Journal Article

FZJ-2024-07607

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Adaptive time step selection for spectral deferred correction

Baumann, T. (Corresponding author)FZJ* ; Götschel, S. ; Lunet, T. ; Ruprecht, D. ; Speck, R.FZJ*

2024
Springer Science Business Media B.V.

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Please use a persistent id in citations: doi:10.1007/s11075-024-01964-z

Abstract: Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.

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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)

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; DEAL Springer ; DEAL Springer ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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