Irksome: Automating Runge--Kutta time-stepping for finite element\n methods

2020/06/29 by Patrick E. Farrell, Farrell, Patrick E., Robert C. Kirby +3 · 3 citations
Engineering · Mathematics · #65-04 #65M60 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #G.1.8 #J.2 #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2006.16282

openalex publication_date 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While implicit Runge--Kutta methods possess high order accuracy and important\nstability properties, implementation difficulties and the high expense of\nsolving the coupled algebraic system at each time step are frequently cited as\nimpediments. We present IIrksome, a high-level library for manipulating UFL\n(Unified Form Language) expressions of semidiscrete variational forms to obtain\nUFL expressions for the coupled Runge--Kutta stage equations at each time step.\nIrksome works with the Firedrake package to enable the efficient solution of\nthe resulting coupled algebraic systems. Numerical examples confirm the\nefficacy of the software and our solver techniques for various problems.\n

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