{"id":"https://openalex.org/W2080552677","doi":"https://doi.org/10.1007/s00791-014-0220-0","title":"Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems","display_name":"Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems","publication_year":2013,"publication_date":"2013-02-01","ids":{"openalex":"https://openalex.org/W2080552677","doi":"https://doi.org/10.1007/s00791-014-0220-0","mag":"2080552677"},"language":"en","primary_location":{"id":"doi:10.1007/s00791-014-0220-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00791-014-0220-0","pdf_url":null,"source":{"id":"https://openalex.org/S55464786","display_name":"Computing and Visualization in Science","issn_l":"1432-9360","issn":["1432-9360","1433-0369"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing and Visualization in Science","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/A5027648225","display_name":"Alfio Borz\u0131\u0300","orcid":"https://orcid.org/0000-0002-8050-1336"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alfio Borz\u00ec","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t W\u00fcrzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074, W\u00fcrzburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t W\u00fcrzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060944643","display_name":"Valentina De Simone","orcid":"https://orcid.org/0000-0002-3357-5252"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Valentina De Simone","raw_affiliation_strings":["Dipartimento di Matematica e Fisica, Seconda Universit\u00e0 degli Studi di Napoli, viale A.\u00a0Lincoln 5, 81100, Caserta, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica, Seconda Universit\u00e0 degli Studi di Napoli, viale A.\u00a0Lincoln 5, 81100, Caserta, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044144663","display_name":"Daniela di Serafino","orcid":"https://orcid.org/0000-0001-8215-0771"},"institutions":[{"id":"https://openalex.org/I3005160176","display_name":"Institute for High Performance Computing and Networking","ror":"https://ror.org/04r5fge26","country_code":"IT","type":"facility","lineage":["https://openalex.org/I3005160176","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Daniela di Serafino","raw_affiliation_strings":["Dipartimento di Matematica e Fisica, Seconda Universit\u00e0 degli Studi di Napoli, viale A.\u00a0Lincoln 5, 81100, Caserta, Italy","Istituto di Calcolo e Reti ad Alte Prestazioni (ICAR), CNR, via P. Castellino 111, 80131, Naples, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica, Seconda Universit\u00e0 degli Studi di Napoli, viale A.\u00a0Lincoln 5, 81100, Caserta, Italy","institution_ids":["https://openalex.org/I71267560"]},{"raw_affiliation_string":"Istituto di Calcolo e Reti ad Alte Prestazioni (ICAR), CNR, via P. Castellino 111, 80131, Naples, Italy","institution_ids":["https://openalex.org/I3005160176"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027648225"],"corresponding_institution_ids":["https://openalex.org/I25974101"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.13228837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"1","first_page":"1","last_page":"14"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","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/T11416","display_name":"Numerical methods for differential equations","score":0.9977999925613403,"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":0.6712325811386108},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6329858899116516},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.592510461807251},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5438554286956787},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.522482693195343},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5065799951553345},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.46870964765548706},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4661520719528198},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.46116727590560913},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41196680068969727},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32930833101272583},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.29355084896087646},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.19815433025360107},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19179898500442505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1677544116973877}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6712325811386108},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6329858899116516},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.592510461807251},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5438554286956787},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.522482693195343},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5065799951553345},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.46870964765548706},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4661520719528198},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.46116727590560913},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41196680068969727},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32930833101272583},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.29355084896087646},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.19815433025360107},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19179898500442505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1677544116973877},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00791-014-0220-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00791-014-0220-0","pdf_url":null,"source":{"id":"https://openalex.org/S55464786","display_name":"Computing and Visualization in Science","issn_l":"1432-9360","issn":["1432-9360","1433-0369"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing and Visualization in Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.433.4695","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.433.4695","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2011/12/3299.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4399999976158142,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1523714122","https://openalex.org/W1542243431","https://openalex.org/W1548589512","https://openalex.org/W1589918049","https://openalex.org/W1961194538","https://openalex.org/W1981462986","https://openalex.org/W1991540805","https://openalex.org/W1992107487","https://openalex.org/W2009250131","https://openalex.org/W2013555402","https://openalex.org/W2017085690","https://openalex.org/W2019872467","https://openalex.org/W2022916138","https://openalex.org/W2022977680","https://openalex.org/W2031887218","https://openalex.org/W2032715328","https://openalex.org/W2043713199","https://openalex.org/W2049664825","https://openalex.org/W2051917325","https://openalex.org/W2055914968","https://openalex.org/W2063228755","https://openalex.org/W2064745921","https://openalex.org/W2068395392","https://openalex.org/W2094534199","https://openalex.org/W2095508660","https://openalex.org/W2100858639","https://openalex.org/W2119507700","https://openalex.org/W2123458460","https://openalex.org/W2142304406","https://openalex.org/W2152741328","https://openalex.org/W2252040419","https://openalex.org/W2329059021","https://openalex.org/W2536303343","https://openalex.org/W2915344229","https://openalex.org/W4239804747","https://openalex.org/W4244685536","https://openalex.org/W4249613779","https://openalex.org/W4298228534"],"related_works":["https://openalex.org/W2189576811","https://openalex.org/W2091296067","https://openalex.org/W2075755912","https://openalex.org/W2951334208","https://openalex.org/W1980455776","https://openalex.org/W193118763","https://openalex.org/W1994486759","https://openalex.org/W2883804816","https://openalex.org/W1996147937","https://openalex.org/W1795839839"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}