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.

翻译：本文介绍了微/宏观parareal算法在一维能量平衡气候模型中的应用，该模型包含不连续且非单调的系数与强迫项。该微/宏观parareal方法采用基于底层（微观）一维模型的（宏观）零维近似构建粗传播子。我们比较了不同宏观模型版本以及不同微观传播子数值格式（即定步长显式欧拉法与自适应库例程）的性能。在并行处理器实现中，我们研究了该方法的收敛性及理论计算时间增益。结果表明，在本例所有设置下，微/宏观parareal方法的收敛迭代次数均少于所使用的parareal子区间数量，且理论性能增益可达10倍。