Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time dependent transport equation. Using these solutions we use the dynamic mode decomposition (DMD) to form an approximate transport operator. This approximate operator has eigenvalues that can be directly related to the time eigenvalues of the neutron transport equation. This approach works for systems of any level of criticality and does not require the user to have estimates for the eigenvalues. Numerical results are presented for homogeneous and heterogeneous media. The numerical results indicate that the method finds the eigenvalues that are most important to the solution evolution over a given time range, and the eigenvalue with the largest real part is not necessarily important to the system evolution.