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

Abstract

Abstract 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†-CN) method to numerically solve multigroup adjoint transport problems in the discrete ordinates formulation. Described here is the methodology to obtain the discretized SGF†-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.