Shifting Strategy in the Spectral Analysis for the Spectral Green’s Function Nodal Method for Slab-Geometry Adjoint Transport Problems in the Discrete Ordinates Formulation

We present the positive features in the shifting strategy that we use in the homogeneous component of the general solution of the monoenergetic, slab-geometry, adjoint discrete ordinates (S N ) equations inside each discretization node for neutral particle source-detector transport problems. The adjoint spectral Green’s function (SGF) method uses the standard spatially discretized adjoint S N balance equations and nonstandard SGF adjoint auxiliary equations, which have parameters that need to be determined to preserve this local solution. We remark that the shifting strategy scales the N exponential functions of the local solution in the interval (0, 1). One advantage is to avoid the overflow in computational finite arithmetic calculations in high-order angular quadrature and/or coarse-mesh calculations.