Generalized Partitioned Matrix Acceleration for Variational Nodal Diffusion Method

The Generalized Partitioned Matrix (GPM) acceleration method for the Variational Nodal Method (VNM) with diffusion approximation is presented. In the GPM method, the vectors of expansion coefficients of the scalar flux, source, and partial currents are divided into low-order and high-order terms. For each outer iteration, the low-order terms of the flux, fission source, and partial currents are first solved with fixed higher-order terms from the preceding outer iteration, and then a full matrix sweep through the energy groups is performed to update the full set of expansion coefficients. The GPM method increases the CPU time per outer iteration but reduces the overall computational time significantly by reducing the number of outer iterations required for convergence. The GPM acceleration method has been implemented in the NODAL code, and its performance was compared with that of the traditional Partitioned Matrix (PM) acceleration scheme for four problems: two- and three-dimensional C5G7 problems, a NuScale modular core problem, and a large pressurized water reactor problem. The numerical results show that the PM acceleration consistently reduces the computational time by a factor of 2.0 and the GPM acceleration yields two to three times higher speedup than with PM acceleration by reducing the number of outer iterations. The GPM speedups over the unaccelerated VNM range between 4.3 and 6.3. Moreover, the speedup ratio achieved with the GPM acceleration increases with an increasing dominance ratio of the problem since the required number of outer iterations increases with an increasing dominance ratio.