通过横向电极化中的直接采样方法检测小不均匀体
Detection of small inhomogeneities via direct sampling method in transverse electric polarization
AI总结：
研究通过直接采样方法检测小不均匀体的位置，揭示其在介质渗透率不同时无法准确识别的原因，并通过数值实验验证。
摘要：
各种研究已确认通过直接采样方法可以识别小不均匀体的位置；然而，当其渗透率不同于背景时，其位置无法被满意地识别。然而，这种现象的理论解释尚未得到验证。在本研究中，我们证明直接采样方法的指示函数可以表示为第一类一次贝塞尔函数，并解释为何无法准确识别不均匀体的精确位置。通过带有噪声的数据的数值结果来支持我们的研究。
英文摘要：
Various studies have confirmed the possibility of identifying the location of a set of small inhomogeneities via a direct sampling method; however, when their permeability differs from that of the background, their location cannot be satisfactorily identified. However, no theoretical explanation for this phenomenon has been verified. In this study, we demonstrate that the indicator function of the direct sampling method can be expressed by the Bessel function of order one of the first kind and explain why the exact locations of inhomogeneities cannot be identified. Numerical results with noisy data are exhibited to support our examination.
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