Fast Sub-Grid Scale Finite Element Method for the First Order Neutron Transport Equation

This paper presents a fast sub-grid scale (SGS) finite element method for the first order neutron transport equation. The spherical harmonics method is adopted for the angular discretization. The sub-grid scale discretization embeds discontinuous component in each element to provide a stabilization term for the continuous finite element formulation. Traditional SGS method uses Riemann decomposition and vacuum boundary assumption to decouple the discontinuous component. Here we propose a new method to perform the decoupling based on the assumption that the convection term of the discontinuous component is proportional to the residual of angular flux in each element. The computing costs for the establishment of the coefficient matrix of discontinuous component are reduced to O(1) from O(n³). Further more, the computing costs for the inversion of the coefficient matrix are reduced to O(n) from O(n³) by applying mass lumping technique. Numerical results show that the new method is not only more efficient but also yields more accurate solution than traditional sub-grid scale method.