{"id":"https://openalex.org/W2030097566","doi":"https://doi.org/10.1137/120865872","title":"Robust Multilevel Methods for General Symmetric Positive Definite Operators","display_name":"Robust Multilevel Methods for General Symmetric Positive Definite Operators","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2030097566","doi":"https://doi.org/10.1137/120865872","mag":"2030097566"},"language":"en","primary_location":{"id":"doi:10.1137/120865872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120865872","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/A5039271890","display_name":"J. Willems","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. Willems","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039271890"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2466,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86533792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"52","issue":"1","first_page":"103","last_page":"124"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8806359171867371},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5805174112319946},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5610980987548828},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5537906885147095},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5420982837677002},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5147023797035217},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5070037841796875},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.5005927085876465},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.4862000346183777},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46216464042663574},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.4546133279800415},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.44642212986946106},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.44069138169288635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8806359171867371},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5805174112319946},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5610980987548828},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5537906885147095},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5420982837677002},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5147023797035217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5070037841796875},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.5005927085876465},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.4862000346183777},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46216464042663574},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4546133279800415},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.44642212986946106},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.44069138169288635},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120865872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120865872","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:CiteSeerX.psu:10.1.1.300.915","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.300.915","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ricam.oeaw.ac.at/publications/reports/12/rep12-06.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W145711262","https://openalex.org/W359661129","https://openalex.org/W654805605","https://openalex.org/W1480928214","https://openalex.org/W1519509134","https://openalex.org/W1542243431","https://openalex.org/W1548589512","https://openalex.org/W1582734821","https://openalex.org/W1966480196","https://openalex.org/W1968536045","https://openalex.org/W1973633019","https://openalex.org/W1981142209","https://openalex.org/W1986442363","https://openalex.org/W2018074366","https://openalex.org/W2019810268","https://openalex.org/W2030373618","https://openalex.org/W2030947573","https://openalex.org/W2083715026","https://openalex.org/W2102295719","https://openalex.org/W2108533624","https://openalex.org/W2109005370","https://openalex.org/W2131738355","https://openalex.org/W2140202900","https://openalex.org/W2498157954","https://openalex.org/W2612782048","https://openalex.org/W2953188243","https://openalex.org/W2963631308","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2966383146","https://openalex.org/W4288024825","https://openalex.org/W2123186262","https://openalex.org/W1992244398","https://openalex.org/W2056066177","https://openalex.org/W1977469992","https://openalex.org/W89608191","https://openalex.org/W161456815","https://openalex.org/W2003145294","https://openalex.org/W2142282665"],"abstract_inverted_index":{"A":[0],"general":[1,94],"robust":[2,127],"multilevel":[3,64],"method":[4,30,56,88],"for":[5,69,118],"solving":[6],"symmetric":[7],"positive":[8],"definite":[9],"systems":[10],"resulting":[11],"from":[12],"discretizing":[13],"elliptic":[14,100,121],"partial":[15],"differential":[16],"equations":[17,103,108],"is":[18,72,89],"developed.":[19],"The":[20,55,66,87],"term":[21],"\u201crobust\u201d":[22],"refers":[23],"to":[24,58,97],"the":[25,29,37,59,73,98,102,111,119],"convergence":[26,128],"rate":[27],"of":[28,33,45,61,75,79,104,113],"being":[31],"independent":[32],"discretization":[34],"parameters,":[35],"i.e.,":[36],"problem":[38,41,47],"size,":[39],"and":[40,107],"parameters.":[42],"Important":[43],"instances":[44],"such":[46],"parameters":[48],"are":[49,123],"in":[50,91,110],"particular":[51],"(highly":[52],"varying)":[53],"coefficients.":[54],"belongs":[57],"class":[60],"(nonlinear)":[62],"algebraic":[63],"iterations.":[65],"crucial":[67],"ingredient":[68],"obtaining":[70],"robustness":[71],"construction":[74],"a":[76,92],"nested":[77],"sequence":[78],"spaces":[80],"based":[81],"on":[82],"local":[83],"generalized":[84],"eigenvalue":[85],"problems.":[86],"analyzed":[90],"rather":[93],"setting":[95],"applying":[96],"scalar":[99,120],"equation,":[101],"linear":[105],"elasticity,":[106],"arising":[109],"solution":[112],"Maxwell's":[114],"equations.":[115],"Numerical":[116],"results":[117],"equation":[122],"presented":[124],"showing":[125],"its":[126],"behavior.":[129]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}