Abstract
We present a new approach to calculating time eigenvalues of the neutron transport operator (also known as eigenvalues) by extending the dynamic mode decomposition (DMD) to allow for nonuniform time steps. The new method, called variable dynamic mode decomposition (VDMD), is shown to be accurate when computing eigenvalues for systems that were infeasible with DMD due to a large separation in timescales (such as those that occur in delayed supercritical systems). The
eigenvalues of an infinite medium neutron transport problem with delayed neutrons, and consequently having multiple, very different relevant timescales, are computed. Furthermore, VDMD is shown to be of similar accuracy to the original DMD approach when computing eigenvalues in other systems where the previously studied DMD approach can be used.
Acknowledgments
Ilham Variansyah’s portion of this work was funded by the Center for Exascale Monte-Carlo Neutron Transport (CEMeNT), a Predictive Science Academic Alliance Program (PSAAP-III) project funded by the U.S. Department of Energy, grant number DE-NA003967. Ethan Smith was supported by Los Alamos National Laboratory under contract number 633356/CW7080.
Disclosure Statement
No potential conflict of interest was reported by the authors.
Notes
a The DMD method, and our extension, can be applied to nonlinear problems. However, because we are interested in neutron transport problems primarily, beginning from a linear system is natural.