Irksome: Automating Runge–Kutta Time-stepping for Finite Element Methods
Irksome: Automating Runge–Kutta Time-stepping for Finite Element Methods
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DOI：
10.1145/3466168
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发表时间：
2020-06
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影响因子：
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通讯作者：
P. Farrell;R. Kirby;J. Marchena-Menendez
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文献类型：
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作者：
P. Farrell;R. Kirby;J. Marchena-Menendez
虽然隐式龙格-库塔（RK）方法具有高阶精度和重要的稳定性，但在每个时间步求解耦合代数系统的实现困难和高费用经常被引用为障碍。我们提出了Irksome，一个高层次的库操纵UFL（统一形式语言）表达的半离散变分形式，以获得UFL表达的耦合龙格-库塔阶段方程在每个时间步。Irksome与Firedrake软件包一起工作，以实现所产生的耦合代数系统的有效解决方案。数值算例证实了该软件的有效性和我们的求解技术的各种问题。
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.