从双调和远场数据恢复夹紧腔的直接采样法
Direct sampling for recovering a clamped cavity from biharmonic far field data
AI总结：
本文针对薄板中未知夹紧腔的形状反演问题，首次将直接采样法拓展至双调和波远场数据场景，利用Funk--Hecke恒等式分析成像函数性能，并通过数值算例验证了方法的有效性。
摘要：
本文研究嵌入无限薄板中的未知夹紧腔的形状反演问题，模型问题由频域下的二维双调和波动方程控制。基于远场数据，本文通过直接采样法对腔体恢复开展了分辨率分析，利用Funk--Hecke积分恒等式分析两种成像函数的性能。分析表明，常用于声学形状反问题的同类成像函数同样适用于双调和波动场景，这是首次将直接采样法拓展至利用远场数据的双调和波问题。文中还提供了数值算例，验证了这些成像函数在恢复夹紧腔方面的有效性。
英文摘要：
This paper concerns the inverse shape problem of recovering an unknown clamped cavity embedded in a thin infinite plate. The model problem is assumed to be governed by the two-dimensional biharmonic wave equation in the frequency domain. Based on the far-field data, a resolution analysis is conducted for cavity recovery via the direct sampling method. The Funk--Hecke integral identity is employed to analyze the performance of two imaging functions. Our analysis demonstrates that the same imaging functions commonly used for acoustic inverse shape problems are applicable to the biharmonic wave context. This work presents the first extension of direct sampling methods to biharmonic waves using far-field data. Numerical examples are provided to illustrate the effectiveness of these imaging functions in recovering a clamped cavity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
