Hi Wang, KDIM sets the size of the Krylov space used to evaluate updates to the current eigenvector approximation. In general, the procedure will run at least the number of iterations equal to KDIM, each time adding one vector to the sub-space until there is a KDIM of them (see the .evl file, that stores some information on the solution process). Than, the procedure start replacing vectors with new approximations, until convergence criterion is met. My observation is, that having this value to small can lead to a large number of iterations that you have to perform, and having it to large, forces a large number of iteration to start with, but past KDIM vectors the convergence should be quicker. So I would advice practicing with a channel test case, to get a feel. In my opinion this value should have no relation to the final frequency, but will influence convergence. NumSteps determines the number of time steps run in the linear solver. The larger it is, the longer the time that the linear operator evolves the current perturbation. So IMHO the longer it is, the more distinct should the leading eigen mode become - leading to faster convergence. But then, if you have some spurious osculations in your solution, those would be amplified as well, obfuscating the convergence. Finally, I have found, that ModifiedArnoldi driver will in general be rather slowly converging, and I tend to use the Arpack driver, with a relatively large KDIM (64,128 and up). One issue is, Arpack is serial only, so if your case is very large this could be an issue. Pozdrawiam, dr inż. Stanisław Gepner, *Wydział Mechaniczny Energetyki i Lotnictwa* Nowowiejska 21/25 Str. 00-665 Warszawa, Polska tel. +48 (22) 234 51 70 <http://www.pw.edu.pl/> On 18.06.2023 12:00, 王舟阳 wrote:

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Dear nektar++ users and developers. Sorry to bother everyone here, however, I need some help the modifiedArnoldi solver. In the linear stability solver, there are NUMSTEPS and KDIM to be filled in, what is the relationship between the setting of these two variables and the frequency of the unstable mode to be solved? For example, if the frequency of the unstable mode is approximately 0.1 Hz (0.2pi for the circle frequency) and TIMESTEP = 0.002, should NUMSTEPS and KDIM be set relatively large or small in order to capture this unstable mode? I wonder if anyone has any relevant experience in setting this up and I would appreciate any help. Thanks again to the users and developers of nektar++.

Best Regards, Wang Zhouyang

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