### The Finite-Element With Discontiguous Support Multigroup Method

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Andrew Till, Texas A&M University
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Accurate and efficient computation of radiation interaction with matter undergirds numerous important applications. The popular “deterministic method” of simulating these interactions discretizes the six-dimensional phase space (physical space, particle direction and particle kinetic energy) upon which the radiation field depends and solves the discretized equations for the expected radiation distribution. Discretizing in energy has historically been a difficult problem because nuclei and atoms possess resonances where the probability of interacting with a nearby radiation particle changes many orders of magnitude for a very small change in incident radiation energy due to quantum mechanical effects. While these resonances may be well-characterized, resolving them in deterministic codes in addition to the full problem geometry is impractical and may require more memory than is available in modern and foreseeable high-performance computing systems.

This work proposes a new method to increase the accuracy of these computations by using a novel energy discretization scheme to treat resolved resonances. We represent the solution as a finite element in energy that lives on an energy mesh that is composed of energy elements, each of which is a non-contiguous combination of many energy intervals. The energy elements are chosen to maximally capture the resonance-scale detail of the solution. We use machine learning, specifically the hierarchical agglomeration clustering algorithm, to determine the energy elements. Results show the method to be convergent and accurate, even with few energy unknowns.

**Abstract Author(s): **Andrew T. Till, Marvin L. Adams, Jim E. Morel