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Isakov, V. (1998) Inverse problem for partial differential equations. Springer-Verlag, New York.

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期刊名称: 《Advances in Applied Mathematics》, Vol.4 No.2, 2015-05-27

摘要: 电阻抗成像问题是通过测量物体表面的电流和电压值，来对物体内部的电参数进行成像。本文针对电阻抗成像中带有空腔的均匀介质的重构给出一种算法。算法的基本思想是利用解析延拓，将原问题转化为圆环域上的Cauchy问题，然后利用Newton迭代法求解此非线性方程组，得到Cauchy问题的解所满足的法向导数为零的集合，进而得到空腔的边界。同时给出几种特殊形状空腔重构的数值算例来说明算法的可行性。 Electrical impedance tomography problem refers to the imaging of electrical parameters inside the object by measuring the current and voltage value of object surfaces. An algorithm is proposed aiming at the reconstruction of homogeneous medium in the electrical impedance to-mography with cavity. The basic idea of the algorithm is using analytic continuation to transfer the original problem to the Cauchy problem of circle domain; Newton-type iterative method is used to solve the nonlinear equations, getting the assemblage whose normal derivative is zero satisfying the solution of Cauchy problem, and then the boundary of the cavity is gotten. At the same time, numerical examples of several kinds of special shaped cavity reconstruction are presented to demonstrate the feasibility of this algorithm.