| 基于等参元的三维电阻抗成像的数值模拟和分析 |
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| 引用本文： | 李久平. 基于等参元的三维电阻抗成像的数值模拟和分析[J]. 工程数学学报, 2006, 23(6): 966-972 |
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| 作者姓名： | 李久平 |
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| 作者单位： | 山东大学数学与系统科学学院,济南,250100 |
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| 基金项目： | 国家重点基础研究发展计划(973计划);国家自然科学基金;高等学校博士学科点专项科研项目 |
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| 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。
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| 关 键 词： | 阻抗成像 反问题 伪单元刚度矩阵 牛顿法 |
| 文章编号： | 1005-3085(2006)06-0966-07 |
| 收稿时间： | 2004-10-12 |
| 修稿时间： | 2004-10-12 |
Numerical Simulation and Analysis for 3-dimensional Electrical Impedance Tomography Based on Isoparametric Finite Elements |
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| LI Jiu-ping. Numerical Simulation and Analysis for 3-dimensional Electrical Impedance Tomography Based on Isoparametric Finite Elements[J]. Chinese Journal of Engineering Mathematics, 2006, 23(6): 966-972 |
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| Authors: | LI Jiu-ping |
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| Affiliation: | School of Math. and System Sci,, Shandong Univ,, Jinan 250100 |
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| Abstract: | 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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| Keywords: | electrical impedance tomography inverse problem quasi-element stiffness matrix Newton method |
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