{"id":"https://openalex.org/W2789952879","doi":"https://doi.org/10.1137/17m1129751","title":"Automatic Symbolic Computation for Discontinuous Galerkin Finite Element Methods","display_name":"Automatic Symbolic Computation for Discontinuous Galerkin Finite Element Methods","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2789952879","doi":"https://doi.org/10.1137/17m1129751","mag":"2789952879"},"language":"en","primary_location":{"id":"doi:10.1137/17m1129751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1129751","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1804.02338","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035584552","display_name":"Paul Houston","orcid":"https://orcid.org/0000-0002-3588-2029"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul Houston","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045312608","display_name":"Nathan Sime","orcid":"https://orcid.org/0000-0002-2319-048X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nathan Sime","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035584552"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.02253948,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"40","issue":"3","first_page":"C327","last_page":"C357"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6522184610366821},{"id":"https://openalex.org/keywords/multiphysics","display_name":"Multiphysics","score":0.6131872534751892},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5979025363922119},{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"Automatic differentiation","score":0.5928512215614319},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5897271633148193},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.587192952632904},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.5335187315940857},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5042101144790649},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.49563515186309814},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4871954321861267},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4629884958267212},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.43497759103775024},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42755404114723206},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3902502655982971},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35726767778396606},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3480381369590759},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34521520137786865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3116919994354248},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12009832262992859},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11973333358764648},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09139031171798706}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6522184610366821},{"id":"https://openalex.org/C46435376","wikidata":"https://www.wikidata.org/wiki/Q1829750","display_name":"Multiphysics","level":3,"score":0.6131872534751892},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5979025363922119},{"id":"https://openalex.org/C133512626","wikidata":"https://www.wikidata.org/wiki/Q787371","display_name":"Automatic differentiation","level":3,"score":0.5928512215614319},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5897271633148193},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.587192952632904},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.5335187315940857},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5042101144790649},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.49563515186309814},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4871954321861267},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4629884958267212},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.43497759103775024},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42755404114723206},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3902502655982971},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35726767778396606},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3480381369590759},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34521520137786865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3116919994354248},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12009832262992859},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11973333358764648},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09139031171798706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/17m1129751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1129751","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:1804.02338","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.02338","pdf_url":"https://arxiv.org/pdf/1804.02338","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"},{"id":"mag:2789952879","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.02338v1","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:eprints.nottingham.ac.uk:50449","is_oa":true,"landing_page_url":"http://eprints.nottingham.ac.uk/50449/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402013","display_name":"Nottingham ePrints (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":"Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:943433","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/943433","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":null,"raw_type":"acceptedVersion"},{"id":"doi:10.48550/arxiv.1804.02338","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.02338","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1804.02338","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.02338","pdf_url":"https://arxiv.org/pdf/1804.02338","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W608535524","https://openalex.org/W1583515859","https://openalex.org/W1989153275","https://openalex.org/W1994841670","https://openalex.org/W2029197194","https://openalex.org/W2050051055","https://openalex.org/W2071430609","https://openalex.org/W2082002555","https://openalex.org/W2082187902","https://openalex.org/W2089366649","https://openalex.org/W2102295719","https://openalex.org/W2106476375","https://openalex.org/W2109314821","https://openalex.org/W2110187357","https://openalex.org/W2121296933","https://openalex.org/W2130350269","https://openalex.org/W2136256106","https://openalex.org/W2622561926"],"related_works":["https://openalex.org/W2964123168","https://openalex.org/W2073833852","https://openalex.org/W395566770","https://openalex.org/W181271750","https://openalex.org/W2122331903","https://openalex.org/W2110868652","https://openalex.org/W2014523017","https://openalex.org/W2296435929","https://openalex.org/W1717332568","https://openalex.org/W2749378979","https://openalex.org/W2076823026","https://openalex.org/W2018788382","https://openalex.org/W1857817569","https://openalex.org/W2977858512","https://openalex.org/W2082511834","https://openalex.org/W2125202430","https://openalex.org/W206134560","https://openalex.org/W2088028858","https://openalex.org/W2025751258","https://openalex.org/W977568565"],"abstract_inverted_index":{"The":[0],"implementation":[1,172],"of":[2,18,29,34,41,50,77,81,89,92,110,113,133,144,171,173,179,182],"discontinuous":[3],"Galerkin":[4],"finite":[5],"element":[6],"methods":[7],"(DGFEMs)":[8],"represents":[9],"a":[10,46,51,55,100,130,137,180],"very":[11],"challenging":[12],"computational":[13],"task,":[14],"particularly":[15],"for":[16,97,140,175],"systems":[17,112],"coupled":[19,111],"nonlinear":[20],"PDEs,":[21],"including":[22],"multiphysics":[23],"problems,":[24],"whose":[25,59],"parameters":[26],"may":[27],"consist":[28],"power":[30],"series":[31],"or":[32],"functionals":[33],"the":[35,39,63,74,78,87,93,108,141,153,159,169,176],"solution":[36],"variables.":[37],"Thereby,":[38,124],"exploitation":[40],"symbolic":[42,106],"algebra":[43],"to":[44,122],"express":[45],"given":[47],"DGFEM":[48,94,145],"approximation":[49,178],"PDE":[52,183],"problem":[53],"within":[54,99,152],"high":[56],"level":[57],"language,":[58],"syntax":[60],"closely":[61],"resembles":[62],"mathematical":[64],"definition,":[65],"is":[66],"an":[67],"invaluable":[68],"tool.":[69],"Indeed,":[70],"this":[71,126],"then":[72],"facilitates":[73],"automatic":[75,142],"assembly":[76],"resulting":[79],"system":[80],"(nonlinear)":[82],"equations,":[83],"as":[84,86],"well":[85],"computation":[88,143],"Fr\u00e9chet":[90],"derivatives":[91],"scheme,":[95],"needed,":[96],"example,":[98],"Newton-type":[101],"solver.":[102],"However,":[103],"even":[104],"exploiting":[105,158],"algebra,":[107],"discretization":[109],"PDEs":[114],"can":[115],"still":[116],"be":[117],"extremely":[118],"verbose":[119],"and":[120],"hard":[121],"debug.":[123],"in":[125],"article":[127],"we":[128],"develop":[129],"further":[131],"layer":[132],"abstraction":[134],"by":[135],"designing":[136],"class":[138],"structure":[139],"formulations.":[146],"This":[147],"work":[148],"has":[149],"been":[150],"implemented":[151],"FEniCS":[154],"package,":[155],"based":[156],"on":[157],"Unified":[160],"Form":[161],"Language.":[162],"Numerical":[163],"examples":[164],"are":[165],"presented":[166],"which":[167],"highlight":[168],"simplicity":[170],"DGFEMs":[174],"numerical":[177],"range":[181],"problems.":[184]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
