Hi Timo Thanks for your answer!
> Do you have an inner inner solve or do you just use a single SparseILU > application? I do not have an inner inner solve, I just use a single SparseILU<double> initialized with system_matrix.block(0,0) to approximate its inverse. It is the trick used in step-22. > ILU is not great in 3d. This is even true if you consider the velocity > block of the Stokes problem (which is Laplace-like). See the tables in > > https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dealii.org_8.5.0_doxygen_deal.II_step-5F56.html-23Results&d=DwIBaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=4k7iKXbjGC8LfYxVJJXiaYVu6FRWmEjX38S7JmlS9Vw&m=--nG2SHIoX884s0M9k-XskKi6u9iVsUaE8GaIsVH_Yw&s=PXVWQ3PvRgczuV6a0GPJS7sH7uTPr9z0O-LNq7vuRtA&e= > > for > example. You can clearly see that ILU is h-dependent. So ILU should > "work" but I am not surprised that it degrades for larger problem > sizes. Your system is even harder to solve because of Grad-Div and the > non-symmetric convective term. > Looks like the direct solver is the best choice except for multigrid. The size of problem will certainly be limited on a single machine because of the memory usage. But what if I parallelize my code using distributed-memory? Does dealii have a parallel version of direct solver? My ultimate problem size will have less than 10 million dofs. The cluster I have access to has 16G memory on each node, I can probably use 64 nodes or even more. Will I be able to solve such a problem using direct solver for system_matrix.block(0,0)? > I am afraid this will be difficult. While not easy to do, step-56 > allows you to solve larger problems using geometric multigrid. > Extending this to Navier-Stokes is not easy either (and we are getting > close to state-of-the-art research). > I have no experience in multigrid. Forgive me if I am asking the wrong question: is algebraic multigrid method a black box comparing to the geometric one? By black box I mean it requires no additional information other than the matrix itself hence no additional coding. Thank you 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 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]. For more options, visit https://groups.google.com/d/optout.
