{"id":"https://openalex.org/W1548892666","doi":"https://doi.org/10.1007/bf02238513","title":"The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids","display_name":"The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids","publication_year":1996,"publication_date":"1996-09-01","ids":{"openalex":"https://openalex.org/W1548892666","doi":"https://doi.org/10.1007/bf02238513","mag":"1548892666"},"language":"en","primary_location":{"id":"doi:10.1007/bf02238513","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02238513","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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","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/A5100699455","display_name":"Jianhua Xu","orcid":"https://orcid.org/0000-0001-6134-4833"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Xu","raw_affiliation_strings":["Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA, USA","Dept. of Mathematics, The Pennsylvania State University, University Park, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Dept. of Mathematics, The Pennsylvania State University, University Park, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100699455"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":7.5192,"has_fulltext":false,"cited_by_count":190,"citation_normalized_percentile":{"value":0.9746387,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"56","issue":"3","first_page":"215","last_page":"235"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9966999888420105,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/multigrid-method","display_name":"Multigrid method","score":0.9008981585502625},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8415713310241699},{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.649759829044342},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.637726902961731},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5433635711669922},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5343500971794128},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5128424763679504},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5099164247512817},{"id":"https://openalex.org/keywords/unstructured-grid","display_name":"Unstructured grid","score":0.4981575012207031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48429766297340393},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.48334524035453796},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4479856789112091},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.43733203411102295},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.412598580121994},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3888496160507202},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32319608330726624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23345741629600525},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2211226224899292},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21372359991073608},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0908437967300415},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.08872684836387634}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.9008981585502625},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8415713310241699},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.649759829044342},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.637726902961731},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5433635711669922},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5343500971794128},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5128424763679504},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5099164247512817},{"id":"https://openalex.org/C134620963","wikidata":"https://www.wikidata.org/wiki/Q17078677","display_name":"Unstructured grid","level":3,"score":0.4981575012207031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48429766297340393},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.48334524035453796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4479856789112091},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.43733203411102295},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.412598580121994},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3888496160507202},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32319608330726624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23345741629600525},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2211226224899292},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21372359991073608},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0908437967300415},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.08872684836387634},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02238513","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02238513","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W85656838","https://openalex.org/W590402726","https://openalex.org/W1532656300","https://openalex.org/W1969742554","https://openalex.org/W1977347555","https://openalex.org/W1994484297","https://openalex.org/W1995788694","https://openalex.org/W1997831216","https://openalex.org/W2012492661","https://openalex.org/W2017085690","https://openalex.org/W2024706945","https://openalex.org/W2025095941","https://openalex.org/W2031804122","https://openalex.org/W2042732056","https://openalex.org/W2063483315","https://openalex.org/W2064991465","https://openalex.org/W2072463419","https://openalex.org/W2074189597","https://openalex.org/W2116226692","https://openalex.org/W2151317657","https://openalex.org/W4300509647","https://openalex.org/W6635142151","https://openalex.org/W7018537812"],"related_works":["https://openalex.org/W4389317411","https://openalex.org/W1492522302","https://openalex.org/W4226460012","https://openalex.org/W2096454229","https://openalex.org/W2042199958","https://openalex.org/W2103149966","https://openalex.org/W2177482563","https://openalex.org/W2120298265","https://openalex.org/W2464766188","https://openalex.org/W4366778284"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
