Dear Jike.Wang,
We wrote a paper where we analysed the performance of time-dependent-RSDDH: Tal et al., Phys. Rev. Research, 032019 (2020).
In short: this approach shows a very good performance for the calculation of the dielectric function. But it makes a number of approximations compared to the full BSE-GW calculations. Hence, one should not expect it to perform better than BSE-GW. At best TD-RSDDH can reproduce the BSE results. Hence, if in your system the BSE-GW spectrum doesn't agree well with experiment, one should not expect that TD-RSDDH would do better. For example, the lack of the phonons in the calculation can be responsible for a large discrepancy in BSE-GW and experiment.
Furthermore, in some systems the GW band gap and the RS-DDH band gaps show a substantial discrepancy. Hence, the peaks in the dielectric function will be shifted for BSE-GW vs TD-RSDDH. But the overall shape of the spectrum calculation with these two methods might be in a very good agreement.
In your document in particular, it seem that the overall shape of the spectrum is reproduced reasonable well. However, it looks to me that the spectra of Si and LiF are not well converged with the number of k-points, which is especially important when the results are compared to experiment.
I hope that helps.
Best wishes,
Alexey