On the Use of Symmetrized Transport Equation in Goal-Oriented Adaptivity

ABSTRACT In this paper, we revisit the self-adjoint formulation of the transport equation based on the general symmetrization procedure of Marchuk and Agoshkov. In particular, we show how this formulation can be used to obtain solutions of both the forward and the adjoint transport equations with arbitrary source terms from only one solution and one post-processing step. This feature fits well into the well established dual-weighted residual framework for goal-oriented adaptivity, which we use to develop an adaptive finite-element method for solving neutron transport problems. We also describe the relationship to the well known self-adjoint angular flux (SAAF) formulation, allowing us to view the resulting method as an efficient way of performing goal-oriented adaptivity for SAAF. The paper concludes with preliminary numerical experiments that show the viability of the presented method and encourage further research.

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