A spectral nodal method for the adjoint SN neutral particle transport equations in X, Y-geometry: Application to direct and inverse multigroup source-detector problems

In this work, we apply an adjoint technique to solve two-dimensional direct and inverse source-detector transport problems. In order to obtain the neutral-particle importance maps, we have developed the extended adjoint spectral Green's function constant-nodal (SGF(dagger)-CN) method to numerically solve multigroup adjoint transport problems in the discrete ordinates formulation. Described here is the methodology to obtain the discretized SGF(dagger)-CN equations and the adjoint partial one-node block inversion scheme used to iteratively solve these equations. Then, the Levenberg-Marquardt method is applied to minimize a least-squares difference in order to identify the multigroup sources. To illustrate the accuracy of the present methodology, we present and discuss numerical results to two typical model problems. (C) 2020 Elsevier Ltd. All rights reserved.