{"id":"https://openalex.org/W2889483471","doi":"https://doi.org/10.1007/s10915-018-0802-y","title":"Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods","display_name":"Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods","publication_year":2018,"publication_date":"2018-08-29","ids":{"openalex":"https://openalex.org/W2889483471","doi":"https://doi.org/10.1007/s10915-018-0802-y","mag":"2889483471"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-018-0802-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-0802-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-0802-y.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-0802-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063675442","display_name":"Paola F. Antonietti","orcid":"https://orcid.org/0000-0002-2138-3878"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paola F. Antonietti","raw_affiliation_strings":["MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leondardo da Vinci 32, 20133, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leondardo da Vinci 32, 20133, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035584552","display_name":"Paul Houston","orcid":"https://orcid.org/0000-0002-3588-2029"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Paul Houston","raw_affiliation_strings":["School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065701859","display_name":"Giorgio Pennesi","orcid":"https://orcid.org/0000-0003-3118-9283"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giorgio Pennesi","raw_affiliation_strings":["MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leondardo da Vinci 32, 20133, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leondardo da Vinci 32, 20133, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035584552"],"corresponding_institution_ids":["https://openalex.org/I142263535"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.9345,"has_fulltext":true,"cited_by_count":47,"citation_normalized_percentile":{"value":0.93677326,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"77","issue":"3","first_page":"1339","last_page":"1370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9993000030517578,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.8345645666122437},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7423797845840454},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6256108283996582},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6245988011360168},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.5891449451446533},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5226490497589111},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4911453425884247},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4580466151237488},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.4378988742828369},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4120084047317505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3981868028640747},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2320350706577301}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8345645666122437},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7423797845840454},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6256108283996582},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6245988011360168},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.5891449451446533},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5226490497589111},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4911453425884247},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4580466151237488},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.4378988742828369},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4120084047317505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3981868028640747},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2320350706577301},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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":3,"locations":[{"id":"doi:10.1007/s10915-018-0802-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-0802-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-0802-y.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:1031787","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/1031787","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:re.public.polimi.it:11311/1061214","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s10915-018-0802-y","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10915-018-0802-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-0802-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-0802-y.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5158774923","display_name":null,"funder_award_id":"RBSI14VT0S","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G87317965","display_name":null,"funder_award_id":"2015-0182","funder_id":"https://openalex.org/F4320321499","funder_display_name":"Fondazione Cariplo"}],"funders":[{"id":"https://openalex.org/F4320321499","display_name":"Fondazione Cariplo","ror":"https://ror.org/01gb56c55"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320326078","display_name":"Regione Lombardia","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2889483471.pdf","grobid_xml":"https://content.openalex.org/works/W2889483471.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W178921856","https://openalex.org/W568020624","https://openalex.org/W1488217046","https://openalex.org/W1514379823","https://openalex.org/W1528879660","https://openalex.org/W1585842086","https://openalex.org/W1738124305","https://openalex.org/W1790345590","https://openalex.org/W1904912646","https://openalex.org/W1963803848","https://openalex.org/W1967710518","https://openalex.org/W1968754888","https://openalex.org/W1974288061","https://openalex.org/W1978682560","https://openalex.org/W1982576260","https://openalex.org/W1993443533","https://openalex.org/W1998894128","https://openalex.org/W1999747594","https://openalex.org/W2000602850","https://openalex.org/W2004110058","https://openalex.org/W2004791619","https://openalex.org/W2008325195","https://openalex.org/W2009012285","https://openalex.org/W2010549570","https://openalex.org/W2020005049","https://openalex.org/W2028185400","https://openalex.org/W2036595722","https://openalex.org/W2038653724","https://openalex.org/W2040382997","https://openalex.org/W2042387166","https://openalex.org/W2045237378","https://openalex.org/W2063625946","https://openalex.org/W2066240717","https://openalex.org/W2070232376","https://openalex.org/W2073237186","https://openalex.org/W2079211982","https://openalex.org/W2091183786","https://openalex.org/W2097158696","https://openalex.org/W2097964994","https://openalex.org/W2099760642","https://openalex.org/W2100520873","https://openalex.org/W2111450821","https://openalex.org/W2116404756","https://openalex.org/W2117496726","https://openalex.org/W2130350269","https://openalex.org/W2142596047","https://openalex.org/W2158943855","https://openalex.org/W2159668006","https://openalex.org/W2167745263","https://openalex.org/W2168914934","https://openalex.org/W2170976551","https://openalex.org/W2200733728","https://openalex.org/W2280689009","https://openalex.org/W2321807048","https://openalex.org/W2404390473","https://openalex.org/W2537434835","https://openalex.org/W2558016433","https://openalex.org/W2759204989","https://openalex.org/W2883313970","https://openalex.org/W2889483471","https://openalex.org/W2907521988","https://openalex.org/W2908252308","https://openalex.org/W2962814658","https://openalex.org/W2962924286","https://openalex.org/W2963313365","https://openalex.org/W2964307594","https://openalex.org/W4229971479","https://openalex.org/W4240596267","https://openalex.org/W4241481980","https://openalex.org/W4289684174","https://openalex.org/W4293028925","https://openalex.org/W4297968680","https://openalex.org/W4379503616"],"related_works":["https://openalex.org/W2035232447","https://openalex.org/W4237740072","https://openalex.org/W2056088350","https://openalex.org/W2144321310","https://openalex.org/W2001419904","https://openalex.org/W2065399919","https://openalex.org/W1982234448","https://openalex.org/W66167457","https://openalex.org/W2560252838","https://openalex.org/W2024733137"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"present":[4],"efficient":[5],"quadrature":[6,77],"rules":[7],"for":[8],"the":[9,45,53,56,62,65,80,83,87,90,96],"numerical":[10],"approximation":[11],"of":[12,14,28,41,55,64,82,89,110],"integrals":[13],"polynomial":[15],"functions":[16],"over":[17],"general":[18],"polygonal/polyhedral":[19],"elements":[20],"that":[21],"do":[22],"not":[23],"require":[24],"an":[25,72],"explicit":[26],"construction":[27],"a":[29],"sub-tessellation":[30],"into":[31],"triangular/tetrahedral":[32],"elements.":[33],"The":[34],"method":[35],"is":[36],"based":[37],"on":[38],"successive":[39],"application":[40],"Stokes\u2019":[42],"theorem;":[43],"thereby,":[44],"underlying":[46],"integral":[47],"may":[48],"be":[49],"evaluated":[50],"using":[51],"only":[52],"values":[54],"integrand":[57],"and":[58,68,98],"its":[59],"derivatives":[60],"at":[61],"vertices":[63,81],"polytopic":[66],"domain,":[67],"hence":[69],"leads":[70],"to":[71],"exact":[73],"cubature":[74],"rule":[75],"whose":[76],"points":[78],"are":[79],"polytope.":[84],"We":[85],"demonstrate":[86],"capabilities":[88],"proposed":[91],"approach":[92],"by":[93],"efficiently":[94],"computing":[95],"stiffness":[97],"mass":[99],"matrices":[100],"arising":[101],"from":[102],"hp-version":[103],"symmetric":[104],"interior":[105],"penalty":[106],"discontinuous":[107],"Galerkin":[108],"discretizations":[109],"second-order":[111],"elliptic":[112],"partial":[113],"differential":[114],"equations.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}