Abstract An absorbing boundary condition (ABC) is particularly important for finite element simulation of wave propagation in a multilayered medium. In this paper, a spatially and temporally local high-order absorbing boundary condition is proposed for scalar wave propagation in semi-infinite multilayered media. A semi-discrete motion equation is derived by discretizing the truncation boundary of the semi-infinite domain along the vertical direction. The scalar dynamic stiffness in the frequency domain for a single degree of freedom (DOF) on the truncation boundary is obtained by only considering the first mode of the semi-infinite domain. The scalar dynamic stiffness is expressed as a continued fraction expansion that is stable and converges exponentially to the exact solution. The ABC based on the continued fraction for a single DOF on the truncation boundary is established by introducing auxiliary variables. The proposed ABC is always stable and it can be coupled straightforwardly with the existing finite element method. Since it is spatially decoupled and the coefficients in it are easy to obtain, the proposed ABC is convenient to apply in engineering. Numerical examples demonstrate the superior properties of the proposed method with high accuracy, high efficiency, and good stability.

中文翻译：

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多层介质中标量波传播的局部时域吸收边界条件

摘要 吸收边界条件（ABC）对于多层介质中波传播的有限元模拟尤为重要。在本文中，提出了一种空间和时间局部高阶吸收边界条件，用于半无限多层介质中的标量波传播。通过将半无限域的截断边界沿垂直方向离散化，推导出半离散运动方程。截断边界上单自由度 (DOF) 的频域标量动态刚度是通过仅考虑半无限域的第一模态获得的。标量动态刚度表示为稳定的连续分数扩展，并以指数方式收敛到精确解。通过引入辅助变量建​​立基于截断边界上单个自由度的连分数的 ABC。所提出的 ABC 始终是稳定的，并且可以直接与现有的有限元方法耦合。由于它在空间上是解耦的，并且其中的系数很容易获得，因此所提出的 ABC 便于工程应用。数值例子证明了所提出的方法具有高精度、高效率和良好稳定性的优越特性。