ACCELERATION OF THE FLATTENED POWER METHOD WITH DYNAMIC MODE DECOMPOSITION

摘要

Overall, the results indicate that the DMD-FPM(n) algorithm can provide significant acceleration relative to the unaccelerated flattened power method. One key topic to explore is a more accurate way to estimate the eigenvalue to be paired with the DMD eigenvalue prediction. In addition, a study should be made of the performance of DMD-FPM(n) relative to established acceleration schemes, including nonlinear diffusion acceleration. While these results are promising, the DMD-FPN(n) algorithm is not expected to outperform current methods such as the generalized Davidson method[12] or coarse-mesh finite difference[13] based on the performance of DMD-PM(n) relative to Arnoldi iteration [7]. However, as has been suggested [7] the DMD-FPN(n) method may be able to accelerate Monte Carlo eigenvalue problems in which the use of smaller population sizes may be comparable to the use of flattened operators in deterministic transport methods.