{"id":"https://openalex.org/W2757864265","doi":"https://doi.org/10.1137/17m1148384","title":"A Stencil Scaling Approach for Accelerating Matrix-Free Finite Element Implementations","display_name":"A Stencil Scaling Approach for Accelerating Matrix-Free Finite Element Implementations","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2757864265","doi":"https://doi.org/10.1137/17m1148384","mag":"2757864265"},"language":"en","primary_location":{"id":"doi:10.1137/17m1148384","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1148384","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.06793","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024844886","display_name":"Simon Bauer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Bauer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026096803","display_name":"Daniel Drzisga","orcid":"https://orcid.org/0000-0003-3757-2136"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Drzisga","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3757-2136","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021181231","display_name":"Marcus Mohr","orcid":"https://orcid.org/0000-0003-2942-8484"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Mohr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"U. R\u00fcde","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"U. R\u00fcde","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075106453","display_name":"Christian Waluga","orcid":"https://orcid.org/0000-0002-1071-6374"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Waluga","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5018841476","display_name":"Barbara Wohlmuth","orcid":"https://orcid.org/0000-0001-6908-6015"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Wohlmuth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00620676,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"6","first_page":"C748","last_page":"C778"},"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":0.9994000196456909,"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":0.9994000196456909,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stencil","display_name":"Stencil","score":0.7102125287055969},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6259710192680359},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6159220337867737},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5322427749633789},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5198712348937988},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.49008047580718994},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.4419345259666443},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.43721163272857666},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4302179515361786},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4129009246826172},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.41277679800987244},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37977927923202515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3744939863681793},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14261943101882935},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10480207204818726},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.09807974100112915}],"concepts":[{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.7102125287055969},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6259710192680359},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6159220337867737},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5322427749633789},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5198712348937988},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.49008047580718994},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.4419345259666443},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43721163272857666},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4302179515361786},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4129009246826172},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.41277679800987244},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37977927923202515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3744939863681793},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14261943101882935},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10480207204818726},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.09807974100112915},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1148384","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1148384","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:arXiv.org:1709.06793","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1709.06793","pdf_url":"https://arxiv.org/pdf/1709.06793","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2757864265","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1709.06793","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1709.06793","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.06793","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.06793","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1709.06793","pdf_url":"https://arxiv.org/pdf/1709.06793","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.75}],"awards":[{"id":"https://openalex.org/G256124521","display_name":null,"funder_award_id":"WO671/11\u20101","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G771346270","display_name":null,"funder_award_id":"WO671/11-1","funder_id":"https://openalex.org/F4320323383","funder_display_name":"Technische Universit\u00e4t M\u00fcnchen"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"},{"id":"https://openalex.org/F4320323390","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55"},{"id":"https://openalex.org/F4320331625","display_name":"Gauss Centre for Supercomputing","ror":"https://ror.org/0585fsj26"},{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"},{"id":"https://openalex.org/F4320336863","display_name":"Leibniz-Rechenzentrum","ror":"https://ror.org/05558nw16"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2757864265.pdf","grobid_xml":"https://content.openalex.org/works/W2757864265.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W996450974","https://openalex.org/W1572617741","https://openalex.org/W1589492941","https://openalex.org/W1961751213","https://openalex.org/W1974122416","https://openalex.org/W1987403652","https://openalex.org/W1998902021","https://openalex.org/W2002555321","https://openalex.org/W2018225490","https://openalex.org/W2034029678","https://openalex.org/W2045075499","https://openalex.org/W2052084709","https://openalex.org/W2058111044","https://openalex.org/W2058398001","https://openalex.org/W2072132691","https://openalex.org/W2096642134","https://openalex.org/W2104215969","https://openalex.org/W2121743872","https://openalex.org/W2146683922","https://openalex.org/W2154865023","https://openalex.org/W2159612519","https://openalex.org/W2330793397","https://openalex.org/W2619854663","https://openalex.org/W2622174129","https://openalex.org/W2622491854","https://openalex.org/W2750714358","https://openalex.org/W2963879940"],"related_works":["https://openalex.org/W2956719309","https://openalex.org/W2762142658","https://openalex.org/W1965111703","https://openalex.org/W2986911722","https://openalex.org/W2189435013","https://openalex.org/W2028673793","https://openalex.org/W2189498504","https://openalex.org/W2157925536","https://openalex.org/W2113385788","https://openalex.org/W2981393605","https://openalex.org/W3005617612","https://openalex.org/W2020681688","https://openalex.org/W2212587874","https://openalex.org/W2963063923","https://openalex.org/W2003292056","https://openalex.org/W2122714614","https://openalex.org/W3203098483","https://openalex.org/W2964030165","https://openalex.org/W2767214835","https://openalex.org/W3109067951"],"abstract_inverted_index":{"We":[0],"present":[1,87],"a":[2,32,54,88,114,148],"novel":[3,103],"approach":[4,30,63,104],"to":[5,113,137],"fast":[6],"on-the-fly":[7],"low":[8],"order":[9,70],"finite":[10,116],"element":[11,117],"assembly":[12,118],"for":[13,26],"scalar":[14],"elliptic":[15],"partial":[16],"differential":[17],"equations":[18],"of":[19,95,108,153,163],"Darcy":[20],"type":[21],"with":[22,135,145],"variable":[23],"coefficients":[24],"optimized":[25],"matrix-free":[27],"implementations.":[28],"Our":[29,123],"introduces":[31],"new":[33,165],"operator":[34],"that":[35,58,91,101,131],"is":[36],"obtained":[37,60],"by":[38,61,128],"appropriately":[39],"scaling":[40,166],"the":[41,46,73,76,83,96,109,133,161,164],"reference":[42],"stiffness":[43],"matrix":[44],"from":[45],"constant":[47],"coefficient":[48],"case.":[49],"Assuming":[50],"sufficient":[51],"regularity,":[52],"an":[53],"priori":[55],"analysis":[56],"shows":[57],"solutions":[59],"this":[62],"are":[64,126],"unique":[65],"and":[66,75,139],"have":[67],"asymptotically":[68],"optimal":[69],"convergence":[71],"in":[72],"$H^1$-":[74],"$L^2$-norms":[77],"on":[78,156],"hierarchical":[79],"hybrid":[80],"grids.":[81],"For":[82],"preasymptotic":[84],"regime,":[85],"we":[86],"local":[89],"modification":[90],"guarantees":[92],"uniform":[93],"ellipticity":[94],"operator.":[97],"Cost":[98],"considerations":[99,125],"show":[100],"our":[102],"requires":[105],"roughly":[106],"one-third":[107],"floating-point":[110],"operations":[111],"compared":[112],"classical":[115],"scheme":[119],"employing":[120],"nodal":[121],"integration.":[122],"theoretical":[124],"illustrated":[127],"numerical":[129],"tests":[130],"confirm":[132],"expectations":[134],"respect":[136],"accuracy":[138],"run-time.":[140],"A":[141],"large":[142],"scale":[143],"application":[144],"more":[146],"than":[147],"hundred":[149],"billion":[150],"($1.6\\cdot10^{11}$)":[151],"degrees":[152],"freedom":[154],"executed":[155],"14310":[157],"compute":[158],"cores":[159],"demonstrates":[160],"efficiency":[162],"approach.":[167]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}