应用于具有不连续非单调系数和振荡强迫项的气候模型的微/宏观时间并行（parareal）算法
A micro/macro parallel-in-time (parareal) algorithm applied to a climate model with discontinuous non-monotone coefficients and oscillatory forcing
AI总结：
本文提出一种微/宏观 parareal 算法用于求解具有不连续非单调系数和振荡强迫项的一维能量平衡气候模型，通过零维宏观近似构建粗传播器，实验表明该方法收敛所需迭代次数少于子区间数，理论性能增益最高可达 10 倍。
摘要：
我们提出了一种微/宏观 parareal 算法在具有不连续非单调系数和强迫项的一维能量平衡气候模型中的应用。该方法使用了一个粗传播器，它基于底层（微观）一维模型的（宏观）零维近似。我们比较了使用不同版本的宏观模型以及不同微观传播器数值方案时的方法性能，即定步长的显式 Euler 方法和自适应库例程。我们在并行处理器上的一次实现中研究了该方法的收敛性和计算时间的理论增益。结果表明，在此示例及所有设置下，微/宏观 parareal 方法的迭代次数少于所用的 parareal 子区间数，且理论上性能增益最高可达 10 倍。
英文摘要：
We present the application of a micro/macro parareal algorithm for a 1-D energy balance climate model with discontinuous and non-monotone coefficients and forcing terms. The micro/macro parareal method uses a coarse propagator, based on a (macroscopic) 0-D approximation of the underlying (microscopic) 1-D model. We compare the performance of the method using different versions of the macro model, as well as different numerical schemes for the micro propagator, namely an explicit Euler method with constant stepsize and an adaptive library routine. We study convergence of the method and the theoretical gain in computational time in a realization on parallel processors. We show that, in this example and for all settings, the micro/macro parareal method converges in fewer iterations than the number of used parareal subintervals, and that a theoretical gain in performance of up to 10 is possible.
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