In the aim of reducing the computational cost of the resolution of parameter-dependent eigenvalue problems, a model order reduction (MOR) procedure is proposed. We focus on the case of non-self-adjoint generalized eigenvalue problems, such as the stationary multigroup neutron diffusion equations. The method lies in an approximation of the manifold of solutions using a Proper Orthogonal Decomposition approach. The numerical method is composed of two stages. In the offline stage, we build a reduced space which approximates the manifold. In the online stage, for any given new set of parameters, we solve a reduced problem on the reduced space within a much smaller computational time than the required time to solve the high-fidelity problem. This method is applied to core computations in the APOLLO3 code.

翻译：为降低参数依赖特征值问题的求解计算成本，本文提出了一种模型降阶（MOR）方法。我们重点研究非自伴广义特征值问题，如稳态多群中子扩散方程。该方法基于本征正交分解（POD）技术对解流形进行近似。数值方法包含两个阶段：离线阶段构建逼近解流形的降阶空间，在线阶段针对任意新参数集，在降阶空间中求解缩减问题，其计算时间远小于高保真问题的求解耗时。该方法已应用于APOLLO3程序的堆芯计算。