基于不定常极化张量的微小声学夹杂重构
Reconstruction of a small acoustic inclusion via Time-dependent Polarization Tensors
摘要：
本文旨在引入不定常极化张量（TDPT）的概念，将其应用于直径较小的声学夹杂的波动方程，该夹杂的本构参数不同于背景参数，尺寸小于工作波长。首先，Helmholtz方程的解决方案被认为是一个严格的系统推导的完整的渐近展开的散射场由于存在的夹杂物。然后，通过应用傅里叶变换，在截断高频之后容易地获得对应的时域扩展。TDPT的新概念被证明是有前途的执行成像。驱动数值模拟，示出从噪声测量重建的TDPT允许成像夹杂物的精细形状细节。
英文摘要：
This paper aims at introducing the concept of time-dependent polarization tensors (TDPTs) for the wave equation associated to a diametrically small acoustic inclusion, with constitutive parameters different from those of the background and size smaller than the operating wavelength. Firstly, the solution to the Helmholtz equation is considered, and a rigorous systematic derivation of a complete asymptotic expansion of the scattered field due to the presence of the inclusion is presented. Then, by applying the Fourier transform, the corresponding time-domain expansion is readily obtained after truncating the high frequencies. The new concept of TDPTs is shown to be promising for performing imaging. Numerical simulations are driven, showing that the TDPTs reconstructed from noisy measurements allow to image fine shape details of the inclusion.
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