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首页> 外文期刊>Journal of Computational Physics >A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
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A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

机译：非均质和分层介质中与时间相关的波动方程的完美匹配层

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摘要

A mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions.
机译：提出了一种在异质和分层介质中基于时间的波动方程的完全匹配层（PML）的数学分析。我们证明了具有分段常数的不连续介质的PML的稳定性，并推导了具有分段平滑系数的不连续介质的能量估计。我们考虑由较小的结构化子域组成的计算设置，这些子域使用高阶精确有限差分算子离散化，以近似空间导数。然后，通过使用惩罚来弱化接口条件，将子域修补到一个全局域中。为了确保离散PML的稳定性，有必要将接口条件转换为包括辅助变量。在离散设置中，转换后的界面条件对于得出类似于连续能量估计的离散能量估计至关重要，因此证明了数值方法的稳定性和收敛性。最后，我们提供了数值实验，证明了PML在分层介质中的稳定性以及所提出的界面条件的高阶精度。

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