A new mathematical adjoint for the modified SAAF_-SN equations

We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF_-SN) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF_-SN method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF_-SN . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both for fixed source and eigenvalue problems.