Stability Analysis of the Quasidiffusion Method on Periodic Heterogeneous 1D Transport Problems

We study the convergence of the quasidiffusion (QD) method on one-dimensional spatially periodic heterogeneous problems. The QD method is a nonlinear projection-iterative method. A Fourier analysis of the linearized QD equations is performed. The convergence rates of the QD method in the vicinity of the solution are obtained. We also analyze the Second Moment (SM) method, which can be interpreted as a linear version of the QD method. The presented analysis gives a new insight on the convergence behavior of the QD method in a discretized form and reveals the differences in the convergence of the QD and SM methods. Numerical results are presented to confirm theoretical predictions.