Energy-Dependent, Self-Adaptive Mesh <i>h</i> ( <i>p</i> )-Refinement of a Constraint-Based Continuous Bubnov-Galerkin Isogeometric Analysis Spatial Discretization of the Multi-Group Neutron Diffusion Equation with Dual-Weighted Residual Error Measures
Seth Wilson, M.D. Eaton, J. Kópházi
Abstract
Energy-dependent self-adaptive mesh refinement algorithms are developed for a continuous Bubnov-Galerkin spatial discretization of the multi-group neutron diffusion equation using NURBSbased isogeometric analysis (IGA). The spatially self-adaptive algorithms employ both mesh (h) and polynomial degree (p) refinement. Constraint-based equations are established across irregular interfaces with hanging-nodes; they are based upon master-slave relationships and the conservative interpolation between surface meshes. A similar Galerkin projection is employed in the conservative interpolation between volume meshes to evaluate group-to-group source terms over energydependent meshes; and to evaluate interpolation-based error measures. Enforcing continuity over an irregular mesh does introduce discretization errors. However, local mesh refinement allows for a better allocation of computational resources; and thus, more accuracy per degree of freedom. Two a posteriori interpolation-based error measures are proposed. The first heuristically minimizes local contributions to the discretization error, which becomes competitive for global quantities of interest (QoIs). However, for localized QoIs, over energydependent meshes, certain multi-group components may become under-resolved. The second employs duality arguments to minimize important error contributions, which consistently and reliably reduces the error in the QoI.