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不完全喬列斯基分解共軛梯度法在磁感應(yīng)成像三維有限元正問題中的應(yīng)用

宣楊,  王旭,  劉承安,  楊丹,  張志美

宣楊, 王旭, 劉承安, 楊丹, 張志美. 不完全喬列斯基分解共軛梯度法在磁感應(yīng)成像三維有限元正問題中的應(yīng)用[J]. 電子與信息學(xué)報, 2016, 38(1): 187-194. doi: 10.11999/JEIT150437
引用本文: 宣楊, 王旭, 劉承安, 楊丹, 張志美. 不完全喬列斯基分解共軛梯度法在磁感應(yīng)成像三維有限元正問題中的應(yīng)用[J]. 電子與信息學(xué)報, 2016, 38(1): 187-194. doi: 10.11999/JEIT150437
XUAN Yang, WANG Xu, LIU Cheng’an, YANG Dan, ZHANG Zhimei. Incomplete Cholesky Conjugate Gradient Method for the Three- dimensional Forward Problem in Magnetic Induction Tomography Using Finite Element Method[J]. Journal of Electronics & Information Technology, 2016, 38(1): 187-194. doi: 10.11999/JEIT150437
Citation: XUAN Yang, WANG Xu, LIU Cheng’an, YANG Dan, ZHANG Zhimei. Incomplete Cholesky Conjugate Gradient Method for the Three- dimensional Forward Problem in Magnetic Induction Tomography Using Finite Element Method[J]. Journal of Electronics & Information Technology, 2016, 38(1): 187-194. doi: 10.11999/JEIT150437

不完全喬列斯基分解共軛梯度法在磁感應(yīng)成像三維有限元正問題中的應(yīng)用

doi: 10.11999/JEIT150437 cstr: 32379.14.JEIT150437
  • 1.

    (東北大學(xué)中荷生物醫(yī)學(xué)與信息工程學(xué)院 沈陽 110004) ②(東北大學(xué)信息科學(xué)與工程學(xué)院 沈陽 110004)

基金項目: 

中央高校基本科研業(yè)務(wù)費專項(N130404004)

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: 磁感應(yīng)成像(MIT)3維正問題中，直接求解法計算有限元方程組時，計算速度慢且因舍入誤差造成計算結(jié)果不正確。該文為了解決這一問題，采用不完全喬列斯基分解共軛梯度(ICCG)迭代求解法?；贏NSYS平臺建立有限元數(shù)值模型，采用ICCG法迭代求解。通過仿真實驗獲得設(shè)定收斂容差的最優(yōu)值。對仿真結(jié)果進行對比，與直接求解法、雅克比共軛梯度(JCG)法相比，ICCG法計算速度快、穩(wěn)健性高。計算結(jié)果表明ICCG法受網(wǎng)格粗細影響小，能夠正確求解磁感應(yīng)成像3維正問題。
    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.
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出版歷程
  • 收稿日期:  2015-04-15
  • 修回日期:  2015-08-25
  • 刊出日期:  2016-01-19

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