On the Use of Symmetrized Transport Equation in Goal-Oriented Adaptivity. Issue 4 (6th June 2016)

• Record Type: Journal Article
• Authors: Hanuš, M.; McClarren, R. G.
• Is Part Of: Journal of computational and theoretical transport. Volume 45:Issue 4(2016)
• Page Start: 314
• Page End: 333
• Publication Date: 2016-06-06
• Subjects: neutron transport equation; self-adjoint formulation; finite element method; Galerkin approximation; goal-oriented adaptivity; symmetrization; Transport theory -- Periodicals; Statistical physics -- Periodicals; Statistical physics; Transport theory; Periodicals; 530.138
• DOI: 10.1080/23324309.2016.1164722
• Languages: English
• ISSNs: 2332-4309

Abstract

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.