{"id":"https://openalex.org/W2918053456","doi":"https://doi.org/10.1137/18m1226580","title":"The Surrogate Matrix Methodology: A Priori Error Estimation","display_name":"The Surrogate Matrix Methodology: A Priori Error Estimation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2918053456","doi":"https://doi.org/10.1137/18m1226580","mag":"2918053456"},"language":"en","primary_location":{"id":"doi:10.1137/18m1226580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1226580","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1902.07333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Daniel Drzisga","orcid":"https://orcid.org/0000-0003-3757-2136"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Drzisga","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3757-2136","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Brendan Keith","orcid":"https://orcid.org/0000-0002-6969-6857"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brendan Keith","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6969-6857","affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Barbara Wohlmuth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barbara 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":0.7471,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.67134013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"41","issue":"6","first_page":"A3806","last_page":"A3838"},"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":0.802299976348877,"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":0.802299976348877,"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":0.11050000041723251,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.02250000089406967,"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":0.7573000192642212},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5648999810218811},{"id":"https://openalex.org/keywords/curvilinear-coordinates","display_name":"Curvilinear coordinates","score":0.5254999995231628},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.499099999666214},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4724000096321106},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4514000117778778},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4422000050544739},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42879998683929443},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4262999892234802},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.424699991941452}],"concepts":[{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.7573000192642212},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7559999823570251},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5788000226020813},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5648999810218811},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.5254999995231628},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5148000121116638},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.499099999666214},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4724000096321106},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4514000117778778},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4422000050544739},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42879998683929443},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.424699991941452},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4235999882221222},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.34880000352859497},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.32899999618530273},{"id":"https://openalex.org/C72249523","wikidata":"https://www.wikidata.org/wiki/Q492260","display_name":"Flexibility method","level":3,"score":0.3176000118255615},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C147370603","wikidata":"https://www.wikidata.org/wiki/Q3801506","display_name":"Hyperelastic material","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.2847999930381775},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.2827000021934509},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.27559998631477356},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.2632000148296356},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1226580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1226580","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:1902.07333","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1902.07333","pdf_url":"https://arxiv.org/pdf/1902.07333","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1902.07333","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1902.07333","pdf_url":"https://arxiv.org/pdf/1902.07333","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"awards":[{"id":"https://openalex.org/G1456954421","display_name":null,"funder_award_id":"WO671/11-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7531481501","display_name":"EXAscale Quantification of Uncertainties for Technology and Science Simulation","funder_award_id":"800898","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8254871785","display_name":null,"funder_award_id":"800898","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320331625","display_name":"Gauss Centre for Supercomputing","ror":"https://ror.org/0585fsj26"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"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":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1572617741","https://openalex.org/W1973166496","https://openalex.org/W1974122416","https://openalex.org/W1987403652","https://openalex.org/W1998902021","https://openalex.org/W2009985306","https://openalex.org/W2012437014","https://openalex.org/W2018225490","https://openalex.org/W2070299075","https://openalex.org/W2072132691","https://openalex.org/W2104215969","https://openalex.org/W2121743872","https://openalex.org/W2159612519","https://openalex.org/W2330793397","https://openalex.org/W2525918983","https://openalex.org/W2591911531","https://openalex.org/W2750714358","https://openalex.org/W2887308724","https://openalex.org/W2904537507","https://openalex.org/W2963706349","https://openalex.org/W2963879940"],"related_works":[],"abstract_inverted_index":{"We":[0],"give":[1],"the":[2,33,42,47,61,76,90,108,142,150,158,164,182,210],"first":[3],"mathematically":[4],"rigorous":[5],"analysis":[6,14,140],"of":[7,46,63,75,92,96,110,124,144,157,166,184],"an":[8,214],"emerging":[9],"approach":[10],"to":[11,31,103,120,200],"finite":[12,53],"element":[13,54],"(see,":[15],"e.g.,":[16],"Bauer":[17],"et":[18],"al.":[19],"[Appl.":[20],"Numer.":[21],"Math.,":[22],"122":[23],"(2017),":[24],"pp.":[25],"14--38]),":[26],"which":[27],"we":[28,180],"hereby":[29],"refer":[30],"as":[32],"surrogate":[34,77,147],"matrix":[35,78,97],"methodology.":[36],"This":[37],"methodology":[38,79,116,159],"is":[39,80,160,207],"based":[40],"on":[41,60],"piecewise":[43],"smooth":[44,64],"approximation":[45],"matrices":[48],"involved":[49],"in":[50,82,188,204],"a":[51,93,121,137,145,189,201],"standard":[52],"discretization.":[55],"In":[56,176,196],"particular,":[57],"it":[58],"relies":[59],"projection":[62],"so-called":[65],"stencil":[66,86],"functions":[67],"onto":[68],"high-order":[69],"polynomial":[70],"subspaces.":[71],"The":[72,155],"performance":[73],"advantage":[74],"seen":[81],"constructions":[83,100],"where":[84],"each":[85],"function":[87],"uniquely":[88],"determines":[89],"values":[91],"significant":[94],"collection":[95],"entries.":[98],"Such":[99],"are":[101],"shown":[102],"be":[104,118],"widely":[105],"achievable":[106],"through":[107,163],"use":[109],"locally":[111],"structured":[112],"meshes.":[113],"Therefore,":[114],"this":[115],"can":[117],"applied":[119],"wide":[122],"variety":[123],"physically":[125],"meaningful":[126],"problems,":[127],"including":[128],"nonlinear":[129,173],"problems":[130,132],"and":[131,172],"with":[133,192,213],"curvilinear":[134],"geometries.":[135],"Rigorous":[136],"priori":[138],"error":[139],"certifies":[141],"convergence":[143],"novel":[146,167],"method":[148,212],"for":[149,169],"variable":[151],"coefficient":[152],"Poisson":[153],"equation.":[154],"flexibility":[156],"also":[161],"demonstrated":[162],"construction":[165],"methods":[168,187],"linear":[170],"elasticity":[171],"diffusion":[174],"problems.":[175],"numerous":[177],"numerical":[178],"experiments,":[179,198],"demonstrate":[181],"efficacy":[183],"these":[185],"new":[186],"matrix-free":[190],"environment":[191],"geometric":[193],"multigrid":[194],"solvers.":[195],"our":[197],"up":[199],"twenty-fold":[202],"decrease":[203],"computation":[205],"time":[206],"witnessed":[208],"over":[209],"classical":[211],"otherwise":[215],"identical":[216],"implementation.":[217]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2019-03-02T00:00:00"}
