标题： 双调和波的逆腔散射问题的采样方法 显示英文标题

标题： Sampling methods for the inverse cavity scattering problem of biharmonic waves

摘要： 本文解决了通过远场测量定量恢复薄弹性板中夹紧空腔的反问题。 我们通过仔细检查远场算子的范围并利用双调和远场模式的互易关系，对线性采样方法进行了加强分析。 此外，我们在有限孔径数据下实现了用于重建空腔的线性采样方法和用于定位空腔的扩展采样方法。 数值实验表明了这两种方法的有效性和鲁棒性。 显示英文摘要

摘要： This paper addresses the inverse problem of qualitatively recovering a clamped cavity in a thin elastic plate using far-field measurements. We present a strengthened analysis of the linear sampling method by carefully examining the range of the far-field operator and employing the reciprocity relation of the biharmonic far-field pattern. In addition, we implement both the linear sampling method for reconstructing the cavity and the extended sampling method for localizing the cavity under limited-aperture data. Numerical experiments demonstrate the effectiveness and robustness of both methods.