An adjoint-based method for improving computational estimates of a functional obtained from the solution of the Boltzmann Transport Equation

This paper describes an adjoint-based a posteriori error method for improving computational estimates of a functional. Examples of a functional occur in many areas of physics and engineering; they include lift and drag past an obstacle in aircraft and ship design and glacier movement in geology. In nuclear physics they include quantities such as power in a reactor fuel pin, the Key eigenvalues in a criticality problem, or radiation input to a shield or the response of a detector. This paper shows how to use the adjoint system of equations to derive an error measure for improving these types of functional. The approach is to compute a reliable approximation to the error contained within the functional. A novel scheme for locally enriching the solution in order to obtain a higher order solution is used to define this approximation to the error, which is then subtracted from the functional to improve it. This goal-based scheme also has potential use in automating mesh adaption and is well aligned, therefore, with current work of other groups. The scheme developed in this paper offers an alternative to adapting the mesh in order to improve a functional. (C) 2012 Published by Elsevier Ltd.