不完全乔列斯基分解共轭梯度法在磁感应成像三维有限元正问题中的应用

宣杨; 王旭; 刘承安; 杨丹; 张志美

doi:10.11999/JEIT150437

不完全乔列斯基分解共轭梯度法在磁感应成像三维有限元正问题中的应用

doi: 10.11999/JEIT150437

1.
(东北大学中荷生物医学与信息工程学院沈阳 110004) ②(东北大学信息科学与工程学院沈阳 110004)

基金项目:

中央高校基本科研业务费专项(N130404004)

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出版历程
- 收稿日期: 2015-04-15
- 修回日期: 2015-08-25
- 刊出日期: 2016-01-19

Incomplete Cholesky Conjugate Gradient Method for the Three- dimensional Forward Problem in Magnetic Induction Tomography Using Finite Element Method

1.
(Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang 110004, China)

Funds:

The Fundmental Reseach Funds for the Central Universities of China (N130404004)

摘要

摘要: 磁感应成像(MIT)3维正问题中，直接求解法计算有限元方程组时，计算速度慢且因舍入误差造成计算结果不正确。该文为了解决这一问题，采用不完全乔列斯基分解共轭梯度(ICCG)迭代求解法。基于ANSYS平台建立有限元数值模型，采用ICCG法迭代求解。通过仿真实验获得设定收敛容差的最优值。对仿真结果进行对比，与直接求解法、雅克比共轭梯度(JCG)法相比，ICCG法计算速度快、稳健性高。计算结果表明ICCG法受网格粗细影响小，能够正确求解磁感应成像3维正问题。
- 磁感应成像 /
- 不完全乔列斯基分解共轭梯度法 /
- 3维正问题 /
- 有限元法
Abstract: In 3D forward problem of Magnetic Induction Tomography (MIT), the problems are slow computation speeds and incorrect results due to round-off errors, when calculating the finite element equations with the direct method. Incomplete Cholesky Conjugate Gradient (ICCG) iteration method is used to solve these problems. Round-off errors are compensated by iteration method. An Finite-Element Model (FEM) is built based on the ANSYS software. The FEM equations are solved by the ICCG method. The optimal convergence tolerance value is calculated. Simulation result shows that the ICCG method has advantages in speed and stability compared with direct and Jacobi Conjugate Gradient (JCG) method. The results show that the ICCG method is not affected by meshing perturbation, it can solve the 3D forward problem of MIT correctly.
- Magnetic Induction Tomography (MIT) /
- Incomplete Cholesky Conjugate Gradient (ICCG) method /
- Three-dimensional forward problem /
- Finite Element Method (FEM)

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