Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements
Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements
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DOI：
10.1088/0266-5611/16/4/311
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发表时间：
2000-08
期刊：
影响因子：
2.1
通讯作者：
Masaru Ikehata;S. Siltanen
中科院分区：
文献类型：
--
作者：
Masaru Ikehata;S. Siltanen
本文研究了在C∞边界为<$Ω的有界区域Ω <$2中，电导率为γ = 1 + χDh的二维电导率反问题.这里D <$Ω和hL∞（D）使得γ沿着<$D有一个跳跃。Ikehata（Ikehata M J. Inverse and Ill-Posed Problems at press）证明了Dirichlet-Neumann映射决定了可用于求D的凸船体的指示函数Iω（τ，t）.本文数值地求出了h为常数的例子的指示函数，并恢复了D的凸船体。
We consider the 2D inverse conductivity problem for conductivities of the form γ = 1 + χDh defined in a bounded domain Ω⊂2 with C∞ boundary ∂Ω. Here D⊂Ω and hL∞(D) are such that γ has a jump along ∂D. It was shown by Ikehata (Ikehata M J. Inverse and Ill-Posed Problems at press) that the Dirichlet-Neumann map determines the indicator function Iω(τ,t) that can be used to find the convex hull of D. In this paper we find numerically the indicator function for examples with constant h and recover the convex hull of D.