Adjoint-Based Constant-Mass Partial Derivatives

It is well known that the adjoint equation in transport theory provides an economical means of computing derivatives of a system response to system parameters. It is also well known, though not often remarked on, that adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to dimensions (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. In this paper, we derive a formula for the constant-mass partial derivative of a response with respect to internal interface locations and the outer system boundary. The formula uses the partial derivatives for density and dimensions, which may be adjoint-based. This paper includes numerical comparisons for a two-dimensional (r-z) cylinder that also demonstrate the correctness of the regular adjoint-based derivatives for surface locations. Adjoint-based derivatives for the neutron problems were computed using the new SENSMG code at Los Alamos National Laboratory