Dear Isabel, I think you are speaking of the Stokes not NS, isn't it?
Anyway, I believe that your mesh is too fine for an iterative solver without a multigrid preconditioner. Try with less than 1000 DoF, if it works, you need a multigrid... Cheers Thomas On Tue, 25 Nov 2008, Isabel Gil wrote: > Dear DealII's users, > > Thanks Martin, Thomas, Ruhollah and Wolgang for your replies. > > My system comes from Navier-Stokes equation. > I use Q2 for velocity and Q1 for pressure, so LBB is satisfied. > > The geometry and boundary conditions are the following ones: > _________________2____________ > | | > 1| | > |____2____ | > | | > 2 | |3 > _____2___| | > | | > 1| | > |________________2____________| > > Where in 1 we put Dirichlet boundary condition, that is a parabolic flow in > component U and zero in componet V, in 2 we put (U,V)=(0,0) and in 3 we put a > Neumann condition that is > (p*n-viscosity(grad(u)*n)) =0, where n is the normal component on boundary 3. > > If I use GMRES+Precondition_Identity (that if UMFPACK solver works, this > should work too) in the first iteration I have: > > DEAL:GMRES::Starting value 0.00852830 > DEAL:GMRES::Failure step 100000 value 1.06883e-05 > terminate called after throwing an instance of > 'dealii::SolverControl::NoConvergence' > what(): Iterative method reported convergence failure in step 100000 with > residual 1.06883e-05 > > And as I said in my previous email, using Vanka and ILU precondition, the > behaviour is even worse. > > Again, thanks in advance. > Best > Isa > > > > Martin Kronbichler wrote: > > Dear Isabel, > > > > > > > I am trying to solve a matricial system Ax=b, where > > > A=|A11 A12| > > > |A21 0| > > > > > > with four different solvers: > > > > > > - SparseDirectUMFPACK > > > - GMRES + Precondition_Identity() as preconditioner > > > - GMRES + SparseILU<double> ilu as preconditioner > > > - GMRES + Vanka preconditioner as preconditioner > > > > > > The only one that seems to get good results is the first one, i.e., the > > > direct one. I decided to use the other ones because in the future this > > > system will have a huge quantity of nodes, so direct solver won't be > > > feasible. > > > > > > GMRES with SparseILU as preconditioner has a Starting Value of 946,719 > > > GMRES with Vanka as preconditioner has a Staring Value of 2.99566E+12 > > > In those cases, the solver breaks down in the first iteration. > > > > > > GMRES with Precondition_Identity as preconditioner has a Starting Value of > > > 0.0129254 (i.e. the same as doing "by hand", norm L2 of(b-Ax)). In this > > > case, the solver solves the first iteration but it breaks down just in the > > > second one. > > > > > > > Since the direct solver does not break down, the matrix system seems to > > be solvable (i.e., there seems to be one unique solution, otherwise > > UMFPACK would complain/fail). In such a case, GMRES with > > Precondition_Identity() should actually work fine as well (even though > > it might need lots of iterations). The only reason that makes GMRES fail > > is when some matrix inner product y^T A x gets zero, which means that > > the matrix is actually not solvable (but singular). > > > > Are you sure that your matrix is non-singular (maybe you were just lucky > > to get UMFPACK running)? Where does the matrix come from (I guess some > > Stokes or Navier-Stokes system) and what were the boundary conditions? > > > > Best regards, > > Martin > > > > > > _______________________________________________
