{"id":"https://openalex.org/W3040832794","doi":"https://doi.org/10.1145/3442378","title":"fenicsR13: A Tensorial Mixed Finite Element Solver for the Linear R13 Equations Using the FEniCS Computing Platform","display_name":"fenicsR13: A Tensorial Mixed Finite Element Solver for the Linear R13 Equations Using the FEniCS Computing Platform","publication_year":2021,"publication_date":"2021-04-20","ids":{"openalex":"https://openalex.org/W3040832794","doi":"https://doi.org/10.1145/3442378","mag":"3040832794"},"language":"en","primary_location":{"id":"doi:10.1145/3442378","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3442378","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2007.05944","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079339105","display_name":"Lambert Theisen","orcid":"https://orcid.org/0000-0001-5460-5425"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lambert Theisen","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany","CCSE - Center for Computational Engineering Science [Aachen] (Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"CCSE - Center for Computational Engineering Science [Aachen] (Germany)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054338152","display_name":"Manuel Torrilhon","orcid":"https://orcid.org/0000-0003-0008-2061"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Manuel Torrilhon","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany","CCSE - Center for Computational Engineering Science [Aachen] (Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"CCSE - Center for Computational Engineering Science [Aachen] (Germany)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":2.2826,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.87133875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"47","issue":"2","first_page":"1","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9995999932289124,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.8501019477844238},{"id":"https://openalex.org/keywords/python","display_name":"Python (programming language)","score":0.7173562049865723},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6983541250228882},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6541323661804199},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4855656325817108},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4843655526638031},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48167574405670166},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.45709648728370667},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.45049089193344116},{"id":"https://openalex.org/keywords/source-code","display_name":"Source code","score":0.43167823553085327},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.37661218643188477},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36804628372192383},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3226114511489868},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23376598954200745},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10217157006263733}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.8501019477844238},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.7173562049865723},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6983541250228882},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6541323661804199},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4855656325817108},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4843655526638031},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48167574405670166},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.45709648728370667},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.45049089193344116},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.43167823553085327},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.37661218643188477},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36804628372192383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3226114511489868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23376598954200745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10217157006263733},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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:10.1145/3442378","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3442378","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2007.05944","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.05944","pdf_url":"https://arxiv.org/pdf/2007.05944","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":"pmh:oai:HAL:hal-04671360v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04671360","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Mathematical Software, 2021, 47 (2), pp.1-29. &#x27E8;10.1145/3442378&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2007.05944","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.05944","pdf_url":"https://arxiv.org/pdf/2007.05944","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/G7181204602","display_name":null,"funder_award_id":"IRTG 2379","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W962773237","https://openalex.org/W1513593694","https://openalex.org/W1598578620","https://openalex.org/W1645527346","https://openalex.org/W1673742782","https://openalex.org/W1972727539","https://openalex.org/W1973166496","https://openalex.org/W1983655899","https://openalex.org/W1998442001","https://openalex.org/W1998518575","https://openalex.org/W2002527269","https://openalex.org/W2005304385","https://openalex.org/W2023141162","https://openalex.org/W2039661575","https://openalex.org/W2048948096","https://openalex.org/W2061374290","https://openalex.org/W2068102804","https://openalex.org/W2068154398","https://openalex.org/W2070299075","https://openalex.org/W2100418324","https://openalex.org/W2107979247","https://openalex.org/W2112311198","https://openalex.org/W2124866833","https://openalex.org/W2127786991","https://openalex.org/W2128095813","https://openalex.org/W2146396721","https://openalex.org/W2168522485","https://openalex.org/W2184960032","https://openalex.org/W2212370034","https://openalex.org/W2271024129","https://openalex.org/W2496364119","https://openalex.org/W2592319153","https://openalex.org/W2592568386","https://openalex.org/W2605851636","https://openalex.org/W2729832944","https://openalex.org/W2752758543","https://openalex.org/W2764174803","https://openalex.org/W2801593948","https://openalex.org/W2924873015","https://openalex.org/W2970663352","https://openalex.org/W3001184904","https://openalex.org/W3004431888","https://openalex.org/W3012593318","https://openalex.org/W3021082965","https://openalex.org/W3037378812","https://openalex.org/W3039049215","https://openalex.org/W3040832794","https://openalex.org/W3083512472","https://openalex.org/W3100689368","https://openalex.org/W3104566386","https://openalex.org/W3111251720","https://openalex.org/W4211261807","https://openalex.org/W4230194830","https://openalex.org/W4234573198","https://openalex.org/W4245654886"],"related_works":["https://openalex.org/W1667647204","https://openalex.org/W2404647514","https://openalex.org/W4247536566","https://openalex.org/W2018477250","https://openalex.org/W3119814709","https://openalex.org/W4241418540","https://openalex.org/W1508895727","https://openalex.org/W2725786787","https://openalex.org/W2789551765","https://openalex.org/W3011358647"],"abstract_inverted_index":{"We":[0,31,137],"present":[1],"a":[2,33],"mixed":[3],"finite":[4],"element":[5],"solver":[6,58,143],"for":[7,51,63,70],"the":[8,22,27,38,72,82,88,98,102,109,112,122,139],"linearized":[9],"regularized":[10],"13-moment":[11],"equations":[12],"of":[13,41,111,124],"non-equilibrium":[14],"gas":[15,126],"dynamics.":[16],"The":[17,56],"Python":[18],"implementation":[19],"builds":[20],"upon":[21],"software":[23,83],"tools":[24],"provided":[25,86],"by":[26,87],"FEniCS":[28],"computing":[29],"platform.":[30],"describe":[32],"new":[34],"tensorial":[35,65],"approach":[36],"utilizing":[37],"extension":[39],"capabilities":[40],"FEniCS\u2019":[42],"Unified":[43,89],"Form":[44,90],"Language":[45,91],"to":[46,77],"define":[47],"required":[48],"differential":[49],"operators":[50],"tensors":[52],"above":[53],"second":[54],"degree.":[55],"presented":[57],"serves":[59],"as":[60],"an":[61,93],"example":[62],"implementing":[64],"variational":[66],"formulations":[67],"in":[68],"FEniCS,":[69],"which":[71],"documentation":[73],"and":[74,101,141],"literature":[75],"seem":[76],"be":[78],"very":[79],"sparse.":[80],"Using":[81],"abstraction":[84],"levels":[85],"allows":[92],"almost":[94],"one-to-one":[95],"correspondence":[96],"between":[97],"underlying":[99],"mathematics":[100],"resulting":[103],"source":[104],"code.":[105],"Test":[106],"cases":[107,133],"support":[108],"correctness":[110],"proposed":[113],"method":[114],"using":[115],"validation":[116],"with":[117],"exact":[118],"solutions.":[119],"To":[120],"justify":[121],"usage":[123],"extended":[125],"flow":[127],"models,":[128],"we":[129],"discuss":[130],"typical":[131],"application":[132],"involving":[134],"rarefaction":[135],"effects.":[136],"provide":[138],"documented":[140],"validated":[142],"publicly.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-07-16T00:00:00"}
