Abstract The determination of non-fundamental modes of the diffusion equation is required for computing CANDU reactor power distribution from analysis of in-core detector readings. They are also important for understanding subcritical mode instabilities occurring in boiling water reactors. The legacy method for computing these modes is the Hotelling deflation technique based on bi-harmonic decontamination. However, the Hotelling technique becomes unstable as the number of modes increase or as their eigenvalues become closer. Effective and fast alternatives are provided with Implicit Arnoldi Restarted Methods (IRAM). Among them, we investigated the Krylov–Schur method available in the SLEPc library, and we are proposing a custom implementation of the augmented block Householder Arnoldi (ABHA) method, similar to the Open Source implementation of Prof. James Baglama. In our work, the ABHA method is applied to the neutron diffusion equation, discretized with the Raviart–Thomas and Raviart–Thomas-Schneider methods or with the mesh-centered finite difference method.

中文翻译：

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增广块 Householder Arnoldi 方法在扩散方程非基模计算中的应用

摘要 确定扩散方程的非基本模​​式是通过分析堆芯探测器读数计算坎杜反应堆功率分布所必需的。它们对于理解沸水反应堆中发生的亚临界模式不稳定性也很重要。计算这些模式的传统方法是基于双谐波去污的 Hotelling 放气技术。然而，Hotelling 技术随着模式数量的增加或它们的特征值变得更接近而变得不稳定。隐式 Arnoldi 重新启动方法 (IRAM) 提供了有效且快速的替代方法。其中，我们研究了 SLEPc 库中可用的 Krylov–Schur 方法，并且我们提出了增强块 Householder Arnoldi (ABHA) 方法的自定义实现，类似于 James Baglama 教授的开源实现。在我们的工作中，ABHA 方法应用于中子扩散方程，使用 Raviart-Thomas 和 Raviart-Thomas-Schneider 方法或以网格为中心的有限差分方法进行离散化。