I decrease dt by half for each mesh refinement. Now the iterations remain constant (20, 21, and 23), same as you predicted. I guess in practical I should keep dt and h constant (based on frequency and wave speed) for a acceptable accuracy, while increase the dimension of computational space to test the number of iterations? 在2024年10月5日星期六 UTC+8 11:33:36<yy.wayne> 写道：
> I didn't know that dt should be propotional to h/c for accuracy > results. Thank you for > pointing it out. > > 在2024年10月5日星期六 UTC+8 11:15:07<Wolfgang Bangerth> 写道： > >> On 10/4/24 20:39, 'yy.wayne' via deal.II User Group wrote: >> > >> > I'm solving a time-dependent wave equation, and dt is the time step. >> For >> > backward Euler >> > time integration, I get M+dt^2*K = (v,u) + (\delta T)^2*(\nabla v, >> \nabla u). >> > The time step >> > dt does not scale with mesh size h, so the condition number is not >> bounded. >> >> I see. It's of course true that for an implicit discretization you don't >> *have* to choose dt proportional to h. You can then get into a situation >> where >> indeed the condition number grows. >> >> But from a practical perspective, for accuracy (not stability) reasons, >> you >> will want to choose dt \approx h/c where c is the wave speed. You just >> won't >> get accurate solutions otherwise. >> >> Best >> W. >> >> -- >> ------------------------------------------------------------------------ >> Wolfgang Bangerth email: [email protected] >> www: http://www.math.colostate.edu/~bangerth/ >> >> >> -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/2b08701a-1b03-4f66-8f9f-d2f2900bb29fn%40googlegroups.com.
