{"id":"https://openalex.org/W3037005901","doi":"https://doi.org/10.1145/3466168","title":"Irksome: Automating Runge\u2013Kutta Time-stepping for Finite Element Methods","display_name":"Irksome: Automating Runge\u2013Kutta Time-stepping for Finite Element Methods","publication_year":2021,"publication_date":"2021-09-28","ids":{"openalex":"https://openalex.org/W3037005901","doi":"https://doi.org/10.1145/3466168","mag":"3037005901"},"language":"en","primary_location":{"id":"doi:10.1145/3466168","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3466168","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.16282","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102855060","display_name":"Patrick E. Farrell","orcid":"https://orcid.org/0000-0002-1241-7060"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Patrick E. Farrell","raw_affiliation_strings":["University of Oxford, UK","University of Oxford"],"affiliations":[{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018380170","display_name":"Robert C. Kirby","orcid":"https://orcid.org/0009-0009-9663-8394"},"institutions":[{"id":"https://openalex.org/I157394403","display_name":"Baylor University","ror":"https://ror.org/005781934","country_code":"US","type":"education","lineage":["https://openalex.org/I157394403"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert C. Kirby","raw_affiliation_strings":["Baylor University, Waco","\u2020Baylor University"],"affiliations":[{"raw_affiliation_string":"Baylor University, Waco","institution_ids":["https://openalex.org/I157394403"]},{"raw_affiliation_string":"\u2020Baylor University","institution_ids":["https://openalex.org/I157394403"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088333068","display_name":"Jorge Marchena-Men\u00e9ndez","orcid":"https://orcid.org/0000-0002-9612-3069"},"institutions":[{"id":"https://openalex.org/I157394403","display_name":"Baylor University","ror":"https://ror.org/005781934","country_code":"US","type":"education","lineage":["https://openalex.org/I157394403"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jorge Marchena-Men\u00e9ndez","raw_affiliation_strings":["Baylor University, Waco","\u2020Baylor University"],"affiliations":[{"raw_affiliation_string":"Baylor University, Waco","institution_ids":["https://openalex.org/I157394403"]},{"raw_affiliation_string":"\u2020Baylor University","institution_ids":["https://openalex.org/I157394403"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102855060"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":1.2479,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7453652,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"47","issue":"4","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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"}},{"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9990000128746033,"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.9365869760513306},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7679246664047241},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.6432174444198608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6017473936080933},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5667319297790527},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5444731116294861},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5246769785881042},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.473678857088089},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43767446279525757},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4269920587539673},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.42045876383781433},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3829194903373718},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.348810613155365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2939704656600952},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2547127902507782},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.24179363250732422},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15509635210037231},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14017489552497864},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11923253536224365},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.06779113411903381}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.9365869760513306},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7679246664047241},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.6432174444198608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6017473936080933},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5667319297790527},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5444731116294861},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5246769785881042},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.473678857088089},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43767446279525757},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4269920587539673},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.42045876383781433},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3829194903373718},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.348810613155365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2939704656600952},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2547127902507782},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.24179363250732422},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15509635210037231},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14017489552497864},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11923253536224365},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.06779113411903381},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/3466168","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3466168","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:2006.16282","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.16282","pdf_url":"https://arxiv.org/pdf/2006.16282","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:3037005901","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.16282.pdf","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:ora.ox.ac.uk:uuid:698a3e2f-193d-4995-aaf8-8b7d50bc0ebe","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:698a3e2f-193d-4995-aaf8-8b7d50bc0ebe","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"doi:10.48550/arxiv.2006.16282","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.16282","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:2006.16282","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.16282","pdf_url":"https://arxiv.org/pdf/2006.16282","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/G3957501995","display_name":null,"funder_award_id":"EP/R029423/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5750869995","display_name":null,"funder_award_id":"EP/R029423/1 and EP/V001493/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3037005901.pdf","grobid_xml":"https://content.openalex.org/works/W3037005901.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W209576205","https://openalex.org/W1153030042","https://openalex.org/W1544770838","https://openalex.org/W1964070472","https://openalex.org/W1966322936","https://openalex.org/W1973279410","https://openalex.org/W1977542511","https://openalex.org/W1980123729","https://openalex.org/W1983655899","https://openalex.org/W1986367849","https://openalex.org/W1991915199","https://openalex.org/W1995504856","https://openalex.org/W1998953621","https://openalex.org/W2005380085","https://openalex.org/W2015247199","https://openalex.org/W2026106782","https://openalex.org/W2033986961","https://openalex.org/W2041876368","https://openalex.org/W2043660290","https://openalex.org/W2050296550","https://openalex.org/W2051751432","https://openalex.org/W2054882618","https://openalex.org/W2055953382","https://openalex.org/W2057235791","https://openalex.org/W2059371748","https://openalex.org/W2096065504","https://openalex.org/W2096894484","https://openalex.org/W2097012771","https://openalex.org/W2100312757","https://openalex.org/W2107979247","https://openalex.org/W2112311198","https://openalex.org/W2116729868","https://openalex.org/W2119471187","https://openalex.org/W2123895340","https://openalex.org/W2146137988","https://openalex.org/W2168522485","https://openalex.org/W2297728627","https://openalex.org/W2346565616","https://openalex.org/W2463898732","https://openalex.org/W2581973763","https://openalex.org/W2613462647","https://openalex.org/W2622013296","https://openalex.org/W2794515761","https://openalex.org/W2896757125","https://openalex.org/W2923328826","https://openalex.org/W2956395387","https://openalex.org/W2963678007","https://openalex.org/W3009055867","https://openalex.org/W3018184629","https://openalex.org/W3020452323","https://openalex.org/W3099270997","https://openalex.org/W3099651241","https://openalex.org/W3104566386"],"related_works":["https://openalex.org/W3203790089","https://openalex.org/W2120930769","https://openalex.org/W2986595367","https://openalex.org/W3021400897","https://openalex.org/W1982034332","https://openalex.org/W2911979088","https://openalex.org/W3120479070","https://openalex.org/W2048966376","https://openalex.org/W3032611786","https://openalex.org/W2735823969","https://openalex.org/W2588794862","https://openalex.org/W2079474124","https://openalex.org/W1982987094","https://openalex.org/W2064844455","https://openalex.org/W3116961995","https://openalex.org/W2159726494","https://openalex.org/W2724476622","https://openalex.org/W2144916300","https://openalex.org/W2045041282","https://openalex.org/W3133240559"],"abstract_inverted_index":{"While":[0],"implicit":[1],"Runge\u2013Kutta":[2,59],"(RK)":[3],"methods":[4],"possess":[5],"high":[6,17],"order":[7],"accuracy":[8],"and":[9,15,91],"important":[10],"stability":[11],"properties,":[12],"implementation":[13],"difficulties":[14],"the":[16,21,57,69,74,78,86,89],"expense":[18],"of":[19,48,77,88],"solving":[20],"coupled":[22,58,80],"algebraic":[23,81],"system":[24],"at":[25,62],"each":[26,63],"time":[27,64],"step":[28],"are":[29],"frequently":[30],"cited":[31],"as":[32],"impediments.":[33],"We":[34],"present":[35],"Irksome":[36,66],",":[37],"a":[38],"high-level":[39],"library":[40],"for":[41,56,95],"manipulating":[42],"UFL":[43,54],"(Unified":[44],"Form":[45],"Language)":[46],"expressions":[47,55],"semidiscrete":[49],"variational":[50],"forms":[51],"to":[52,72],"obtain":[53],"stage":[60],"equations":[61],"step.":[65],"works":[67],"with":[68],"Firedrake":[70],"package":[71],"enable":[73],"efficient":[75],"solution":[76],"resulting":[79],"systems.":[82],"Numerical":[83],"examples":[84],"confirm":[85],"efficacy":[87],"software":[90],"our":[92],"solver":[93],"techniques":[94],"various":[96],"problems.":[97]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}