Acceleration of the outer iterations of the space-dependent neutron kinetics equations solution

A variant of the Chebyshev iterative procedure, called the Chebyshev Semi-Analytical (CSA) method, is developed for acceleration of outer iterations of the space-dependent neutron kinetics equations solution. A Chebyshev polynomials sequence is chosen to optimize the convergence of residual vectors to the eigenvector of the iteration matrix. When the convergence is attained, the "exact" solution is computed by adding an error vector to the obtained approximate solution. Convergence rate of the CSA method is determined by the second eigenvalue of the iteration matrix in contrast to the Chebyshev Semi-Iterative (CSI) method where it is defined by the spectral radius of the same matrix. An adaptive Chebyshev procedure is modified for estimation of the optimum iteration parameters of the CSA method. The proposed method is implemented in the 3D neutron kinetics computer code SKETCH. The numerical results of benchmark problem calculations demonstrate that the CSA method is 2-5 times faster than the CSI method for delayed critical transient calculations. The relative effectiveness of the CSA method increases with increase in time step size.