Adaptive Mesh Refinement of the Domain Decomposition+L²-Jumps Method applied to the Neutron Diffusion Equation on 3D Structured Meshes

A deterministic solver for neutron calculation is classically based on the two step calculation scheme: the 2D lattice step to find the homogenized cross sections and the 3D core step usually based on the neutron diffusion equation for the whole core domain. In general, this equation can be recast in a mixed variational form, and then discretized by using the Raviart-Thomas-Nédélec Finite Element. More importantly, the neutron diffusion equation usually admits low regularity solution due to heterogeneous coefficients. This requires Adaptive Mesh Refinement (AMR) to improve the accuracy of the solution. In order to have independent local refinement on each subdomain, the AMR strategy is combined with the domain decomposition+L² jumps as illustrated in [1] with two subdomains on 2D numerical test cases. The goal of this work is to extend the above strategy to 3D structured meshes with multiple subdomains which leads to a more optimal refinement for the full 3D core calculation.