Talk (non-conference) (Invited)

FZJ-2025-02416

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Spectral Deferred Correction

Baumann, T. (Corresponding author)FZJ*

2025

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Please use a persistent id in citations: doi:10.34734/FZJ-2025-02416

Abstract: Spectral deferred correction (SDC) is a time integration method that is closely related to Runge-Kutta methods (RKM). In SDC, fully implicit RKM are solved iteratively, using similar computations as required to compute the stages in RKM. While explicit SDC often cannot compete with explicit RKM, SDC has been shown to perform very well for stiff PDEs. One major advantage of SDC is the flexibility afforded by using a low-order solver inside an iterative method for obtaining high-order solutions. This makes it simple to construct high-order splitting methods, for instance. SDC is also popular in the parallel-in-time community. Efficient small-scale parallelism within the method has recently been achieved and SDC is also employed within various parallel-in-time algorithms. This talk will encompass an introduction to SDC, some recent developments, numerical experiments where time-parallel SDC is preferable to RKM, and an advertisement for the prototyping library pySDC, which allows to rapidly explore all things SDC.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)
2. TIME-X - TIME parallelisation: for eXascale computing and beyond (955701) (955701)

Appears in the scientific report 2025

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