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Title: 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 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.  more » « less
Award ID(s):
1912653
PAR ID:
10348287
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
ACM Transactions on Mathematical Software
Volume:
47
Issue:
4
ISSN:
0098-3500
Page Range / eLocation ID:
1 to 26
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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