论文标题
irksome：自动化runge - kutta时间步长以获取有限元方法
Irksome: Automating Runge--Kutta time-stepping for finite element methods
论文作者
论文摘要
虽然隐式runge-kutta方法具有高阶的准确性和重要的稳定性，但实施困难和在每个时间步骤中求解耦合代数系统的高昂费用经常被视为障碍。我们提出了Iirksome，这是一个高级库，用于操纵半分化变化形式的UFL（统一形式语言）表达式，以在每个时间步骤中获得耦合runge-kutta阶段方程的UFL表达式。 Irksome与Firedrake软件包合作，以实现所得耦合代数系统的有效解决方案。数值示例证实了该软件和我们的求解器技术的功效。
While implicit Runge--Kutta 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 IIrksome, 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.
