An Application of Reduced Basis Methods to Core Computation in APOLLO3

Abstract: 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.