org/W132556536"],"abstract_inverted_index":{"According":[0],"to":[1,9,45,185,363],"classical":[2,47,364],"theory,":[3],"one":[4,120],"level":[5,121],"Schwarz":[6,122,176,336,358,365],"methods":[7],"applied":[8],"elliptic":[10,145],"problems":[11,136],"are":[12],"not":[13,125],"scalable":[14],"in":[15,53,113,255,300,338,360],"general":[16,321],"[A.":[17],"Toselli":[18],"and":[19,58,84,101,193,219,236,258],"O.":[20],"Widlund,":[21],"Springer":[22],"Ser.":[23],"Comput.":[24],"Math.,":[25],"34,":[26],"Springer,":[27],"New":[28],"York,":[29],"2005].":[30],"This":[31,132],"means":[32],"that":[33,112,250],"their":[34],"convergence":[35,117,318,326],"deteriorates":[36],"when":[37],"the":[38,116,119,128,138,143,150,160,164,169,182,251,294,297,301,309,335,349,354,357],"number":[39,129],"of":[40,118,130,140,142,152,163,181,281,296,323,334,356],"subdomains":[41],"increases.":[42],"In":[43,166],"contrast":[44,362],"this":[46,167],"result,":[48],"it":[49],"was":[50],"observed":[51],"numerically":[52],"[E.":[54,189],"Canc\u00e8s,":[55,76,190,211],"Y.":[56,77,99,191,212,234],"Maday,":[57,78,100,192,213,235],"B.":[59,73,85,95,102,194,208,220,230,237],"Stamm,":[60,74,96,195,209,231],"J.":[61,82,87,104,196,217,222,239,260,263],"Chem.":[62,88,105,197,223,240],"Phys.,":[63,89,198,224],"139":[64,199],"(2013),":[65,109,200,244],"054111;":[66,201],"F.":[67,93,202,228],"Lipparini,":[68,94,203,229],"G.":[69,204],"Scalmani,":[70,205],"L.":[71,206],"Lagard\u00e8re,":[72,207],"E.":[75,97,210,232],"J.-P.":[79,214],"Piquemal,":[80,215],"M.":[81,216,259],"Frisch,":[83,218],"Mennucci,":[86,103,221,238],"141":[90,225],"(2014),":[91,226],"184108;":[92,227],"Cances,":[98,233],"Theory":[106,241],"Comput.,":[107,242],"9":[108,243],"pp.":[110,245,268],"3637--3648]":[111],"some":[114,290],"cases":[115],"method":[123,337],"does":[124],"depend":[126],"on":[127],"subdomains.":[131,283],"happens":[133],"for":[134,270,277,293,312,320],"molecular":[135],"where":[137,178],"domain":[139],"definition":[141],"linear":[144],"partial":[146],"differential":[147],"equation":[148,299],"is":[149],"union":[151],"spherical":[153],"van":[154],"der":[155],"Waal's":[156],"cavities":[157],"centered":[158],"at":[159],"atomic":[161],"position":[162],"molecule.":[165],"case,":[168],"computations":[170],"can":[171],"naturally":[172],"be":[173],"performed":[174],"using":[175,305],"methods,":[177],"each":[179],"atom":[180],"molecule":[183],"corresponds":[184],"a":[186,271,329,343],"subdomain,":[187],"see":[188],"3637--3648].":[246],"We":[247],"prove":[248,289],"here":[249],"scalability":[252],"results":[253,292,327],"presented":[254],"[G.":[256],"Ciaramella":[257],"Gander,":[261],"SIAM":[262],"Numer.":[264],"Anal.,":[265],"55":[266],"(2017),":[267],"1330--1356]":[269],"simplified":[272],"rectangular":[273],"geometry":[274],"also":[275],"hold":[276],"realistic":[278],"two-dimensional":[279],"chains":[280],"circular":[282],"To":[284],"do":[285],"so,":[286],"we":[287,315],"first":[288],"characterization":[291],"solution":[295],"Laplace":[298],"unit":[302],"disk.":[303],"Then,":[304],"these":[306,339],"combined":[307],"with":[308],"maximum":[310],"principle":[311],"harmonic":[313],"functions,":[314],"obtain":[316],"our":[317],"theorems":[319],"configurations":[322],"molecules.":[324],"Our":[325],"reveal":[328],"further":[330,351],"very":[331],"unusual":[332],"property":[333],"simulations:":[340],"starting":[341],"from":[342],"certain":[344],"critical":[345],"overlap":[346,350],"size,":[347],"increasing":[348],"actually":[352],"decreases":[353],"performance":[355],"method,":[359],"strong":[361],"theory.":[366]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
