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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- 被引次数: 0
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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参考文献(27)

WEI H Y and SOLEIMANI M. Electromagnetic tomography for medical and industrial applications: challenges and opportunities[J]. Proceedings of the IEEE, 2013, 101(3): 559-565.

LU Ma, HUNT Andy, and SOLEIMANI M. Experimental evaluation of conductive flow imaging using magnetic induction tomography[J]. International Journal of Multiphase Flow, 2015, 72: 198-209.

JIN Gui, SUN Jian, QIN Mingxin, et al. A new method for detecting cerebral hemorrhage in rabbits by magnetic inductive phase shift[J]. Biosensors and Bioelectronics, 2014, 52: 374-378.

王雷, 刘锐岗, 周伟, 等. 磁感应断层成像硬件系统与实验的研究进展[J]. 医疗卫生装备, 2013, 34(2): 85-88.

WANG L, LIU R G, ZHOU W, et al. Research progress of magnetic induction tomography system and experimental results[J]. Chinese Medical Equipment Journal, 2013, 34(2): 85-88.

DARRER B J, WATSON J C, BARTLETT P, et al. Toward an automated setup for magnetic induction tomography[J]. IEEE Transactions on Magnetics, 2015, 51(1): 6500104.

MERWA R, HOLLAUS K, BRANDSTATTER B, et al. Volumetric magnetic induction tomography[J]. Measurement Science and Technology, 2012, 23(5): 055401.

MERWA R, HOLLAUS K, BRANDSTATTER B, et al. Numerical solution of the general 3D eddy current problem for magnetic induction tomography (spectroscopy)[J]. Physiological Measurement, 2003, 24: 545-554.

HOLLAUS K, MAC, MERWA R, et al. Numerical simulation of the eddy current problem in magnetic induction tomography for biomedical applications by edge elements[J]. IEEE Transactions on Magnetics, 2004, 40(2): 623-626.

刘国强, 王涛, 蒙萌, 等. 用棱单元方法求解磁感应成像正问题[J]. 中国生物医学工程, 2006, 25(2): 163-165.

LIU G Q, WANG T, MENG M, et al. Using edge element method to solve the forward problem in magnetic induction tomography[J]. China Medical Engineering, 2006, 25(2): 163-165.

何为, 宋晓栋, 张晓勇, 等. 正弦均匀磁场激励磁感应成像正问题的棱单元法. 重庆大学学报, 2012, 35(10): 159-164.

HE W, SONG X D, ZHANG X Y, et al. The edge element method in the forward problem of magnetic induction tomography with homogeneous sinusoidal magnetic excitation[J]. Journal of Chongqing University, 2012, 35(10): 159-164.

柯丽, 赵璐璐, 杜强, 等. 颅脑血肿 MIT 涡流场仿真与分析[J]. 系统仿真学报, 2014, 26(3): 517-522.

KE L, ZHAO L L, DU Q, et al. Simulation and analysis of cerebral hematoma eddy current field in magnetic induction tomography[J]. Journal of System Simulation, 2014, 26(3): 517-522.

ZHAO Q, CHEN G, HAO J N, et al. Numerical approach for the sensitivity of a high-frequency magnetic induction tomography system based on boundary elements and perturbation method[J]. Measurement Science and Technology, 2013, 4: 074004.

蒙萌, 江凌彤, 李士强, 等. 三维磁共振磁感应成像重建方法研究[J]. 中国生物医学工程学报, 2008, 27(5): 650-653.

MENG M, JIANG L T, LI S Q, et al. 3-D reconstruction algorithm of magnetic resonance magnetic induction tomography[J]. Chinese Journal of Biomedical Engineering, 2008, 27(5): 650-653.

SOLEIMANI M, WILLIAM R, and LIONHEART B. Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method[J]. IEEE Transactions on Medical Imaging, 2006, 25(12): 1521-1530.

SOLEIMANI1 M, LIONHEART W R B, PEYTON1 A J, et al. A three-dimensional inverse finite-element method applied to experimental eddy-current imaging Data[J]. IEEE Transactions on Magnetics, 2006, 42(5): 1560-1567.

林莘, 刘志刚. ICCG算法在SF6罐式高压断路器三维电场有限元计算中的应用[J]. 中国电机工程学报, 2001, 21(2): 21-24.

LIN X and LIU Z G. The application of ICCG algorithm in the three dimensional electric field calculation of SF6 tank-type circuit breaker[J]. Proceedings of the CSEE, 2001, 21(2): 21-24.

谢德馨, 杨仕友. 工程电磁场数值分析与综合[M]. 北京: 机械工业出版社, 2008: 84-85.

XIE D X and YANG S Y. Numerical Analysis and Synthesis of Engineering Electromagnetic Field[M]. Beijing: China Machine Press, 2008: 84-85.

KAMEARI A. Symetric second order edge elements for triangles and terahedra[J]. IEEE Transactions on Magnetics, 1999, 35: 1394-1397.

GRIFFITHS H, STEWART W R, and GOUGH W. Magnetic induction tomography a measuring system for biological tissues[J]. Annals New York Academy of Sciences, 1999, 20: 335-345.

HERMANN S, HELMUT K L, and JAVIER R. Magnetic induction tomography: hardware for multi-frequency measurement in biological tissues[J]. Physiological Measurement, 2001, 22: 131-146.

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