Dear Timo It's been a month since I started this thread, during this time I managed to write a time-dependent navier-stokes solver with Grad-Div stablization using IMEX scheme. My major references are your PhD thesis (beautiful work by the way), Dr. Kronbichler's paper and steps 20, 22, 57. I used SparseDirectUMFPACK to solve for A_inverse and it works well in 2D. I tried to use the same trick as in step-22, where an InnerPreconditioner was defined to switch between SparseDirectUMFPACK in 2D and SparseILU in 3D. However I found that SparseILU won't work even when in small 2D cases. To verify this I tried to replace the SparseDirectUMFPACK in step-57 with SparseILU, same thing happened. Without additional off-diagonals the GMRES solver won't converge; with additional off-diagonals, the program runs unbearably slow. Why is the performance of SparseILU so much worse than SparseDirectUMFPACK? Am I using it the right way?
At this point I totally understand parallelization is necessary for larger problems. But I still want to enable my toy program to run problems slightly out the scope of SparseDirectUMFPACK. After that I will try parallelize it. Thanks Jie On Wednesday, October 18, 2017 at 10:12:58 AM UTC-4, Timo Heister wrote: > > Jie, > > did you see the "Possibilities for extensions" section in step-57? For > large problems (especially in 3d), one would need to parallelize and > switch to algebraic of geometric multigrid. See step-55 and step-56. > > On Wed, Oct 18, 2017 at 10:06 AM, Wolfgang Bangerth > <[email protected] <javascript:>> wrote: > > > > Jie, > > > >> I attempted to use FGMRES solver without preconditioner to replace Line > >> 269 as following: > >> > >> SolverControl solver_control (stokes_matrix.block(0,0).m(), > >> 1e-6*utmp.l2_norm(), true); > >> SolverFGMRES<Vector<double> > gmres(solver_control); > >> gmres.solve(stokes_matrix.block(0,0), dst.block(0), utmp, > >> PreconditionIdentity()); > >> > >> But it couldn't converge even in 2D. I also tried SolverBicgstab > without > >> preconditioning, it did converge but no improvement compared to direct > >> solver was observed in the cases that I ran. > > > > > > Yes, not using a preconditioner is not an option. You need to use > > *something* or you will not be able to converge in any reasonable number > of > > iterations. > > > > If your problem is advection-dominated (i.e., a high Reynolds number) > then I > > would try to use downstream numbering of unknowns (via the corresponding > > DoFRenumbering function) and then use SSOR as a preconditioner. There > are > > many better preconditioners for the N-S equations, but that's an easy > start. > > > > Best > > W. > > > > -- > > ------------------------------------------------------------------------ > > Wolfgang Bangerth email: [email protected] > <javascript:> > > www: > > > https://urldefense.proofpoint.com/v2/url?u=http-3A__www.math.colostate.edu_-7Ebangerth_&d=DwIBaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=R5lvg9JC99XvuTgScgbY_QFS80R7PEA2q0EPwDy7VQw&m=uU9whAhMqT-pR4C08zqYt7CewVh_JJIJ1bnG4T1vLig&s=yTFbl6BueN9SAskjznG16VzTBmdIoIWbULpbDNjT75w&e= > > > -- > > The deal.II project is located at > > > https://urldefense.proofpoint.com/v2/url?u=http-3A__www.dealii.org_&d=DwIBaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=R5lvg9JC99XvuTgScgbY_QFS80R7PEA2q0EPwDy7VQw&m=uU9whAhMqT-pR4C08zqYt7CewVh_JJIJ1bnG4T1vLig&s=AMjdmsQWdgeDKpbHZuDMpbISzaSJjFn5Is7GfbBdfAY&e= > > > For mailing list/forum options, see > > > https://urldefense.proofpoint.com/v2/url?u=https-3A__groups.google.com_d_forum_dealii-3Fhl-3Den&d=DwIBaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=R5lvg9JC99XvuTgScgbY_QFS80R7PEA2q0EPwDy7VQw&m=uU9whAhMqT-pR4C08zqYt7CewVh_JJIJ1bnG4T1vLig&s=N263oHkyuceyJeW21Kye7uazp1_iJ2RJm-Xms0lczvc&e= > > > --- 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] <javascript:>. > > For more options, visit > > > https://urldefense.proofpoint.com/v2/url?u=https-3A__groups.google.com_d_optout&d=DwIBaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=R5lvg9JC99XvuTgScgbY_QFS80R7PEA2q0EPwDy7VQw&m=uU9whAhMqT-pR4C08zqYt7CewVh_JJIJ1bnG4T1vLig&s=3Y5ZXSFU7VEOtEd72-RWoDIjFNvIER7VX75FoZ3c_WE&e= > > > . > > > > -- > Timo Heister > http://www.math.clemson.edu/~heister/ > -- 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.
