Improving efficiency of parallel across the method spectral deferred corrections

Parallel across the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDCs) with a diagonal sweeper, closely related to iterated Runge-Kutta methods proposed by Van der Houwen and Sommeijer, can use a number of threads equal to the number of quadrature nodes in the underlying collocation method. However, convergence speed, efficiency, and stability depend critically on the coefficients of the used SDC preconditioner. Previous approaches used numerical optimization to find good diagonal coefficients. Instead, we propose an approach that allows one to find optimal diagonal coefficients analytically. We show that the resulting parallel SDC methods provide stability domains and convergence order very similar to those of well established serial SDC variants. Using a model for computational cost that assumes 80% efficiency of an implementation of parallel SDCs, we show that our variants are competitive with serial SDC, previously published parallel SDC coefficients, Picard iteration, and a fourth-order explicit as well as a fourth-order implicit diagonally implicit Runge-Kutta method.

Subjects

iterated Runge-Kutta methods | parallel across the method | parallel in time (PinT) | spectral deferred correction | stiff and non-stiff problems

DDC Class

600: Technology

Funding(s)

Leistungsverbesserung des ICON-O Ozeanmodells auf heterogenen Exascale-Supercomputern mit Methoden des Maschinellen Lernens

TIME parallelisation: for eXascale computing and beyond

Publication version

publishedVersion

Lizenz

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

Name

24m1649800.pdf

Type

Main Article

Size

1.03 MB

Format

Adobe PDF

Options

Improving efficiency of parallel across the method spectral deferred corrections