Dear Wolgang, thank you for the answers On Sunday, December 6, 2020 at 8:00:09 p.m. UTC-5 Wolfgang Bangerth wrote:
> On 12/6/20 12:27 PM, blais...@gmail.com wrote: > > > > In this case, even using ILU(1) is extremely expensive (e.g. it takes 2X > more > > time than to assemble the matrix and it really doubles up the iteration > time). > > Consequently, we are using ILU(0), which in the present case is > performing > > relatively well (say between 40-100 iterations per newton step). I was > > wondering if there were any other suggestions in terms of preconditioner > that > > we could use? > > > > Our system : GLS stabilized Navier-Stokes, monolithic matrix formulation > > (single matrix for u,v,w,p). The matrix is non-symmetric. > > Our solver : Either GMRES or BiCGStab. In our case it seems GMRES is a > bit > > faster (around 20%) because the iterations are cheaper. I have tried all > of > > the solvers in the TrilinosWrappers except FGMRES actually. > > Our current preconditioner : ILU(0) > > Library used : Trilinos through the deal.II wrappers > > Element order : Q2-Q2, Q3-Q3 or Q4-Q4. > > > > Any suggestions would be appreciated. I am doing all I can right now to > > speed-up matrix assembly, but in general we only need to assemble the > matrix > > every 3-5 time steps, so I am just trying to find a good compromise > between a > > good preconditioner that is not crazy expensive. Would I be better to > accept > > having a poorer jacobian matrix, use a more expensive preconditioner and > > keeping it for a longer time (say 10-20 time-steps)? > > Have you played with the trade-off of having a more expensive > preconditioner > but building it less often? For example, using ILU(1) instead of ILU(0), > but > only build it every few time steps? > How come you get away with only assembling the matrix every 3-5 time > steps? > Are you treating advection explicitly? > We get off by assembling the matrix every N time-steps for two main reasons: - We use SDIRK which has a constant diagonal for all stages, hence this part of the matrix does not change significantly - We are willing to sacrifice one non-linear iteration there and there, at the cost of less assembly. The idea is that we use an exact jacobian when we assemble the matrix, but then we let it become innacurate as we continue iterating, while just updating the rhs. This is not a good approach when the time-step is large, but when the time-step is small (say CFL<1), it really does not affect significantly the number of newton iterations. Consequently, we can update the jacobian matrix every 3 to 5 time-steps or so. This is just an indication, generally we update it as soon as a non-linear step has not lead to a decrease of more than 10x of the residual, meaning that our Newton method is becoming inefficient. > > I'm also curious about what the matrix you use looks like. It must be > something like > A B > B^T C > What terms are in A,B,C? > It has exactly this shape. The full weak form and some results are detailed in : https://www.sciencedirect.com/science/article/pii/S2352711020302922 A is momentum + SUPG C is the PSPG block. In essence it looks very much like a stiffness matrix weighted by the stabilization parameter. Hence, I really don't think it is "well conditioned". > Best > Wolfgang > Thank you for your time. As always, I really appreciate this community :)! > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > 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 dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/77c9d3ee-73e1-430a-8c3f-9f00dcb2b141n%40googlegroups.com.
