A stable parareal-like method for the second order wave equation
A stable parareal-like method for the second order wave equation
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DOI：
10.1016/j.jcp.2019.109156
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Hieu Nguyen;R. Tsai
中科院分区：
文献类型：
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作者：
Hieu Nguyen;R. Tsai
提出了一种新的时间并行迭代方法来求解齐次二阶波动方程。新方法涉及一个粗尺度传播器，允许更大的时间步长，以及一个细尺度传播器，它使用更精细的空间网格并使用更短的时间步长来完全解析介质。细尺度传播器在短时间间隔内并行运行。这两个传播器以迭代方式耦合，类似于标准的parareal方法[24]。我们提出了一种数据驱动策略，其中从每次迭代收集的计算数据被重新使用，通过最小化精细和粗略传播解的波能残差来稳定耦合。提供了几个例子，包括具有不连续性的波速，以证明所提出方法的有效性。
A new parallel-in-time iterative method is proposed for solving the homogeneous second-order wave equation. The new method involves a coarse scale propagator, allowing for larger time steps, and a fine scale propagator which fully resolves the medium using finer spatial grid and uses shorter time steps. The fine scale propagator is run in parallel for short time intervals. The two propagators are coupled in an iterative way that resembles the standard parareal method [24]. We present a data-driven strategy in which the computed data gathered from each iteration are re-used to stabilize the coupling by minimizing the wave energy residual of the fine and coarse propagated solutions. Several examples, including a wave speed with discontinuities, are provided to demonstrate the effectiveness of the proposed method.