Affiliation:
1. University of Oxford, UK
2. Baylor University, Waco
Abstract
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.
Funder
Engineering and Physical Sciences Research Council
National Science Foundation
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Reference53 articles.
1. Shrirang Abhyankar Jed Brown Emil Constantinescu Debojyoti Ghosh Barry Smith and Hong Zhang. 2018. PETSc/TS: a modern scalable ODE/DAE solver library. arXiv:1806.01437. Retrieved from https://arxiv.org/abs/1806.01437. Shrirang Abhyankar Jed Brown Emil Constantinescu Debojyoti Ghosh Barry Smith and Hong Zhang. 2018. PETSc/TS: a modern scalable ODE/DAE solver library. arXiv:1806.01437. Retrieved from https://arxiv.org/abs/1806.01437.
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