Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is 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 depends critically on the used coefficients. Previous approaches have used numerical optimization to find good parameters. Instead, we propose an ansatz that allows to find optimal parameters 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 SDC we show that our variants are competitive with serial SDC, previously published parallel SDC coefficients as well as Picard iteration, explicit RKM-4 and an implicit fourth-order diagonally implicit Runge-Kutta method.

翻译：跨方法并行时间积分可以在求解初值问题时提供小规模并行性。采用对角线扫掠器的谱延迟校正（SDC）与Van der Houwen和Sommeijer提出的迭代龙格-库塔方法密切相关，能够使用与底层配置法中求积节点数量相等的线程数。然而，收敛速度、效率和稳定性关键取决于所使用的系数。以往的方法采用数值优化来寻找良好参数。相反，我们提出了一种能够通过解析方式找到最优参数的假设。结果表明，由此产生的并行SDC方法提供的稳定域和收敛阶与成熟的串行SDC变体非常相似。利用假设计算开销模型（假设并行SDC实现效率为80%），我们证明了所提变体与串行SDC、先前发表的并行SDC系数、Picard迭代、显式RKM-4以及一种四阶对角隐式龙格-库塔方法相比具有竞争力。