Parallel performance of shared memory parallel spectral deferred corrections

Abstract

We investigate the parallel performance of Parallel Spectral Deferred corrections, a numerical approach that provides small-scale parallelism for the numerical solution of initial value problems. The scheme is applied to the shallow-water equation and uses an implicit-explicit splitting that, in order to be efficient, integrates fast modes implicitly and slow modes explicitly. We describe parallel \OpenMP-based implementations of parallel Spectral Deferred Corrections for two well established simulation codes: the finite volume based operational ocean model \ICON and the spherical harmonics based research code \SWEET. We also develop a performance model and benchmark our implementations on a single node of the JUSUF (\SWEET) and JUWELS (\ICON) system at J\"ulich Supercomputing Centre. A reduction of time-to-solution across a range of accuracies is demonstrated. For \ICON, we show speedup over the currently used Adams--Bashforth-2 integrator with \OpenMP loop parallelization. For \SWEET, we show speedup over serial Spectral Deferred Corrections and a second order implicit-explicit integrator.