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.

中文翻译：

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用有限元法讨论梯度线圈优化中出现的线性系统的解

在梯度线圈优化过程中，通常需要求解一个密集的线性系统。当使用网格离散化方法时，矩阵会非常大，这使得直接方法非常低效。本文讨论了线性系统的解决方案，用于用有限元方法优化梯度线圈。最后，设计了横向平面梯度线圈，并比较了不同方法的效率以解决问题。数值结果表明 GMRES 求解器是最有效的方法。