[petsc-users] having issues with nullspace

Matthew Knepley knepley at gmail.com
Thu Mar 6 17:33:02 CST 2014

On Thu, Mar 6, 2014 at 5:24 PM, Mohammad Mirzadeh <mirzadeh at gmail.com>wrote:

> Hi guys,
> I have a discretization of Poisson equation with Neumann bc for embedded
> boundary grids in such a way that that nullspace is not the usual constant
> vector. Instead the nullspace is constant in the domain of interest and
> zero elsewhere.
> I compute this nullspace myself and have checked it against MATLAB by
> dumping the matrix and computing the nullspace explicitly using null
> function -- they match and there is only this single vector. Then I take
> this calculated vector and subtract it off the matrix and rhs.

"subtract it off the matrix" does not make sense to me. Are you calling


> However, I am having convergence issues. For instance this is the output
> of ksp_monitor_true_residual for one particular run:
>   0 KSP preconditioned resid norm 3.033840960250e+02 true resid norm 2.332886580745e-01 ||r(i)||/||b|| 1.000000000000e+00
>   1 KSP preconditioned resid norm 1.018974811826e+01 true resid norm 1.941629896918e-02 ||r(i)||/||b|| 8.322864527335e-02
>   2 KSP preconditioned resid norm 5.450493684941e-02 true resid norm 1.029339589324e-02 ||r(i)||/||b|| 4.412300185615e-02
>   3 KSP preconditioned resid norm 3.944064039516e-02 true resid norm 1.030277925024e-02 ||r(i)||/||b|| 4.416322394443e-02
>   4 KSP preconditioned resid norm 6.286181172600e-05 true resid norm 1.030243055045e-02 ||r(i)||/||b|| 4.416172923059e-02
>   5 KSP preconditioned resid norm 4.349133658643e-06 true resid norm 1.030239080406e-02 ||r(i)||/||b|| 4.416155885630e-02
>   6 KSP preconditioned resid norm 9.279429568232e-08 true resid norm 1.030239169298e-02 ||r(i)||/||b|| 4.416156266666e-02
>   7 KSP preconditioned resid norm 3.032522248740e-09 true resid norm 1.030239175066e-02 ||r(i)||/||b|| 4.416156291393e-02
>   8 KSP preconditioned resid norm 6.533747246875e-09 true resid norm 1.030239175718e-02 ||r(i)||/||b|| 4.416156294184e-02
>   9 KSP preconditioned resid norm 6.083185162500e-12 true resid norm 1.030239175259e-02 ||r(i)||/||b|| 4.416156292220e-02
>  10 KSP preconditioned resid norm 5.510319622225e-12 true resid norm 1.030239175259e-02 ||r(i)||/||b|| 4.416156292221e-02
>  11 KSP preconditioned resid norm 5.456758524534e-12 true resid norm 1.030239175259e-02 ||r(i)||/||b|| 4.416156292221e-02
>  12 KSP preconditioned resid norm 5.456756081783e-12 true resid norm 1.030239175259e-02 ||r(i)||/||b|| 4.416156292221e-02
>  13 KSP preconditioned resid norm 5.456755930952e-12 true resid norm 1.030239175259e-02 ||r(i)||/||b|| 4.416156292221e-02
>  14 KSP preconditioned resid norm 5.456755930949e-12 true resid norm 1.030239175259e-02 ||r(i)||/||b|| 4.416156292221e-02
>  15 KSP preconditioned resid norm 5.456755930949e-12 true resid norm 1.030239175259e-02 ||r(i)||/||b|| 4.416156292221e-02
> As you can see, the true residual is quite large and moreover it does not reduce beyond a certain point. This is using hypre as preconditioner, but the situation is equally bad with several other preconditioner (ilu, sor, jacobi, or even none). As for the solution itself, the error has poor to none convergence under grid refinement. All this suggests that the linear system is not converging in my case.
> Do you have any idea/suggestions why this is happening and how I can avoid it?
> Thanks

What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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