> On Mar 22, 2022, at 9:55 AM, Marco Cisternino <[email protected]> > wrote: > > Thank you Barry! > No, no reason for FGMRES (some old tests showed shorter wall-times relative > to GMRES), I’m going to use GMRES. > I tried GMRES with GAMG using PCSVD on the coarser level on real cases, > larger than the toy case, I cannot get machine epsilon mean value of the > solution, as in the toy case but about 10e-5, which is much better than > before. The rest of GAMG is on default configuration. The mesh is much more > complicated being an octree with immersed geometries. I get the same > behaviour using GMRES+ASM+ILU as well. > I cannot really get why the solution is not at zero mean value. I’m using a > rtol~1.0e-8 but I get the same mean value using rtol~1.o-6, I tried 1.0-12 > too, but no improvement in the constant, definitely tiny but not zero. > Thanks.
Are you using GMRES in the smoother or Chebyshev? Recommend using Chebyshev. I have no explanation why the average is not much closer to zero. Here is one thing to try. Use KSPMonitorSet() to provide a monitor that calls KSPBuildSolution() and then computes the average and prints it. Is the average always around 1e-5 from the first iteration or does it start close to 1e-12 and get larger with more iterations? > > Marco Cisternino > > From: Barry Smith <[email protected] <mailto:[email protected]>> > Sent: lunedì 21 marzo 2022 19:49 > To: Marco Cisternino <[email protected] > <mailto:[email protected]>> > Cc: Mark Adams <[email protected] <mailto:[email protected]>>; > [email protected] <mailto:[email protected]> > Subject: Re: [petsc-users] Null space and preconditioners > > > Marco, > > I have confirmed your results. > > Urgg, it appears we do not have something well documented. The removal > of the null space only works for left preconditioned solvers and FGMRES only > works with right preconditioning. Here is the reasoning. > > The Krylov space for left preconditioning is built from [r, BAr, (BA)^2 > r, ...] and the solution space is built from this basis. If A has a null > space of n then the left preconditioned Krylov methods simply remove n from > the "full" Krylov space after applying each B preconditioner and the > resulting "reduced" Krylov space has no components in the n directions hence > the solution built by GMRES naturally has no component in the n. > > But with right preconditioning the Krylov space is [s ABs (AB)^2 s, > ....] We would need to remove B^-1 n from the Krylov space so that (A B) B^-1 > n = 0 In general we don't have any way of applying B^-1 to a vector so we > cannot create the appropriate "reduced" Krylov space. > > If I run with GMRES (which defaults to left preconditioner) and the > options ./testPreconditioners -pc_type gamg -ksp_type gmres > -ksp_monitor_true_residual -ksp_rtol 1.e-12 -ksp_view -mg_coarse_pc_type svd > > Then it handles the null space correctly and the solution has Solution > mean = 4.51028e-17 > > Is there any reason to use FGMRES instead of GMRES? You just cannot use GMRES > as the smoother inside GAMG if you use GMRES on the outside, but for pressure > equations you don't want use such a strong smoother anyways. > > Barry > > I feel we should add some information to the documentation on the removal > of the null space to the user's manual when using right preconditioning and > maybe even have an error check in the code so that people don't fall into > this trap. But I am not sure exactly what to do. When the A and B are both > symmetric I think special stuff happens that doesn't require providing a null > space; but I am not sure. > > > > > > > On Mar 21, 2022, at 12:41 PM, Marco Cisternino <[email protected] > <mailto:[email protected]>> wrote: > > Thank you, Mark. > However, doing this with my toy code > mpirun -n 1 ./testpreconditioner -pc_type gamg > -pc_gamg_use_parallel_coarse_grid_solver -mg_coarse_pc_type jacobi > -mg_coarse_ksp_type cg > > I get 16 inf elements. Do I miss anything? > > Thanks again > > Marco Cisternino > > > From: Mark Adams <[email protected] <mailto:[email protected]>> > Sent: lunedì 21 marzo 2022 17:31 > To: Marco Cisternino <[email protected] > <mailto:[email protected]>> > Cc: [email protected] <mailto:[email protected]> > Subject: Re: [petsc-users] Null space and preconditioners > > And for GAMG you can use: > > -pc_gamg_use_parallel_coarse_grid_solver -mg_coarse_pc_type jacobi > -mg_coarse_ksp_type cg > > Note if you are using more that one MPI process you can use 'lu' instead of > 'jacobi' > > If GAMG converges fast enough it can solve before the constant creeps in and > works without cleaning in the KSP method. > > On Mon, Mar 21, 2022 at 12:06 PM Mark Adams <[email protected] > <mailto:[email protected]>> wrote: > The solution for Neumann problems can "float away" if the constant is not > controlled in some way because floating point errors can introduce it even if > your RHS is exactly orthogonal to it. > > You should use a special coarse grid solver for GAMG but it seems to be > working for you. > > I have lost track of the simply way to have the KSP solver clean the constant > out, which is what you want. > > can someone help Marco? > > Mark > > > > > > On Mon, Mar 21, 2022 at 8:18 AM Marco Cisternino <[email protected] > <mailto:[email protected]>> wrote: > Good morning, > I’m observing an unexpected (to me) behaviour of my code. > I tried to reduce the problem in a toy code here attached. > The toy code archive contains a small main, a matrix and a rhs. > The toy code solves the linear system and check the norms and the mean of the > solution. > The problem into the matrix and the rhs is the finite volume discretization > of the pressure equation of an incompressible NS solver. > It has been cooked as tiny as possible (16 cells!). > It is important to say that it is an elliptic problem with homogeneous > Neumann boundary conditions only, for this reason the toy code sets a null > space containing the constant. > > The unexpected (to me) behaviour is evident by launching the code using > different preconditioners, using -pc-type <pctype> > I tested using PCNONE (“none”), PCGAMG (“gamg”) and PCILU (“ilu”). The > default solver is KSPFGMRES. > Using the three PC, I get 3 different solutions. It seems to me that they > differ in the mean value, but GAMG is impressive. > PCNONE gives me the zero mean solution I expected. What about the others? > > Asking for residuals monitor, the ratio ||r||/||b|| shows convergence for > PCNONE and PCILU (~10^-16), but it stalls for PCGAMG (~10^-4). > I cannot see why. Am I doing anything wrong or incorrectly thinking about the > expected behaviour? > > Generalizing to larger mesh the behaviour is similar. > > Thank you for any help. > > Marco Cisternino
