Irksome: automating Runge–Kutta time-stepping for finite element methods
While implicit Runge–Kutta (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 Irksome, a high-level library for manipul...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Association for Computing Machinery
2021
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| _version_ | 1826277071190491136 |
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| author | Farrell, PE Kirby, RC Marchena-Menéndez, J |
| author_facet | Farrell, PE Kirby, RC Marchena-Menéndez, J |
| author_sort | Farrell, PE |
| collection | OXFORD |
| description | While implicit Runge–Kutta (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 Irksome, a high-level library for manipulating UFL (Unified Form Language) expressions of semidiscrete variational forms to obtain UFL expressions for the coupled Runge–Kutta stage equations at each time step. Irksome 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. |
| first_indexed | 2024-03-06T23:23:23Z |
| format | Journal article |
| id | oxford-uuid:698a3e2f-193d-4995-aaf8-8b7d50bc0ebe |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:23:23Z |
| publishDate | 2021 |
| publisher | Association for Computing Machinery |
| record_format | dspace |
| spelling | oxford-uuid:698a3e2f-193d-4995-aaf8-8b7d50bc0ebe2022-03-26T18:51:43ZIrksome: automating Runge–Kutta time-stepping for finite element methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:698a3e2f-193d-4995-aaf8-8b7d50bc0ebeEnglishSymplectic ElementsAssociation for Computing Machinery2021Farrell, PEKirby, RCMarchena-Menéndez, JWhile implicit Runge–Kutta (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 Irksome, a high-level library for manipulating UFL (Unified Form Language) expressions of semidiscrete variational forms to obtain UFL expressions for the coupled Runge–Kutta stage equations at each time step. Irksome 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. |
| spellingShingle | Farrell, PE Kirby, RC Marchena-Menéndez, J Irksome: automating Runge–Kutta time-stepping for finite element methods |
| title | Irksome: automating Runge–Kutta time-stepping for finite element methods |
| title_full | Irksome: automating Runge–Kutta time-stepping for finite element methods |
| title_fullStr | Irksome: automating Runge–Kutta time-stepping for finite element methods |
| title_full_unstemmed | Irksome: automating Runge–Kutta time-stepping for finite element methods |
| title_short | Irksome: automating Runge–Kutta time-stepping for finite element methods |
| title_sort | irksome automating runge kutta time stepping for finite element methods |
| work_keys_str_mv | AT farrellpe irksomeautomatingrungekuttatimesteppingforfiniteelementmethods AT kirbyrc irksomeautomatingrungekuttatimesteppingforfiniteelementmethods AT marchenamenendezj irksomeautomatingrungekuttatimesteppingforfiniteelementmethods |