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 Jülich 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.

翻译：我们研究了并行谱延迟校正的并行性能，这是一种为初值问题数值解提供小规模并行化的数值方法。该方案应用于浅水方程，并采用隐式-显式分裂策略，为提升效率，将快速模态隐式积分而慢速模态显式积分。我们描述了基于OpenMP的并行谱延迟校正方法在两个成熟仿真代码中的实现：基于有限体积的业务化海洋模型ICON和基于球谐函数的研究代码SWEET。我们还建立了性能模型，并在于利希超级计算中心的JUSUF（SWEET）和JUWELS（ICON）系统单节点上对实现进行了基准测试。实验证明该方法能在不同精度范围内减少求解时间。对于ICON，我们展示了其相对于当前使用的Adams-Bashforth-2积分器结合OpenMP循环并行化的加速效果。对于SWEET，我们展示了其相对于串行谱延迟校正方法和二阶隐式-显式积分器的加速优势。