{"id":"https://openalex.org/W2523496060","doi":"https://doi.org/10.1137/15m1036683","title":"Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method","display_name":"Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2523496060","doi":"https://doi.org/10.1137/15m1036683","mag":"2523496060"},"language":"en","primary_location":{"id":"doi:10.1137/15m1036683","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1036683","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":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/1368024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002167323","display_name":"Delyan Z. Kalchev","orcid":"https://orcid.org/0000-0002-2251-1827"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Z. Kalchev","raw_affiliation_strings":["Univ. of Colorado, Boulder, CO (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of Colorado, Boulder, CO (United States)","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003575107","display_name":"Chak Shing Lee","orcid":"https://orcid.org/0000-0002-9573-3463"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. S. Lee","raw_affiliation_strings":["Texas A & M Univ., College Station, TX (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A & M Univ., College Station, TX (United States)","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083076229","display_name":"Umberto Villa","orcid":"https://orcid.org/0000-0002-5142-2559"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"U. Villa","raw_affiliation_strings":["Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072220697","display_name":"Y. Efendiev","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Y. Efendiev","raw_affiliation_strings":["Texas A & M Univ., College Station, TX (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A & M Univ., College Station, TX (United States)","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. S. Vassilevski","raw_affiliation_strings":["Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)","institution_ids":["https://openalex.org/I1282311441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5002167323"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":2.8836,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.91671318,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","issue":"5","first_page":"A2912","last_page":"A2933"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/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/T11558","display_name":"Composite Material Mechanics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/discretization","display_name":"Discretization","score":0.7412198781967163},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7403773069381714},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6631780862808228},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5146639943122864},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.45608657598495483},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.4429614543914795},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.42730337381362915},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.41512227058410645},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.41317862272262573},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.34240788221359253},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.3382481038570404},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32376354932785034},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3125496804714203},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2031886875629425}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7412198781967163},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7403773069381714},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6631780862808228},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5146639943122864},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.45608657598495483},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4429614543914795},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.42730337381362915},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.41512227058410645},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.41317862272262573},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.34240788221359253},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.3382481038570404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32376354932785034},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3125496804714203},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2031886875629425},{"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":2,"locations":[{"id":"doi:10.1137/15m1036683","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1036683","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:osti.gov:1368024","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1368024","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:1368024","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1368024","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1980053021","https://openalex.org/W1981142209","https://openalex.org/W1981415318","https://openalex.org/W1983139887","https://openalex.org/W1994810579","https://openalex.org/W1997596109","https://openalex.org/W2000272165","https://openalex.org/W2003637147","https://openalex.org/W2005788407","https://openalex.org/W2018074366","https://openalex.org/W2029918260","https://openalex.org/W2030373618","https://openalex.org/W2035668454","https://openalex.org/W2038330765","https://openalex.org/W2070232376","https://openalex.org/W2078045751","https://openalex.org/W2082312113","https://openalex.org/W2089139137","https://openalex.org/W2108533624","https://openalex.org/W2112280313","https://openalex.org/W2114051217","https://openalex.org/W2131374225","https://openalex.org/W2142762932","https://openalex.org/W2145062249","https://openalex.org/W2157366329","https://openalex.org/W2235901662","https://openalex.org/W2963631308"],"related_works":["https://openalex.org/W3127021889","https://openalex.org/W4308799551","https://openalex.org/W2390298288","https://openalex.org/W2565231037","https://openalex.org/W2376732695","https://openalex.org/W2465758394","https://openalex.org/W1459983556","https://openalex.org/W1989473560","https://openalex.org/W2213700069","https://openalex.org/W2223541427"],"abstract_inverted_index":{"We":[0,40,155],"propose":[1],"two":[2,203],"multilevel":[3],"spectral":[4,196],"techniques":[5],"for":[6,11,161,180],"constructing":[7],"coarse":[8,49,64,70,91,118,138,153,163],"discretization":[9,139],"spaces":[10,92,109],"saddle-point":[12,165],"problems":[13,78],"corresponding":[14],"to":[15,88,116,141,172,185,209],"PDEs":[16],"involving":[17],"a":[18,22,173],"divergence":[19],"constraint,":[20],"with":[21,67],"focus":[23],"on":[24,36],"mixed":[25,81],"finite":[26,82],"element":[27,42,71,83],"discretizations":[28],"of":[29,60,98,106,127,134,213],"scalar":[30],"self-adjoint":[31],"second":[32],"order":[33],"elliptic":[34],"equations":[35],"general":[37],"unstructured":[38],"grids.":[39],"use":[41,192],"agglomeration":[43],"algebraic":[44],"multigrid":[45],"(AMGe),":[46],"which":[47,170],"employs":[48],"elements":[50],"that":[51],"can":[52],"have":[53],"nonstandard":[54],"shape":[55],"since":[56],"they":[57],"are":[58,207],"agglomerates":[59],"fine-grid":[61],"elements.":[62],"The":[63,120],"basis":[65],"associated":[66],"each":[68],"agglomerated":[69],"is":[72],"constructed":[73],"by":[74,111,167],"solving":[75],"local":[76,80,114],"eigenvalue":[77],"and":[79,93,184,204],"problems.":[84],"This":[85],"construction":[86],"leads":[87,171],"stable":[89],"upscaled":[90,100,108,137],"guarantees":[94],"the":[95,99,103,117,125,132,135,152,162,181,187,211,214],"inf-sup":[96],"compatibility":[97],"discretization.":[101],"Also,":[102],"approximation":[104],"properties":[105],"these":[107],"improve":[110],"adding":[112],"more":[113],"eigenfunctions":[115],"spaces.":[119],"higher":[121],"accuracy":[122],"comes":[123],"at":[124],"cost":[126],"additional":[128,149],"computational":[129],"effort,":[130],"as":[131,142],"sparsity":[133],"resulting":[136],"(referred":[140],"operator":[143],"complexity)":[144],"deteriorates":[145],"when":[146],"we":[147,191],"introduce":[148],"functions":[150],"in":[151,201],"space.":[154],"also":[156],"provide":[157],"an":[158],"efficient":[159],"solver":[160],"(upscaled)":[164],"system":[166,179],"employing":[168],"hybridization,":[169],"symmetric":[174],"positive":[175],"definite":[176],"(s.p.d.)":[177],"reduced":[178],"Lagrange":[182],"multipliers,":[183],"solve":[186],"latter":[188],"s.p.d.":[189],"system,":[190],"our":[193],"previously":[194],"developed":[195],"AMGe":[197],"solver.":[198],"Numerical":[199],"experiments,":[200],"both":[202],"three":[205],"dimensions,":[206],"provided":[208],"illustrate":[210],"efficiency":[212],"proposed":[215],"upscaling":[216],"technique.":[217]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-10T08:33:47.465468","created_date":"2025-10-10T00:00:00"}