Fast solution of neutron diffusion problem with movement of control rods

•An extremely efficient method is proposed to solve the neutron diffusion problem with movement of control rods.•An effective method is proposed to affinely decompose the Heaviside step function.•Three to four orders of speedup is achieved for typical pressurized water reactor cores. Accurate and fast-running reduced order neutronics models are expected in many challenging applications such as multi-physics coupling analysis and data assimilations of reactors. The emphasis of the present study is to investigate an appropriate order reduction method for treating the movement of control rods. The empirical interpolation method is adopted to perform an affine decomposition to the spatial distribution of the cross sections with respect to the positions of control rods. The method can well recover the abrupt change of the cross sections near the end of control rods. With incorporation of the decomposed components, accurate and very efficient reduced order models can be constructed for the neutron diffusion problem with one-step or two-step movements of control rods.