We propose a multi-harmonic numerical method for solving wave scattering problems with moving boundaries, where the scatterer is assumed to move smoothly around an equilibrium position. We first develop an analysis to justify the method and its validity in the one-dimensional case with small-amplitude sinusoidal motions of the scatterer, before extending it to large-amplitude, arbitrary motions in one- and two-dimensional settings. We compare the numerical results of the proposed approach to standard space–time resolution schemes, which illustrates the efficiency of the new method.

中文翻译：

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频域移动边界散射问题的频域方法

我们提出了一种多谐数值方法，用于解决边界移动时的波散射问题，其中假定散射体在平衡位置附近平稳移动。我们首先进行分析，以证明该方法及其在散射体的小振幅正弦运动的一维情况下的合理性，然后再将其扩展到在一维和二维环境中的大振幅，任意运动。我们将建议的方法的数值结果与标准时空分辨率方案进行了比较，从而说明了新方法的有效性。