Abstract The higher eigen-modes of the forward and adjoint neutron diffusion equations are widely used in several application perspectives for engineering purpose, such as the stability analysis and generalized perturbation theory based sensitivity and uncertainty analysis. In this study, the higher eigen-modes of both the forward and adjoint neutron diffusion equations are calculated using IRAM based on domain decomposition and the multi-group multi-domain coupling PGMRES algorithm. The methodology is implemented into the ParaFiDi code. The IAEA-3D benchmark, the PHWR benchmark and a one-group homogenous cubic problem are solved for verification. Numerical results demonstrate that the forward equation and the adjoint equation have the same eigenvalue spectrum, and the obtained higher order eigenvectors follow the orthogonality relationship, indicating that the numerical results agree well with the anticipated theoretical analysis, and ParaFiDi has good accuracy for higher eigen-modes. Additionally, the degeneracy is observed and preliminarily analyzed with respect to the orthogonality relationship.

中文翻译：

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使用基于域分解的 IRAM 算法计算前向和伴随中子扩散方程的高本征模式

摘要 前向和伴随中子扩散方程的高本征模式被广泛用于工程目的的几个应用领域，如稳定性分析和基于广义扰动理论的灵敏度和不确定性分析。在本研究中，使用基于域分解和多组多域耦合 PGMRES 算法的 IRAM 计算前向和伴随中子扩散方程的较高本征模式。该方法在 ParaFiDi 代码中实施。解决了 IAEA-3D 基准、PHWR 基准和一组齐次三次问题以进行验证。数值结果表明，前向方程和伴随方程具有相同的特征值谱，得到的高阶特征向量遵循正交关系，表明数值结果与预期的理论分析非常吻合，并且 ParaFiDi 对于更高的本征模式具有良好的准确性。此外，还观察并初步分析了正交关系的简并性。