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A Discussion on the Solution of Linear Systems Appeared in Gradient Coil Optimization with the Finite Element Method

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Abstract

In the gradient coil optimization process, a dense linear system usually needs to be solved. When the mesh discretization method is used, the matrix will be very large, which makes direct methods very inefficient. The solution of the linear system is discussed in this paper for the optimization of gradient coils with the finite element method. Finally, a transversal planar gradient coil is designed and the efficiency of different methods are compared for the solution of the problem. Numerical results showed that the GMRES solver is the most efficient method.

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Acknowledgements

This work is supported in part by the Fundamental Research Funds for the Central Universities under Grant 2018B57514, in part by the National Natural Science Foundation of China (NSFC) (61701187), in part by the Natural science foundation of the higher education institutions of Jiangsu Province (16KJB510004).

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Authors and Affiliations

  1. College of Computer and Information, HoHai University, Nanjing, 211100, Jiangsu, China

    Xuewei Ping, Hongjie Wang, Xinghui Yin, Xinjun Wang & Changli Li

  2. Jiangsu Key Construction Laboratory of Modern Measurement Technology and Intelligent System, Huaiyin Normal University, Huai’an, China

    Qingbo Li

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  1. Xuewei Ping
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  2. Hongjie Wang
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  3. Qingbo Li
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  4. Xinghui Yin
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Correspondence to Xuewei Ping.

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Ping, X., Wang, H., Li, Q. et al. A Discussion on the Solution of Linear Systems Appeared in Gradient Coil Optimization with the Finite Element Method. Appl Magn Reson 51, 363–373 (2020). https://doi.org/10.1007/s00723-020-01189-y

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  • DOI: https://doi.org/10.1007/s00723-020-01189-y

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