{"id":"https://openalex.org/W4400580907","doi":"https://doi.org/10.1137/23m1573963","title":"Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra","display_name":"Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra","publication_year":2024,"publication_date":"2024-07-12","ids":{"openalex":"https://openalex.org/W4400580907","doi":"https://doi.org/10.1137/23m1573963"},"language":"en","primary_location":{"id":"doi:10.1137/23m1573963","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1573963","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/A5023813245","display_name":"Tristan Montoya","orcid":"https://orcid.org/0000-0002-4259-1449"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Tristan Montoya","raw_affiliation_strings":["Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto M3H 5T6, ON, Canada"],"raw_orcid":"https://orcid.org/0000-0002-4259-1449","affiliations":[{"raw_affiliation_string":"Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto M3H 5T6, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110656578","display_name":"David W. Zingg","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David W. Zingg","raw_affiliation_strings":["Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto M3H 5T6, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto M3H 5T6, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023813245"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":1.3828,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82752835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"46","issue":"4","first_page":"A2270","last_page":"A2297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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":0.9980999827384949,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/mathematics","display_name":"Mathematics","score":0.8386926651000977},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.7511318922042847},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.7312737703323364},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5495742559432983},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5049105286598206},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.46923261880874634},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.45279961824417114},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42714211344718933},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4040912687778473},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33675462007522583},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3191404342651367}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8386926651000977},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.7511318922042847},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.7312737703323364},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5495742559432983},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5049105286598206},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.46923261880874634},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.45279961824417114},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42714211344718933},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4040912687778473},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33675462007522583},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3191404342651367},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1573963","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1573963","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322015","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W96454744","https://openalex.org/W321261355","https://openalex.org/W1570370571","https://openalex.org/W1958241752","https://openalex.org/W1972119727","https://openalex.org/W1976584147","https://openalex.org/W1985144286","https://openalex.org/W1986763038","https://openalex.org/W2007567241","https://openalex.org/W2028680761","https://openalex.org/W2037414284","https://openalex.org/W2066985111","https://openalex.org/W2073839654","https://openalex.org/W2091183786","https://openalex.org/W2127570421","https://openalex.org/W2619381903","https://openalex.org/W2768455612","https://openalex.org/W2772909518","https://openalex.org/W2792127410","https://openalex.org/W2808011578","https://openalex.org/W2949414414","https://openalex.org/W2962801132","https://openalex.org/W2962834680","https://openalex.org/W2963095461","https://openalex.org/W2963179762","https://openalex.org/W2963482900","https://openalex.org/W2977985257","https://openalex.org/W3011811412","https://openalex.org/W3024549653","https://openalex.org/W3080863366","https://openalex.org/W3122973256","https://openalex.org/W3128442286","https://openalex.org/W4205236375","https://openalex.org/W4251197584"],"related_works":["https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W3119989344","https://openalex.org/W2025402442","https://openalex.org/W2098990162","https://openalex.org/W2993813190","https://openalex.org/W2567351266","https://openalex.org/W4386687603","https://openalex.org/W4307007469","https://openalex.org/W4288558775"],"abstract_inverted_index":{".We":[0],"present":[1],"an":[2],"extension":[3],"of":[4,22,26,34,43,58,71,89,123,139,182,200],"the":[5,20,31,41,63,87,99,111,115,121,124,140,152,180,207,219,229,241,252],"summation-by-parts":[6],"(SBP)":[7],"framework":[8],"to":[9,149,162,172,176,239],"tensor-product":[10,79,100],"spectral-element":[11,56,91],"operators":[12,57,82,168],"in":[13,179,243,251],"collapsed":[14,125],"coordinates.":[15],"The":[16,157],"proposed":[17,158],"approach":[18,113],"enables":[19],"construction":[21],"provably":[23],"stable":[24],"discretizations":[25],"arbitrary":[27],"order":[28,60],"which":[29,61],"combine":[30],"geometric":[32],"flexibility":[33],"unstructured":[35],"triangular":[36,53],"and":[37,54,143,169,212,228,234,250],"tetrahedral":[38,55],"meshes":[39,132],"with":[40,120],"efficiency":[42],"sum-factorization":[44],"algorithms.":[45],"Specifically,":[46],"a":[47,68,78,136,144,192,216],"methodology":[48],"is":[49,147],"developed":[50],"for":[51,130,196],"constructing":[52],"any":[59],"possess":[62],"SBP":[64,167],"property":[65],"(i.e.,":[66],"satisfying":[67],"discrete":[69],"analogue":[70],"integration":[72],"by":[73,226],"parts)":[74],"as":[75,77,103,105,215],"well":[76,104],"decomposition.":[80],"Such":[81],"are":[83,133,160,170,246],"then":[84],"employed":[85],"within":[86],"context":[88,181],"discontinuous":[90],"methods":[92],"based":[93],"on":[94,187],"nodal":[95],"expansions":[96,107],"collocated":[97],"at":[98,191,248],"quadrature":[101],"nodes":[102],"modal":[106,154],"employing":[108],"Proriol\u2013Koornwinder\u2013Dubiner":[109],"polynomials,":[110],"latter":[112],"resolving":[114],"time":[116],"step":[117],"limitation":[118],"associated":[119],"singularity":[122],"coordinate":[126],"transformation.":[127],"Energy-stable":[128],"formulations":[129],"curvilinear":[131,153],"obtained":[134],"using":[135,164],"skew-symmetric":[137],"splitting":[138],"metric":[141],"terms,":[142],"weight-adjusted":[145],"approximation":[146],"used":[148],"efficiently":[150],"invert":[151],"mass":[155],"matrix.":[156],"schemes":[159,178],"compared":[161],"those":[163],"nontensorial":[165],"multidimensional":[166],"found":[171],"offer":[173],"comparable":[174],"accuracy":[175],"such":[177],"smooth":[183],"linear":[184],"advection":[185],"problems":[186],"curved":[188],"meshes,":[189],"but":[190],"reduced":[193],"computational":[194,201],"cost":[195],"higher":[197],"polynomial":[198],"degrees.Reproducibility":[199],"results.This":[202],"paper":[203,245],"has":[204],"been":[205],"awarded":[206],"\"SIAM":[208],"Reproducibility":[209],"Badge:":[210],"Code":[211,233],"Data":[213],"Available\"":[214],"recognition":[217],"that":[218,236],"authors":[220],"have":[221],"followed":[222],"reproducibility":[223],"principles":[224],"valued":[225],"SISC":[227],"scientific":[230],"computing":[231],"community.":[232],"data":[235],"allow":[237],"readers":[238],"reproduce":[240],"results":[242],"this":[244],"available":[247],"https://github.com/tristanmontoya/ReproduceSBPSimplex":[249],"supplementary":[253],"materials":[254],"(reproducibility_repository.zip":[255],"[35.7MB]).Keywordsspectral-elementsummation-by-partstensor-producttrianglestetrahedraMSC":[256],"codes65M1265M6065M70":[257]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
