Adaptive time step selection for spectral deferred correction

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.

Subjects

Adaptivity | Parallel-in-time | Spectral deferred correction

DDC Class

510: Mathematics

Funding(s)

TIME parallelisation: for eXascale computing and beyond

Publication version

publishedVersion

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

s11075-024-01964-z.pdf

Type

Main Article

Size

1.36 MB

Format

Adobe PDF

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Adaptive time step selection for spectral deferred correction