[petsc-users] Monotonic convergence in FGMRES.

[Barry Smith]

   This is a sign that the preconditioner is seriously messed up and should not be used in its current form.  It can happen if the matrix is nearly singular and for example you use an incomplete factorization for a preconditioner that just screws up the scaling like totally. Run with -ksp_monitor_true_residual and you'll see that the solver is not really solving the problem even though it thinks it is converging fine.

   Barry



On Dec 21, 2010, at 12:53 PM, Vijay S. Mahadevan wrote:

> Hi all,
> 
> I am running a linear problem discretized with FEM on a diffusion
> reaction system, with discontinuous source distribution. When I run
> FGMRes with geometric multigrid as its preconditioner, I notice that
> every time after the restart in fgmres, the new residual is orders of
> magnitude higher than the previous iteration. I might be wrong on this
> but should the restart not preserve monotonicity in convergence ? Or
> am I thinking of a different variant of Gmres here. Here's the
> residual norm as a function of iteration with number of restarts=50.
> 
> 40 KSP Residual norm 2.489810374358e-06
> 41 KSP Residual norm 1.585813670005e-06
> 42 KSP Residual norm 1.059211836025e-06
> 43 KSP Residual norm 6.701461059247e-07
> 44 KSP Residual norm 4.127634824940e-07
> 45 KSP Residual norm 2.511364148934e-07
> 46 KSP Residual norm 1.307034672896e-07
> 47 KSP Residual norm 7.105770015635e-08
> 48 KSP Residual norm 4.098578230710e-08
> 49 KSP Residual norm 2.426160176080e-08
> -------------------------------------------------------------------------
> 50 KSP Residual norm 1.864914790828e+02
> 51 KSP Residual norm 6.741080961009e+01
> 52 KSP Residual norm 5.191621875736e+01
> 53 KSP Residual norm 4.513782866249e+01
> 54 KSP Residual norm 3.320195603375e+01
> 55 KSP Residual norm 2.699941296855e+01
> 56 KSP Residual norm 1.707998091297e+01
> 57 KSP Residual norm 1.219599670348e+01
> 
> Any suggestions to obtain a more smoother convergence would be much
> appreciated. Thank you,
> 
> Vijay