{"id":"https://openalex.org/W2963024337","doi":"https://doi.org/10.1137/120881038","title":"The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements","display_name":"The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2963024337","doi":"https://doi.org/10.1137/120881038","mag":"2963024337"},"language":"en","primary_location":{"id":"doi:10.1137/120881038","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120881038","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific 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/A5002534118","display_name":"Nathan Collier","orcid":"https://orcid.org/0000-0002-7367-3981"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Nathan Collier","raw_affiliation_strings":["Center for Numerical Porous Media (NumPor), Computer, Electrical and Mathematical Sci-ences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Center for Numerical Porous Media (NumPor), Computer, Electrical and Mathematical Sci-ences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086339580","display_name":"Lisandro Dalc\u00edn","orcid":"https://orcid.org/0000-0001-8086-0155"},"institutions":[{"id":"https://openalex.org/I4210087694","display_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Santa Fe","ror":"https://ror.org/003vet424","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210087694","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Lisandro Dalcin","raw_affiliation_strings":["Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas, Santa Fe, Argentina"],"affiliations":[{"raw_affiliation_string":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas, Santa Fe, Argentina","institution_ids":["https://openalex.org/I4210087694"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082696717","display_name":"David Pardo","orcid":"https://orcid.org/0000-0002-1101-2248"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Pardo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024876563","display_name":"Victor M. Calo","orcid":"https://orcid.org/0000-0002-1805-4045"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"V. M. Calo","raw_affiliation_strings":["Center for Numerical Porous Media (NumPor), Computer, Electrical and Mathematical Sci-ences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Center for Numerical Porous Media (NumPor), Computer, Electrical and Mathematical Sci-ences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002534118"],"corresponding_institution_ids":["https://openalex.org/I71920554"],"apc_list":null,"apc_paid":null,"fwci":10.6206,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.98899662,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"35","issue":"2","first_page":"A767","last_page":"A784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9886999726295471,"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":0.9695000052452087,"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":0.8628503084182739},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6743125319480896},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5683842301368713},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5507331490516663},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.49790310859680176},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.46222934126853943},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44943276047706604},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4417242705821991},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.42314326763153076},{"id":"https://openalex.org/keywords/polynomial-basis","display_name":"Polynomial basis","score":0.4156855344772339},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.41475972533226013},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37103402614593506},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3354008197784424},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19451719522476196}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8628503084182739},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6743125319480896},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5683842301368713},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5507331490516663},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.49790310859680176},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.46222934126853943},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44943276047706604},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4417242705821991},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.42314326763153076},{"id":"https://openalex.org/C2778406171","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Polynomial basis","level":2,"score":0.4156855344772339},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.41475972533226013},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37103402614593506},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3354008197784424},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19451719522476196},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/120881038","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120881038","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:espace.curtin.edu.au:20.500.11937/51388","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11937/51388","pdf_url":null,"source":{"id":"https://openalex.org/S4306401790","display_name":"eSpace (Curtin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205640436","host_organization_name":"Curtin University","host_organization_lineage":["https://openalex.org/I205640436"],"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":"Journal Article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/555666","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/555666","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1974915083","https://openalex.org/W1984104476","https://openalex.org/W1984921897","https://openalex.org/W1985506636","https://openalex.org/W1989512090","https://openalex.org/W2000425991","https://openalex.org/W2001032894","https://openalex.org/W2011301426","https://openalex.org/W2018899033","https://openalex.org/W2028246274","https://openalex.org/W2055529081","https://openalex.org/W2059825112","https://openalex.org/W2063675347","https://openalex.org/W2077463666","https://openalex.org/W2085827032","https://openalex.org/W2101402782","https://openalex.org/W2125494828","https://openalex.org/W2137029533","https://openalex.org/W2146472543","https://openalex.org/W2148144583","https://openalex.org/W2151938016"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W2120874885","https://openalex.org/W1965109456","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642","https://openalex.org/W2604805698","https://openalex.org/W2910360512","https://openalex.org/W2001973533","https://openalex.org/W2081478553"],"abstract_inverted_index":{"In":[0],"this":[1,155,167,196],"paper":[2],"we":[3,33,117],"study":[4,89],"how":[5],"the":[6,17,62,67,74,110,114,128,134,146],"use":[7],"of":[8,13,19,22,36,66,78,104,113,124,176],"a":[9,27,122,174],"more":[10,143,147,190],"continuous":[11,148],"set":[12,193],"basis":[14],"functions":[15],"affects":[16],"cost":[18,65],"solving":[20],"systems":[21],"linear":[23,37],"equations":[24],"resulting":[25],"from":[26],"discretized":[28],"Galerkin":[29],"weak":[30],"form.":[31],"Specifically,":[32],"compare":[34],"performance":[35],"solvers":[38],"when":[39],"discretizing":[40],"using":[41],"$C^0$":[42],"B-splines,":[43,52],"which":[44,53],"span":[45],"traditional":[46],"finite":[47],"element":[48,98],"spaces,":[49],"and":[50,76,88,101],"$C^{p-1}$":[51],"represent":[54],"maximum":[55],"continuity.":[56],"We":[57,81,131],"provide":[58],"theoretical":[59],"estimates":[60,84],"for":[61,73,121,127,145,151,179,200],"increase":[63],"in":[64,107],"matrix-vector":[68,135],"product":[69,136],"as":[70,72,97,205],"well":[71],"construction":[75],"application":[77],"black-box":[79],"preconditioners.":[80],"accompany":[82],"these":[83],"with":[85],"numerical":[86],"results":[87,120],"their":[90],"sensitivity":[91],"to":[92,109,171,187,192],"various":[93],"grid":[94],"parameters":[95],"such":[96,204],"size":[99],"$h$":[100],"polynomial":[102],"order":[103],"approximation":[105],"$p$":[106],"addition":[108],"aforementioned":[111],"continuity":[112],"basis.":[115],"Finally,":[116],"present":[118],"timing":[119],"range":[123],"preconditioning":[125],"options":[126,183],"Laplace":[129],"problem.":[130],"conclude":[132],"that":[133],"operation":[137],"is":[138,157,164],"at":[139,172],"most":[140,173],"$\\left.{33p^2}\\middle/{8}\\right.$":[141],"times":[142,189],"expensive":[144,191],"space,":[149],"although":[150,195],"moderately":[152],"low":[153],"$p$,":[154],"number":[156,168],"significantly":[158,198],"reduced.":[159],"Moreover,":[160],"if":[161],"static":[162],"condensation":[163],"not":[165],"employed,":[166],"further":[169],"reduces":[170],"value":[175],"8,":[177],"even":[178],"high":[180],"$p$.":[181],"Preconditioning":[182],"can":[184],"be":[185],"up":[186],"$p^3$":[188],"up,":[194],"difference":[197],"decreases":[199],"some":[201],"popular":[202],"preconditioners":[203],"incomplete":[206],"LU":[207],"factorization.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
