In this paper, we consider the numerical solution of the time-dependent wave equation in a semi-infinite waveguide. We employ the Double Absorbing Boundary (DAB) method, by introducing two parallel artificial boundaries on the side where waves are outgoing. In contrast to the original implementation of the DAB, where the numerical solution involved either a low-order finite difference scheme or a low-order finite element scheme, here we incorporate the DAB into a high-order spectral element formulation, which provides us with very accurate solutions of wave problems in unbounded domains. This is demonstrated by numerical experiments. While the method is highly accurate, it suffers from long-time instability. We show how to postpone the onset of the instability by a prudent choice of the computational parameters.

中文翻译：

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双吸收边界法结合高阶谱元公式

在本文中，我们考虑了半无限波导中瞬态波动方程的数值解。我们采用双吸收边界 (DAB) 方法，在波出射的一侧引入两个平行的人工边界。与 DAB 的原始实现相比，其中数值解涉及低阶有限差分格式或低阶有限元格式，这里我们将 DAB 合并到高阶谱元公式中，这为我们提供了无界域中波浪问题的非常准确的解决方案。数值实验证明了这一点。虽然该方法非常准确，但它存在长期不稳定性。我们展示了如何通过谨慎选择计算参数来推迟不稳定性的发生。