Acceleration of the power and related methods with dynamic mode decomposition

Abstract

An algorithm based on dynamic mode decomposition (DMD) is presented for acceleration of the power method (PM) and fattened power method (FPM) that takes advantage of prediction from a restarted DMD process to correct an unconverged solution. The power method is a simple iterative scheme for determining the dominant eigenmode, and its variants, such as fattened power method, have long been used to solve the k-eigenvalue problem in reactor analysis. DMD is a data driven technique that extracts dynamics information from time-series data with which a reduced-order surrogate model can be constructed. DMD accelerated PM (DMD-PM) and DMD-accelerated FPM (DMD-FPM) generate “snapshots” from a few iterations and extrapolate space in “fictitious time” to produce a more accurate estimate of the dominant mode. This process is repeated until the solution is converged to within a suitable tolerance. To illustrate the performance of both two schemes, a 1-D test problem designed to resemble a boiling water reactor (BWR) and the well-studied 2-D C5G7 benchmark were analyzed. Compared to the PM without acceleration, these tests have demonstrated that DMD-PM and DMD-FPM method can reduce the number of iterations significantly.