{"id":"https://openalex.org/W2021666101","doi":"https://doi.org/10.1007/s00211-015-0718-5","title":"A massively parallel nonoverlapping additive Schwarz method for discontinuous Galerkin discretization of elliptic problems","display_name":"A massively parallel nonoverlapping additive Schwarz method for discontinuous Galerkin discretization of elliptic problems","publication_year":2015,"publication_date":"2015-04-01","ids":{"openalex":"https://openalex.org/W2021666101","doi":"https://doi.org/10.1007/s00211-015-0718-5","mag":"2021666101","pmid":"https://pubmed.ncbi.nlm.nih.gov/28615738"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-015-0718-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-015-0718-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-015-0718-5.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-015-0718-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111838056","display_name":"Maksymilian Dryja","orcid":null},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Maksymilian Dryja","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland","University of Warsaw , Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"University of Warsaw , Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037193832","display_name":"Piotr Krzy\u017canowski","orcid":"https://orcid.org/0000-0002-6816-746X"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Krzy\u017canowski","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland","University of Warsaw , Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"University of Warsaw , Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111838056"],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.0049,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.75239382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"132","issue":"2","first_page":"347","last_page":"367"},"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":1.0,"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":1.0,"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/T10514","display_name":"Numerical methods in engineering","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8275381326675415},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7858132123947144},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6501874923706055},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.6075024008750916},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.6052361130714417},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5632681846618652},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5342326164245605},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.5269173979759216},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.484304815530777},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47783827781677246},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.46499103307724},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.46213024854660034},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4604654014110565},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42966118454933167},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41854605078697205},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.3585497736930847},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1832074224948883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0845261812210083}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8275381326675415},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7858132123947144},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6501874923706055},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.6075024008750916},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.6052361130714417},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5632681846618652},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5342326164245605},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.5269173979759216},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.484304815530777},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47783827781677246},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.46499103307724},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.46213024854660034},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4604654014110565},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42966118454933167},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41854605078697205},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.3585497736930847},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1832074224948883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0845261812210083},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00211-015-0718-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-015-0718-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-015-0718-5.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmid:28615738","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28615738","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische mathematik","raw_type":null},{"id":"pmh:oai:europepmc.org:4316809","is_oa":false,"landing_page_url":"http://europepmc.org/articles/PMC5445549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:5445549","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5445549","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numer Math (Heidelb)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00211-015-0718-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-015-0718-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-015-0718-5.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2021666101.pdf","grobid_xml":"https://content.openalex.org/works/W2021666101.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W628726389","https://openalex.org/W1493036607","https://openalex.org/W1506342804","https://openalex.org/W1548589512","https://openalex.org/W1979771104","https://openalex.org/W1992066344","https://openalex.org/W2081513515","https://openalex.org/W2086501907","https://openalex.org/W2101354903","https://openalex.org/W2105777174","https://openalex.org/W2108039194","https://openalex.org/W2125906582","https://openalex.org/W2140888960","https://openalex.org/W2464571761","https://openalex.org/W2592623476","https://openalex.org/W2595755998","https://openalex.org/W2600270843","https://openalex.org/W2620258316"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W1515964003","https://openalex.org/W2504287632","https://openalex.org/W1994696552","https://openalex.org/W3046643187","https://openalex.org/W2286395548","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2026475824","https://openalex.org/W2493580937"],"abstract_inverted_index":{"A":[0],"second":[1],"order":[2],"elliptic":[3],"problem":[4,15,40],"with":[5,29,49,55],"discontinuous":[6,24],"coefficient":[7,114],"in":[8],"2-D":[9],"or":[10,124],"3-D":[11],"is":[12,16,41,98,107,118],"considered.":[13],"The":[14,37,100],"discretized":[17],"by":[18,43],"a":[19,44,50,75,78],"symmetric":[20],"weighted":[21],"interior":[22],"penalty":[23],"Galerkin":[25],"finite":[26],"element":[27],"method":[28,48,73,106],"nonmatching":[30],"simplicial":[31],"elements":[32],"and":[33,54],"piecewise":[34],"linear":[35],"functions.":[36],"resulting":[38],"discrete":[39],"solved":[42],"two-level":[45],"additive":[46],"Schwarz":[47],"relatively":[51],"coarse":[52,121],"grid":[53,122],"local":[56,126],"solves":[57],"restricted":[58],"to":[59],"subdomains":[60],"which":[61,134],"can":[62],"be":[63],"as":[64,66],"small":[65],"single":[67],"element.":[68],"In":[69],"this":[70],"way":[71],"the":[72,91,95,105,110,113],"has":[74],"potential":[76],"for":[77],"very":[79],"high":[80],"level":[81],"of":[82,94,102,104,109,112],"fine":[83],"grained":[84],"parallelism.":[85],"Condition":[86],"number":[87],"estimate":[88],"depending":[89],"on":[90,125],"relative":[92],"sizes":[93],"underlying":[96],"grids":[97],"provided.":[99],"rate":[101],"convergence":[103],"independent":[108],"jumps":[111],"if":[115],"its":[116],"variation":[117],"moderate":[119],"inside":[120],"substructures":[123],"solvers'":[127],"subdomain":[128],"boundaries.":[129],"Numerical":[130],"experiments":[131],"are":[132],"reported":[133],"confirm":[135],"theoretical":[136],"results.":[137]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}