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中文摘要：
对于电阻抗成像的数学模型，本文用等参元方法将对应的椭圆型方程离散化，把成像问题转化为非线性优化问题，给出了目标函数梯度及近似Hesee阵的计算公式：提出了伪单元刚度矩阵的概念，给出了利用其在迭代过程中的不变性来提高计算效率的方法：分别用BFGS校正拟Newton算法和Goldfeld修正Gauss-Newton算法对二维成像问题进行了一系列数值模拟实验，证实了算法的有效性，指出了其中存在的问题。
英文摘要：
For the mathematical model of electrical impedance tomography, it is changed into discrete form based on isoparametric finite element methods and described as a nonlinear optimization problem, computational formulas of the gradient and Hessian matrix are presented; The concept of pseudo element stiffness matrix is introduced, and its invariance during the iteration is useful for improving the computational efficiency. The BFGS method and Goldfeld modified Gauss-Newton method are adopted in numerical simulation for 3-dimensional EIT, numerical simulation results show that these methods are valid, and the relevant problems are pointed out.
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