{"id":"https://openalex.org/W2010580838","doi":"https://doi.org/10.1137/050641156","title":"Algebraic Multigrid Based on Computational Molecules, 2: Linear Elasticity Problems","display_name":"Algebraic Multigrid Based on Computational Molecules, 2: Linear Elasticity Problems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2010580838","doi":"https://doi.org/10.1137/050641156","mag":"2010580838"},"language":"en","primary_location":{"id":"doi:10.1137/050641156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050641156","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/A5088656822","display_name":"Johannes Kraus","orcid":"https://orcid.org/0000-0003-2261-599X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. K. Kraus","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088656822"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.45056964,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.89203994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"1","first_page":"505","last_page":"524"},"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":0.9984999895095825,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7757878303527832},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6095740795135498},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.5879073143005371},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5381478071212769},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.536798357963562},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5112349987030029},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.47930803894996643},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4535050392150879},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42618584632873535},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.37430810928344727},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30628344416618347},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2394334077835083}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7757878303527832},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6095740795135498},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.5879073143005371},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5381478071212769},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.536798357963562},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5112349987030029},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.47930803894996643},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4535050392150879},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42618584632873535},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.37430810928344727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30628344416618347},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2394334077835083},{"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050641156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050641156","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":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1974248939","https://openalex.org/W1992935956","https://openalex.org/W1997596109","https://openalex.org/W2009250131","https://openalex.org/W2009860245","https://openalex.org/W2031859223","https://openalex.org/W2034374312","https://openalex.org/W2064908347","https://openalex.org/W2072662440","https://openalex.org/W2075536798","https://openalex.org/W2106088594","https://openalex.org/W2117562284","https://openalex.org/W2142304406","https://openalex.org/W2243781021"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W84272617","https://openalex.org/W613282331","https://openalex.org/W2171218546","https://openalex.org/W3176670060","https://openalex.org/W2543276709","https://openalex.org/W3081031083","https://openalex.org/W2001238277"],"abstract_inverted_index":{"This":[0,53,150],"paper":[1,81],"deals":[2],"with":[3,133,167],"a":[4,55,152],"new":[5,154],"approach":[6,26],"in":[7,142],"algebraic":[8,51],"multigrid":[9],"(AMG)":[10],"for":[11,27,46,60,87,161,171],"self-adjoint":[12],"and":[13,33,57,88],"elliptic":[14],"problems":[15,29,166],"arising":[16],"from":[17,147],"finite-element":[18],"discretization":[19],"of":[20,49,63,66,103,114,119,156,165],"linear":[21,50,96],"elasticity":[22,97],"problems.":[23,98],"Generalizing":[24],"our":[25],"scalar":[28],"[J.":[30],"K.":[31],"Kraus":[32],"J.":[34],"Schicho,":[35],"Computing,":[36],"77":[37],"(2006),":[38],"pp.":[39],"57\u201375],":[40],"we":[41],"propose":[42],"an":[43,162],"edge-matrix":[44,83],"concept":[45,84],"point-block":[47],"systems":[48],"equations.":[52],"gives":[54],"simple":[56],"reliable":[58],"method":[59],"the":[61,64,82,104,126],"evaluation":[62],"strength":[65],"nodal":[67],"dependence":[68],"that":[69,158],"can":[70],"be":[71],"applied":[72,89],"to":[73,90,128],"symmetric":[74,109],"positive":[75,110],"definite":[76],"non-M":[77],"matrices.":[78,149],"In":[79],"this":[80,143],"is":[85],"developed":[86],"(two-":[91],"as":[92,94],"well":[93],"three-dimensional)":[95],"We":[99],"consider":[100],"approximate":[101],"splittings":[102],"problem-related":[105],"element":[106],"matrices":[107,113,121],"into":[108],"semidefinite":[111],"edge":[112,120,148],"rank":[115],"one.":[116],"The":[117,138],"reproduction":[118],"on":[122],"coarse":[123],"levels":[124],"offers":[125],"opportunity":[127],"combine":[129],"classical":[130],"coarsening":[131],"techniques":[132],"robust":[134],"(energy-minimizing)":[135],"interpolation":[136],"schemes:":[137],"\"computational":[139],"molecules\"":[140],"involved":[141],"process":[144],"are":[145],"assembled":[146],"yields":[151],"flexible":[153],"variant":[155],"AMG":[157],"allows":[159],"also":[160],"efficient":[163],"solution":[164],"discontinuous":[168],"coefficients,":[169],"e.g.,":[170],"composite":[172],"materials.":[173]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}