[petsc-users] amg from hypre

[hxie at umn.edu]

On Mar 8 2010, Jed Brown wrote:

>On 06 Mar 2010 15:41:12 -0600, hxie at umn.edu wrote:
>> Hi,
>> 
>> I am solving incompressible navier-stokes equations. The code implements 
>> the Newton iteration and just uses the KSP solver for each iteration. It 
>> takes 14 nonlinear iterations (~8min) to converge using the default 
>> solver
>> in PETSc. But it takes 6 nonlinear iterations (~30min) using boomeramg 
>> from
>> hypre.
>
>Can you confirm that these are the number of NONLINEAR iterations?

Yes.

>Changing the preconditioner should not change this if it behaving
>correctly.  Are you solving incompressible NS in a coupled manner,
>sending the indefinite (momentum + continuity equations) to the
>preconditioner?  

It is a temperature driven flow. Temperature field is also included. We use 
high order method (2nd order for velocity) to discretize the system and 
solve it in a coupled manner. We do a small shifting for the preconditioner 
to avoid zero diagonals.

>In this case, BoomerAMG can be giving you completely
>the wrong answer.  For example, on a different Navier-Stokes example, it
>produces very nice preconditioned residuals
>
>   0 KSP Residual norm 9.526419214320e+00 
>   1 KSP Residual norm 9.406988599189e-02 
>   2 KSP Residual norm 2.767040414824e-03 
>   3 KSP Residual norm 1.649604812054e-03 
>   4 KSP Residual norm 1.611023301144e-03 
>   5 KSP Residual norm 7.073431543229e-04 
>   6 KSP Residual norm 1.404066303578e-04 
>   7 KSP Residual norm 1.347821147393e-04 
>   8 KSP Residual norm 7.713640141302e-05 
>   9 KSP Residual norm 5.121198361232e-05 
>  10 KSP Residual norm 4.790100151952e-05 
>  11 KSP Residual norm 1.769376148248e-05 
>  12 KSP Residual norm 1.671836687758e-05 
>  13 KSP Residual norm 9.561298137614e-06 
>  14 KSP Residual norm 6.509746067580e-07 
>  15 KSP Residual norm 5.863323408081e-07 
>  16 KSP Residual norm 5.120192651612e-07 
>  17 KSP Residual norm 3.403122131501e-07 
>  18 KSP Residual norm 3.342529361191e-07 
>  19 KSP Residual norm 9.178974981883e-08 
>
>but converges to completely the WRONG answer.  This is because the
>preconditioner is singular, and the unpreconditioned residuals (using
>right-preconditioned GMRES) look like
>
>   0 KSP Residual norm 9.899494936612e+05
>   1 KSP Residual norm 3.460941545811e-02
>   2 KSP Residual norm 3.411670842883e-02
>   3 KSP Residual norm 3.406431296292e-02
>   4 KSP Residual norm 3.376198186394e-02
>   5 KSP Residual norm 3.374434209905e-02
>   6 KSP Residual norm 3.370086274150e-02
>   7 KSP Residual norm 3.334190783058e-02
>   8 KSP Residual norm 3.321057363881e-02
>   9 KSP Residual norm 3.321055343672e-02
>  10 KSP Residual norm 3.318392045928e-02
>
>which is NO CONVERGENCE at all after the penalty boundary conditions
>were enforced.  So CPU time aside, the nonlinear iteration count could
>occur because Newton is failing due to an incorrect search direction or
>a vanishing step size, but the answer could be completely wrong.
>
>You have to clear up subtleties like getting the wrong answer before
>looking any further at the amount of time the various preconditioners
>are taking.  Always run with
>
>  -snes_converged_reason -ksp_converged_reason
>
>and check the unpreconditioned residuals, especially when dealing with
>indefinite problems.
>
>Jed
>

The result looks correct. I will double check by computing the real 
residual by b-Ax. For all the methods I set the same options "-ksp_max_it 
500 -ksp_gmres_restart 50". And each nonlinear iteration will take 500 
gmres iteration. Maybe the 500 V cycles takes much more time than the ilu0. 
Will there be a big difference to implement the amg directly from hypre? 
Thanks.

Bests,
Hui