Hi Sebastian, Sorry for the late reply. I do have similar observations that the effect of the preconditioner is related to the time step size and viscosity, and I am not surprised. Because this preconditioner consists of three different parts if I remember correctly, and these two parameters decide the "weights" of the two easy parts: diffusion term and mass term.
Pressure Laplace question: I don't have a good way to deal with that. If you do, please let me know. For the other sub-preconditioners: I played with AMG before but never found a set of parameters that could give me good performance in general. Mp is easy, with or without preconditioners. SparseILU is a bad idea when you do adaptive mesh: for some unknown reason, it always crashes my program when I do local refinement. Also, don't use BlockJacobi when you go parallel, which is also bad. Thank you, Jie On Fri, Nov 9, 2018 at 6:42 PM Sebastian Glane <seb_gl...@gmx.de> wrote: > Hi Jie, > > thanks a lot. The link to your repository was very helpful. I could > significantly reduce the number of iterations using your implementation of > computing the pressure laplacian through: > > K_p = B diag(velocity_mass_matrix)^-1 B^T. > > I have tested the dependence of the preconditioner on the time step and > the mesh size and observed that it is likely to be mesh independent, i.e. > if the mesh is refined the number of outer (GMRES) iterations does not > change, which is great. > > However there is a dependence on the size of the time step. Both variants > with assembly and your implementation show an increase in the number of > iterations. > > time step > iterations with B B^T > iterations with assembly > 1e-5 > 6 to 7 > 6 or 16 ringing > 1e-4 > 8 to 9 > 18 to 19 > 1e-3 > 10 to 11 > 21 to 22 > 1e-2 > 12 to 14 > 24 to 27 > 1e-1 > 23 to 24 > 51 to 54 > > Did you make the same or similar observations? I have read some of the > literature and as far as I understand it the preconditioner should be > independent of the step size and viscosity. > > Another point I would like to raise is related to mesh independence, > which is not quite true. In every step the solution of the pressure laplace > matrix (K_p) requires by far the largest number of iterations. I am > monitoring the iterations of all subsolvers: > > 7 GMRES iterations for stokes system, (A: 8, Kp: 682, Mp: 60) > > For A (velocity block) one cycle of TrilinosWrappers::PreconditionAMG is > used. Mp is preconditioned using PreconditionSSOR and for Kp I am using > SparseILU. For the example quoted the pressure space has 4800 dofs. I am > wondering why the SparseILU with roughly 100 iterations per precondition > step does such a bad job in this case. > > Of course, I don't expect you to answer all of this but it would great if > you make some comments about your experience with this preconditioner. By > the way I am also using an IMEX scheme in my solver, see > https://github.com/sebglane/BoussinesqFluidSolver/tree/modular_version . > > Best wishes, > > Sebastian > On 01.11.18 17:30, Jie Cheng wrote: > > Hi Sebastian, > > I think what you described is correct. I could not see why it did not work > out. But I recommend reading Timo's dissertation. Also, for the > implementation, you can check out my code for the implicit scheme > <https://github.com/OpenIFEM/OpenIFEM/blob/master/source/insim.cpp#L56> > and explicit-implicit scheme > <https://github.com/OpenIFEM/OpenIFEM/blob/master/source/insimex.cpp#L42>. > > Best, > Jie > > On Thu, Nov 1, 2018 at 5:58 PM SebG <seb_gl...@gmx.de> wrote: > >> Dear Jie, dear deai.ii user, >> >> I am working on the Cahouet-Chabbard preconditioner in context >> buoyancy-driven flow problems. Somehow my preconditioner does not work >> quite well. The number of iterations depends on the time step, which should >> not be the case. With more than 50 iterations it is also quite large. I >> would like to ask if you or someone else could provide some details of your >> implementation or give tips. >> >> The velocity block of the system matrix is given by: >> alpha / timestep * M + gamma * c * K . >> M, K are the velocity mass and stiffness matrix. The scalars alpha and >> gamma are related to the time discretization and c is a dimensionless >> parameter. If I am not wrong, the Cahouet-Chabbard Schur complement >> approximation is given by >> S^-1 = alpha / timestep * K_p^-1 + gamma * c * M_p^-1 . >> >> I am assembling the pressure stiffness and pressure mass matrix >> explicitly. However my problem is a pure Dirichlet problem w.r.t. the >> velocity, which in contrast mean that preconditioner is using Neumann BCs. >> Therefore, I am constraining one pressure dof, which regularizes the >> pressure laplace matrix. This approach is discussed in another thread >> <https://groups.google.com/forum/#!msg/dealii/HBQD_WXuNOs/w0A56WAf2WcJ>. >> For this reason I have two ConstraintMatrix object one for the system >> matrix and one for the preconditioner. >> >> I also attached my code which is based step-32 but in serial. >> >> Best wishes, >> Sebastian >> >> Am Freitag, 20. Oktober 2017 09:36:07 UTC-7 schrieb Jie Cheng: >>> >>> Hi Martin and Wolfgang >>> >>> Thank you very much for the helpful comments and references. I'll >>> start to read the works you mentioned. >>> >>> >>>> Jie -- I think this would be a very interesting program for others as >>>> well. >>>> Would you be interested in contributing it to the code gallery? >>>> >>> >>> I'd love to contribute after I work it out! >>> >>> Jie >>> >> -- >> 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 a topic in the >> Google Groups "deal.II User Group" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/dealii/41VjIh5dzng/unsubscribe. >> To unsubscribe from this group and all its topics, send an email to >> dealii+unsubscr...@googlegroups.com. >> For more options, visit https://groups.google.com/d/optout. >> > -- > 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 a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/dealii/41VjIh5dzng/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > dealii+unsubscr...@googlegroups.com. > For more options, visit https://groups.google.com/d/optout. > > -- > 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 a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/dealii/41VjIh5dzng/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > dealii+unsubscr...@googlegroups.com. > For more options, visit https://groups.google.com/d/optout. > -- 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. 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