On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations
On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations
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DOI：
10.1007/3-540-26825-1_43
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
G. Bal
中科院分区：
文献类型：
--
作者：
G. Bal
在给出了一般偏微分方程时间并行化中的Parareal算法的一个抽象收敛性结果后，分析了该算法对常系数方程的稳定性和收敛性。我们表明，适当的阻尼粗计划，确保parareal算法的无条件稳定性，并分析了如何在没有足够的阻尼的情况下，初始条件的正则性影响收敛。
After stating an abstract convergence result for the parareal algorithm used in the parallelization in time of general partial differential equations, we analyze the stability and convergence properties of the algorithm for equations with constant coefficients. We show that suitably damping coarse schemes ensure unconditional stability of the parareal algorithm and analyze how the regularity of the initial condition influences convergence in the absence of sufficient damping.