Fig. 2: Comparison of efficiency and accuracy between EP-LTP and ER-LTI frameworks in eigenstructure calculations.
a CPU time required to compute both eigenvalues and eigenvectors. Points of different shapes represent the EP-LTP model and the ER-LTI models with different truncation numbers m. A third-order polynomial fit (i.e., CPU time∝n3c) is applied to capture the CPU time trend, where nc denotes the model order. Specifically, nc = n for the EP-LTP model and nc = n(2 m + 1) for the ER-LTI models, with n representing the system scale. Additional details are provided in the Supplementary Information. b ER-LTI model fidelity compared with EP-LTP model. Three specific damping ranges (i.e., the real parts of eigenvalues σ > −0.1, −0.4, and −0.8, the modes within these ranges are prone to instability) are focused on, represented as blue, red, and green lines, respectively. Under different damping ranges, the eigenvalue number is Nltp for the EP-LTP model. Besides, the accurate number of eigenvalues obtained by ER-LTI is Nhss. We use the quotient of Nhss and Nltp to represent the fidelity of the HSS models in different damping ranges. c Eigenvector error between EP-LTP and ER-LTI. A comparison is performed in the 813th-order testing system, where a high truncation number guarantees the accuracy of all modes with real parts > −0.8. The corresponding eigenvector results are consistent between the EP-LTP and ER-LTI models with the truncation number 29. See Supplementary Notes 6 for details and a quantitative interpretation of the accuracy indices. Source data are provided as a Source Data file.
