{"id":"https://openalex.org/W4391353546","doi":"https://doi.org/10.1137/23m1569332","title":"Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells","display_name":"Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells","publication_year":2024,"publication_date":"2024-01-30","ids":{"openalex":"https://openalex.org/W4391353546","doi":"https://doi.org/10.1137/23m1569332"},"language":"en","primary_location":{"id":"doi:10.1137/23m1569332","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1569332","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/A5018522541","display_name":"Jeffrey S. Ovall","orcid":"https://orcid.org/0000-0003-1944-2872"},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeffrey S. Ovall","raw_affiliation_strings":["Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA"],"raw_orcid":"https://orcid.org/0000-0003-1944-2872","affiliations":[{"raw_affiliation_string":"Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA","institution_ids":["https://openalex.org/I126345244"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101448916","display_name":"Samuel E. Reynolds","orcid":"https://orcid.org/0000-0002-7489-6474"},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel E. Reynolds","raw_affiliation_strings":["Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA","institution_ids":["https://openalex.org/I126345244"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018522541"],"corresponding_institution_ids":["https://openalex.org/I126345244"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01276863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"1","first_page":"A338","last_page":"A359"},"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":0.9991999864578247,"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":0.9991999864578247,"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":0.9902999997138977,"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/T10514","display_name":"Numerical methods in engineering","score":0.9900000095367432,"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/mathematics","display_name":"Mathematics","score":0.8069201111793518},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7225103378295898},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6604119539260864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4309339225292206},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.41787290573120117},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0951952338218689},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.09102451801300049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8069201111793518},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7225103378295898},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6604119539260864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4309339225292206},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.41787290573120117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0951952338218689},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.09102451801300049},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1569332","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1569332","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:pdxscholar.library.pdx.edu:mth_fac-1405","is_oa":false,"landing_page_url":"https://pdxscholar.library.pdx.edu/mth_fac/401","pdf_url":null,"source":{"id":"https://openalex.org/S4377196300","display_name":"PDXScholar  (Portland State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126345244","host_organization_name":"Portland State University","host_organization_lineage":["https://openalex.org/I126345244"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Statistics Faculty Publications and Presentations","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4967265980","display_name":"RTG: Program in Computation- and Data-Enabled Science","funder_award_id":"2136228","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G90089428","display_name":"A Fitted Finite Element Method for the Modeling of Complex Materials","funder_award_id":"2012285","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W136754282","https://openalex.org/W952213083","https://openalex.org/W1488217046","https://openalex.org/W1697438153","https://openalex.org/W1998527589","https://openalex.org/W2013776667","https://openalex.org/W2030622214","https://openalex.org/W2047049848","https://openalex.org/W2089958289","https://openalex.org/W2101937655","https://openalex.org/W2107205741","https://openalex.org/W2154835217","https://openalex.org/W2168914934","https://openalex.org/W2202877124","https://openalex.org/W2270650927","https://openalex.org/W2298381282","https://openalex.org/W2349468399","https://openalex.org/W2490126082","https://openalex.org/W2766906678","https://openalex.org/W2769410452","https://openalex.org/W2811423774","https://openalex.org/W2889483471","https://openalex.org/W2963633140","https://openalex.org/W2963762466","https://openalex.org/W2963906341","https://openalex.org/W3003257820","https://openalex.org/W3018104034","https://openalex.org/W3034994174","https://openalex.org/W3035965352","https://openalex.org/W3044496412","https://openalex.org/W3048769302","https://openalex.org/W3084401381","https://openalex.org/W3099878876","https://openalex.org/W3125870234","https://openalex.org/W3167093874","https://openalex.org/W4239197373","https://openalex.org/W4243282334"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Abstract.":[0],"In":[1,27],"recent":[2],"years,":[3],"there":[4],"has":[5,201],"been":[6,202],"significant":[7],"interest":[8,115],"in":[9,41,48,80,135,240],"the":[10,28,58,77,112,122,129,159,179,189,204,216,226,238,249],"development":[11],"of":[12,57,70,76,97,114,124,141,161,170,192,196],"finite":[13,49,73,84],"element":[14,50,74,82,85,89],"methods":[15,86],"defined":[16,72,94],"on":[17],"meshes":[18],"that":[19,111,215,233],"include":[20],"rather":[21],"general":[22],"polytopes":[23],"and":[24,64,87,105,209,225,231,248],"curvilinear":[25],"polygons.":[26],"present":[29],"work,":[30],"we":[31],"provide":[32],"tools":[33],"necessary":[34],"to":[35,119,131,151,166,236],"employ":[36],"multiply":[37],"connected":[38],"mesh":[39,125],"cells":[40,45],"planar":[42],"domains,":[43],"i.e.,":[44],"with":[46],"holes,":[47],"computations.":[51],"Our":[52],"focus":[53],"is":[54,144,175],"efficient":[55],"evaluation":[56],"[Formula:":[59,65,180,255],"see":[60,66,181,256],"text]":[61,67,182,257],"semi-inner":[62],"product":[63,69],"inner":[68,183],"implicitly":[71],"functions":[75,92],"types":[78],"arising":[79],"boundary":[81,107],"based":[83],"virtual":[88],"methods.":[90],"Such":[91],"are":[93,243],"as":[95,156,158,212],"solutions":[96],"Poisson":[98],"problems":[99],"having":[100],"a":[101,146,153,171,213],"polynomial":[102],"source":[103],"term":[104],"continuous":[106],"data.":[108],"We":[109],"show":[110],"integrals":[113,120],"can":[116],"be":[117],"reduced":[118],"along":[121],"boundaries":[123],"cells,":[126],"thereby":[127],"avoiding":[128],"need":[130],"perform":[132],"any":[133],"computations":[134],"cell":[136],"interiors.":[137],"The":[138],"dominating":[139],"cost":[140],"this":[142,193,241],"reduction":[143],"solving":[145],"relatively":[147],"small":[148],"Nystr\u00f6m":[149,164],"system":[150],"obtain":[152,167],"Dirichlet-to-Neumann":[154],"map,":[155],"well":[157],"solution":[160],"two":[162],"more":[163],"systems":[165],"an":[168],"\u201canti-Laplacian\u201d":[169],"harmonic":[172],"function,":[173],"which":[174],"used":[176],"for":[177],"computing":[178,228],"product.":[184],"Several":[185],"numerical":[186],"examples":[187],"demonstrate":[188],"high-order":[190],"accuracy":[191],"approach.":[194],"Reproducibility":[195,206],"computational":[197],"results.":[198],"This":[199],"paper":[200,242],"awarded":[203],"\u201cSIAM":[205],"Badge:":[207],"code":[208],"data":[210,232],"available\u201d":[211],"recognition":[214],"authors":[217],"have":[218],"followed":[219],"reproducibility":[220],"principles":[221],"valued":[222],"by":[223],"SISC":[224],"scientific":[227],"community.":[229],"Code":[230],"allow":[234],"readers":[235],"reproduce":[237],"results":[239],"available":[244],"at":[245],"both":[246],"https://github.com/samreynoldsmath/PuncturedFEM":[247],"supplementary":[250],"materials":[251],"(":[252],"PuncturedFEM_v0_2_5.zip":[253],"[1.75MB]).":[254]},"counts_by_year":[],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}
