The finite element with discontiguous support multigroup method: Application
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The Finite-Element-with-Discontiguous-Support Multigroup (FEDS-MG) method, outlined and derived in a companion paper, is a novel energy discretization technique for deterministic particle transport that overcomes many of the challenges associated with the typical Multigroup (MG) method, such as dependence on fixed self-shielding of the cross sections within a coarse group. Much the same way as the MG method requires a group structure, the FEDS-MG method relies on solving a minimization problem to determine an energy mesh made up of discontiguous energy elements. We may generate this mesh without requiring reference solution information and show convergence in energy as energy elements are added for one-dimensional pin-cell problems. Convergence holds for several definitions of basis-function-weighted cross sections. We use our pin-cell calculations to inform our implementation of the FEDS-MG method on an energy-generalized version of the C5G7 problem, which we call the C5Gproblem.
