In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the eigenvalue and left and right eigenvectors. The practical computation of these estimators requires the estimation of a constant called prefactor, which we can express as the spectral norm of some operator. We provide some elements of theoretical analysis which illustrate the link between the expression of the prefactor we obtain here and its well-known expression in the case of symmetric eigenvalue problems, either using the notion of numerical range of the operator, or via a perturbative analysis. Lastly, we propose a practical method in order to estimate this prefactor which yields interesting numerical results on actual test cases. We provide detailed numerical simulations on two-dimensional examples including a multigroup neutron diffusion equation.

翻译：本文针对中子学中核反应堆堆芯装载模式优化所涉及的参数化非对称特征值问题，提出了一种约化基方法。为此，我们推导了特征值及左右特征向量的后验误差估计。这些估计量的实际计算需估算一个称为前置因子的常数，该常数可表示为某算子的谱范数。我们提供了一些理论分析元素，通过算子数值范围概念或微扰分析，阐明了本文获得的前置因子表达式与对称特征值问题中经典表达式之间的关联。最后，我们提出了一种实用的前置因子估算方法，该算法在实际测试案例中获得了令人关注的数值结果。我们提供了包含多群中子扩散方程在内的二维算例的详细数值模拟。