Hi Zhouyang, Thank you for your e-mail. I've some experience with linear stability solvers on nektar++ and I've written my replies in the thread below. Hope you find them useful. Regards, Chi Hin P.S: Please feel free to chip-in if my answers are not 100% correct. ________________________________ From: nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> on behalf of 王舟阳 <wangzhouyang@buaa.edu.cn> Sent: 12 January 2023 15:33 To: nektar-users <nektar-users@imperial.ac.uk> Subject: [Nektar-users] About Modified Arnoldi Driver This email from wangzhouyang@buaa.edu.cn originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list<https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address. Dear Nektar++ Users: I am Wang Zhouyang, and I am sorry to present some questions about the Modified Arnoldi Driver in linear stability analysis: 1. When I was doing parallel computation, I was prompted that Arpack algorithm could not implement parallel in Nektar++. Although this is true based on other user communications here, I still want this issue to be confirmed. Thank you very much. There are 2 ways of computing eigenvalues in nektar++, 1. ARPACK 2. ModifiedArnoldi. The ModifiedArnoldi algorithm doesn't require ARPACK dependency as the k-step Arnoldi iteration is explicitly implemented into nektar++ (for more details refer to Direct optimal growth analysis for timesteppers - Barkley et al. 2008). Parallel executions are only supported with ModifiedArnoldi. 2. As described in the user documentation, the Arpack package can specify properties such as LargestMag or LargestReal etc to output eigenvalues. For the Modified Arnoldi algorithm, what is the property of the eigenvalues utilized to write the result? (For example, nvec=4, do the four eigenvectors output after iteration have the largest four magnitudes or the top four growth rates or other criteria?) For nvec=4, the eigenvalue computation will stop after the 4 eigenvalues have converged (specific by evtol). Based on my experience, the ArpackProblemType is not supported for ModifiedArnoldi and the eigenvalues computed correspond to the largest magnitude. 3. In solving, is it reasonable to have a mode with a frequency of 0? I understand it as a flow phenomenon of pure exponential growth (or decay).In my humble opinion, the frequency may suggest a flow structure with oscillation, and it would be unstable (or attenuated) regarding to the growth rate. Yes, for instance, the Rayleigh-Benard convection has a non-oscillatory (freq = 0) linearly unstable mode. Thank you very much for your help, and I sincerely hope to get your answers. Thanks to the Nektar++ project team. Best Regards, Wang Zhouyang