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Math. Softw."],"published-print":{"date-parts":[[2021,12,31]]},"abstract":"<jats:p>\n            While implicit Runge\u2013Kutta (RK) methods possess high order accuracy and important stability properties, implementation difficulties and the high expense of solving the coupled algebraic system at each time step are frequently cited as impediments. We present\n            <jats:monospace>Irksome<\/jats:monospace>\n            , a high-level library for manipulating UFL (Unified Form Language) expressions of semidiscrete variational forms to obtain UFL expressions for the coupled Runge\u2013Kutta stage equations at each time step.\n            <jats:monospace>Irksome<\/jats:monospace>\n            works with the Firedrake package to enable the efficient solution of the resulting coupled algebraic systems. Numerical examples confirm the efficacy of the software and our solver techniques for various problems.\n          <\/jats:p>","DOI":"10.1145\/3466168","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T20:47:05Z","timestamp":1632862025000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Irksome: Automating Runge\u2013Kutta Time-stepping for Finite Element Methods"],"prefix":"10.1145","volume":"47","author":[{"given":"Patrick E.","family":"Farrell","sequence":"first","affiliation":[{"name":"University of Oxford, UK"}]},{"given":"Robert C.","family":"Kirby","sequence":"additional","affiliation":[{"name":"Baylor University, Waco"}]},{"given":"Jorge","family":"Marchena-Men\u00e9ndez","sequence":"additional","affiliation":[{"name":"Baylor University, Waco"}]}],"member":"320","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Shrirang Abhyankar Jed Brown Emil Constantinescu Debojyoti Ghosh Barry Smith and Hong Zhang. 2018. 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Series A, Mathematical and Physical Sciences 272, 1220 (1972), 47\u201378. Thomas Brooke Benjamin, Jerry Lloyd Bona, and John Joseph Mahony. 1972. Model equations for long waves in nonlinear dispersive systems. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 272, 1220 (1972), 47\u201378."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/0714069"},{"key":"e_1_2_1_7_1","volume-title":"Kevrekidis","author":"Boull\u00e9 Nicolas","year":"2020","unstructured":"Nicolas Boull\u00e9 , Efstathios G. Charalampidis , Patrick E. Farrell , and Panayotis G . Kevrekidis . 2020 . Deflation-based identification of nonlinear excitations of the 3D Gross-Pitaevskii equation.Physical Review A 102, 5 (2020), 053307. DOI:DOI:https:\/\/doi.org\/10.1103\/PhysRevA.102.053307 Nicolas Boull\u00e9, Efstathios G. Charalampidis, Patrick E. Farrell, and Panayotis G. Kevrekidis. 2020. 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