The factorization method for a cavity in an inhomogeneous medium
The factorization method for a cavity in an inhomogeneous medium
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DOI：
10.1088/0266-5611/30/4/045008
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发表时间：
2014-03
期刊：
影响因子：
2.1
通讯作者：
S. Meng;H. Haddar;F. Cakoni
中科院分区：
文献类型：
--
作者：
S. Meng;H. Haddar;F. Cakoni
我们考虑由致密支承的各向异性非均匀介质约束的腔体的逆散射问题，并通过腔内曲线或曲面上的内部测量来确定腔体的形状。我们推导出一种因式分解方法，它根据可由测量数据计算的算子的范围来严格地表征腔的支撑。空腔的支承是在没有周围各向异性介质的本构参数的先验知识的情况下确定的，只要它们满足我们的分析强加的适当的物理和数学假设。数值算例表明了该方法的可行性。
We consider the inverse scattering problem for a cavity that is bounded by a penetrable anisotropic inhomogeneous medium of compact support and seek to determine the shape of the cavity from internal measurements on a curve or surface inside the cavity. We derive a factorization method which provides a rigorous characterization of the support of the cavity in terms of the range of an operator which is computable from the measured data. The support of the cavity is determined without a priori knowledge of the constitutive parameters of the surrounding anisotropic medium provided they satisfy appropriate physical as well as mathematical assumptions imposed by our analysis. Numerical examples are given showing the viability of our method.