基于等参元的三维电阻抗成像的数值模拟和分析  

Numerical Simulation and Analysis for 3-dimensional Electrical Impedance Tomography Based on Isoparametric Finite Elements

作　　者：李久平[1] 

机构地区：[1]山东大学数学与系统科学学院,济南250100

出　　处：《工程数学学报》2006年第6期966-972,共7页Chinese Journal of Engineering Mathematics

基　　金：国家重点基础研究专项经费(G1999032803);国家自然科学基金(10372052;10271066);教育部博士点基金(20030422047)

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算法对三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。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.

关 键 词：阻抗成像 反问题 伪单元刚度矩阵 牛顿法 

分 类 号：O241.82[理学—计算数学] O224[理学—数学]