Preconditioned JFNK discontinuous Galerkin method for the SN neutron transport equation based on the WINGS framework

This paper presents a solution scheme for the SN neutron transport equation using the discontinuous Galerkin method, implemented within the WINGS framework. The resulting SN-DG-WINGS program is capable of solving both steady-state eigenvalue problems and fixed-source problems, and incorporates the JFNK algorithm via the solver interface provided by WINGS. To improve computational efficiency, a preconditioned matrix construction method based on the A-matrix is introduced, along with a computational strategy for generating initial guesses. The accuracy of the program is verified through a series of benchmark cases, including one dimensional fixed source problems with anisotropic scattering and three dimensional criticality problems. Numerical results indicate an eigenvalue deviation within 200 pcm and a flux distribution error below 5%. In terms of computational performance, the proposed preconditioning technique and initial guess strategy significantly improve convergence speed and stability. Large-scale parallel tests show that the program maintains a parallel efficiency of 47.3% even at 1024 processors, demonstrating strong scalability.