A Variant of the Second-Moment Method for k-Eigenvalue Calculations

The second-moment (SM) method is a linear variant of the quasi-diffusion (QD) method for accelerating the iterative convergence of S_n source calculations. It has several significant advantages relative to the QD method, diffusion synthetic acceleration, and nonlinear diffusion acceleration. Here, we define a variant of this method for k-eigenvalue calculations that retains the advantages of the original method, and we computationally demonstrate the efficacy of the method for simple example calculations. In particular, this method has two important properties. First, it is a linear acceleration scheme requiring only the solution of a pure k-eigenvalue diffusion equation with a corrective source term as opposed to a k-eigenvalue drift-diffusion equation. Second, unconditional stability is achieved even when the diffusion equation is not discretized in a manner consistent with the S_n spatial discretization. We are unaware of any other scheme that has these properties. We also show a connection between our method and the k-eigenvalue acceleration technique of Barbu and Adams, which motivated us to develop our SM method.