In this paper, we consider the coupled N/TH problem, in which the termination criterion for the neutronics iteration adopts an adaptive tolerance with respect to the fuel temperature residual at each Picard iteration. We refer to this coupling scheme as the inexact Picard iteration method. Fourier analysis is performed to investigate how the convergence behavior of Picard iteration is influenced by the inexact neutronics solution. It is found that if the convergence of the inner neutronics iteration is slow, Picard coupling may become unstable unless a tighter tolerance is used for the neutronics iteration. Nevertheless, our analysis indicates that a certain amount of over-solving is necessary for maintaining the stability of Picard iteration if the iterative solution of the subproblem is not fast enough. However, this issue has not been addressed in the previous studies.

翻译：本文针对耦合中子学/热工水力学（N/TH）问题，提出中子学迭代的终止准则采用基于每一次Picard迭代中燃料温度残差的自适应容差。我们将这种耦合方案称为非精确Picard迭代法。通过傅里叶分析研究了非精确中子学解对Picard迭代收敛行为的影响。结果表明，若内层中子学迭代收敛缓慢，则Picard耦合可能变得不稳定，除非对中子学迭代采用更严格的容差。尽管如此，我们的分析指出，若子问题的迭代求解速度不够快，则保持Picard迭代的稳定性需要一定程度的过度求解。然而，这一关键问题此前的研究尚未涉及。