###
Bruno Turcksin, Jean C. Ragusa, Wolfgang Bangerth

**Goal-oriented h-adaptivity for the multigroup SP**_{N} equations

Nuclear Science and Engineering, vol. 165 (2010), pp. 305-319.

This article is also available as
IAMCS preprint 2009-068.

We investigate application of
goal-oriented mesh adaptivity
to the *SP*_{N} multigroup equations.
This technique utilizes knowledge of the computational goal and
combines it with mesh adaptivity to accurately and rapidly compute quantities
of interest. Specifically, the local error is weighted by the importance of a
given cell towards the computational goal, resulting in appropriate
goal-oriented error estimates. Even though this approach requires the solution
of an adjoint (dual) problem, driven by a specific source term for a given
quantity of interest, the work reported here clearly shows the benefits of
such a method.

We demonstrate the level of accuracy this method can achieve using
2D and 3D numerical testcases for one-group and
two-group models, and compare results with more traditional mesh refinement
and uniformly refined meshes. The testcases consider situations in which the
radiative flux of a source is shielded and are designed to prototypically
explore the range of conditions under which our methods improve on other
refinement algorithms. In particular, they model strong contrasts in material
properties, a situation ubiquitous in nuclear engineering.

*Wolfgang Bangerth*

* Sun Aug 20 15:19:55 MDT 2017 *