{"id":"https://openalex.org/W2005789613","doi":"https://doi.org/10.1137/08074461x","title":"Collocation Coarse Approximation in Multigrid","display_name":"Collocation Coarse Approximation in Multigrid","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2005789613","doi":"https://doi.org/10.1137/08074461x","mag":"2005789613"},"language":"en","primary_location":{"id":"doi:10.1137/08074461x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08074461x","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/A5032255313","display_name":"R. Wienands","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roman Wienands","raw_affiliation_strings":["wienands@math.uni-koeln.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"wienands@math.uni-koeln.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072314269","display_name":"Irad Yavneh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Irad Yavneh","raw_affiliation_strings":["irad@cs.technion.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"irad@cs.technion.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0698,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77442445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"31","issue":"5","first_page":"3643","last_page":"3660"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9990000128746033,"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/T10491","display_name":"Enhanced Oil Recovery Techniques","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/stencil","display_name":"Stencil","score":0.7342100143432617},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6959877610206604},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6799615621566772},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6580293774604797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6377894878387451},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5936676859855652},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5920187830924988},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5651888251304626},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.508080244064331},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38506999611854553},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3404914140701294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26736968755722046},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.183793842792511},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.17819392681121826},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1508544683456421},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1343238353729248},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.11673015356063843}],"concepts":[{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.7342100143432617},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6959877610206604},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6799615621566772},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6580293774604797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6377894878387451},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5936676859855652},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5920187830924988},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5651888251304626},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.508080244064331},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38506999611854553},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3404914140701294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26736968755722046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.183793842792511},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.17819392681121826},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1508544683456421},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1343238353729248},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.11673015356063843},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/08074461x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08074461x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W26823901","https://openalex.org/W1530872699","https://openalex.org/W1542622005","https://openalex.org/W1961194538","https://openalex.org/W1967011851","https://openalex.org/W1998461805","https://openalex.org/W2005824832","https://openalex.org/W2010049217","https://openalex.org/W2017217780","https://openalex.org/W2031827243","https://openalex.org/W2051320790","https://openalex.org/W2053717271","https://openalex.org/W2063238351","https://openalex.org/W2064878022","https://openalex.org/W2070851600","https://openalex.org/W2078687549","https://openalex.org/W2081708354","https://openalex.org/W2092069198","https://openalex.org/W2102369828","https://openalex.org/W2106088594","https://openalex.org/W2127981460","https://openalex.org/W2140228084","https://openalex.org/W2151317657","https://openalex.org/W2172093368","https://openalex.org/W2521525968","https://openalex.org/W4251173110"],"related_works":["https://openalex.org/W3105129168","https://openalex.org/W2804920739","https://openalex.org/W4316371992","https://openalex.org/W2014327818","https://openalex.org/W1409194387","https://openalex.org/W61888946","https://openalex.org/W2573021234","https://openalex.org/W2106610492","https://openalex.org/W1989122168","https://openalex.org/W124933011"],"abstract_inverted_index":{"The":[0],"two":[1],"common":[2],"approaches":[3],"to":[4,39,41,81],"defining":[5],"coarse":[6,14,19,28,79],"operators":[7],"in":[8],"multigrid":[9,102],"numerical":[10],"algorithms":[11],"are":[12],"discretization":[13],"approximation":[15,20,29,80],"(DCA)":[16],"and":[17,37,60],"Petrov\u2013Galerkin":[18],"(GCA).":[21],"Here,":[22],"a":[23],"new":[24],"approach":[25],"called":[26],"collocation":[27],"(CCA)":[30],"is":[31,85],"introduced,":[32],"which\u2014like":[33],"GCA\u2014is":[34],"algebraically":[35],"defined":[36],"able":[38],"cater":[40],"difficult":[42],"features":[43],"such":[44],"as":[45],"discontinuous":[46],"coefficients,":[47],"but,":[48],"unlike":[49],"GCA,":[50],"allows":[51],"explicit":[52],"control":[53,62],"over":[54,63],"the":[55,64,68,78,82,97,100],"coarse-grid":[56],"sparsity":[57],"pattern":[58],"(stencil)":[59],"therefore":[61],"computational":[65],"complexity":[66],"of":[67,99],"solver.":[69],"CCA":[70],"relies":[71],"on":[72],"certain":[73],"basis":[74],"functions":[75],"for":[76,89],"which":[77],"fine-grid":[83],"problem":[84],"exact.":[86],"Numerical":[87],"experiments":[88],"two-dimensional":[90],"diffusion":[91],"problems":[92],"including":[93],"jumping":[94],"coefficients":[95],"demonstrate":[96],"potential":[98],"resulting":[101],"algorithms.":[103]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}