A postdoctoral fellowship is proposed on the a posteriori estimates for the mixed finite element discretization of the multigroup diffusion criticality problem.
The objective is to develop efficient and reliable a posteriori estimates for a multigroup diffusion criticality problem with strong spatial heterogeneities, i.e. a model where the parameters, typically the coefficients of the equations, vary rapidly in space. Mathemically speaking, the criticality problem is a non-symmetric generalized eigenvalue problem.
At the reactor core scale, using simplified models is common in the nuclear industry. Precisely, the simplified models can be the neutron diffusion model or the simplified transport model. We derived rigorous em a posteriori error estimates for mixed finite
element discretizations of the neutron diffusion source problem, and proposed an adaptive mesh refinement strategy that preserves the Cartesian structure. A first application of this approach to the criticality problem was performed. Regarding the industrial context and specifically the numerical simulations, our approach is part of the development of a mixed finite element solver called MINOS in the APOLLO3 code. Further extensions of the a posteriori estimates were studied such the multigroup diffusion source problem and a Domain Decomposition decomposition denoted the DD+L2 jumps method. The enlisted approaches are based on the formulation of a source problem. The objective is to extend the a posteriori approach to a non-symmetric generalized eigenvalue problem.