This paper proposes a novel adaptive acceleration method based on online Incremental Orthogonal Component Analysis enhanced Dynamic Mode Decomposition (IOCA-DMD) and applies it to a self-developed Nodal Expansion Method (NEM) code for solving the three-dimensional steady-state neutron diffusion equations in rectangular and hexagonal geometries. The code integrates the Semi-Analytical Nodal Method (SANM) with transverse integration technology and the conformal mapping method to ensure numerical accuracy and stability. In the proposed acceleration method, the IOCA algorithm is utilized to adaptively determine online whether to accept newly generated flux error vectors as new basis directions, thereby identifying the optimal number of steps required for each DMD acceleration cycle. Subsequently, the DMD method is applied to predict the converged flux distribution, projecting the iterative solution to achieve rapid convergence. Numerical tests on the 3D IAEA and VVER-440 benchmarks show that the proposed method preserves high accuracy for the effective multiplication factor and normalized power distribution. The total number of iterations is reduced by about 70% for both benchmarks. CPU time is decreased by approximately 66% for the 3D IAEA benchmark and 44% for the 3D VVER-440 benchmark. This research provides a robust data-driven strategy for enhancing the efficiency of reactor physics simulations.
Zhang et al. (Wed,) studied this question.