[Trilinos-Users] AztecOO convergence

[Hoang Giang Bui]

Dear Dr. Mike

The matrix is scaled in my problem. Before solving this, I do a LeftScaling
and observe that it gives better convergence. However, considering that MKL
solver can solve my problem with tolerance 1e-12. I'm confused that
iterative solver cannot give the result with the required tolerance.

BR
Bui



On Tue, Jun 25, 2013 at 5:20 PM, Heroux, Mike <MHeroux at csbsju.edu> wrote:

> Given the large magnitude of your RHS vector, and assuming your initial
> guess is zero, or small, it is possible that double-precision floating
> point arithmetic cannot give you a smaller residual given the conditioning
> of the problem.  Have you tried scaling the problem?  For example, if the
> matrix coefficients are of similar magnitude, you could consider doing
> row-sum scaling of the linear problem first.
>
> Mike
>
> From: Hoang Giang Bui <hgbk2008 at gmail.com<mailto:hgbk2008 at gmail.com>>
> Date: Tuesday, June 25, 2013 9:40 AM
> To: "trilinos-users at software.sandia.gov<mailto:
> trilinos-users at software.sandia.gov>" <trilinos-users at software.sandia.gov
> <mailto:trilinos-users at software.sandia.gov>>
> Subject: Re: [Trilinos-Users] AztecOO convergence
>
> Hi
>
> Thank you for your reply. I tried AztecOO without preconditioner but the
> convergence is the same. For more information, the problem size I tested is
> 60000 and the convergence test is AZ_r0. The rhs norm is 1.493e+07. The
> krylov space is 1000. The preconditioner doesn't involve any local
> iterative solve.
>
> Any idea could help me to improve this ?
>
> BR
> Bui
>
>
>
> On 06/24/13 21:28, Heroux, Michael A wrote:
> A few questions:
>
>
>   *   What is your problem size?
>   *   What residual test are you using?  In particular, if you are scaling
> by the RHS and it has a small norm you might be asking for a convergence
> tolerance that is unachievable in double precision arithmetic.
>
> Mike
>
> From: Hoang Giang Bui <hgbk2008 at gmail.com<mailto:hgbk2008 at gmail.com>>
> Date: Monday, June 24, 2013 1:02 PM
> To: "trilinos-users at software.sandia.gov<mailto:
> trilinos-users at software.sandia.gov>" <trilinos-users at software.sandia.gov
> <mailto:trilinos-users at software.sandia.gov>>
> Subject: [Trilinos-Users] AztecOO convergence
>
>
> Hi
>
> When using AztecOO with user defined preconditioner. I obtained
> convergence behaviour like this:
>
>
> *******************************************************
> ***** Problem: Epetra::CrsMatrix
> ***** Preconditioned GMRES solution
> ***** N4Teko22BlockLowerTriInverseOpE
> ***** No scaling
> *******************************************************
>          iter: 0 residual = 1.000000e+00
>          iter: 100 residual = 1.698526e-03
>          iter: 200 residual = 3.441675e-04
>          iter: 300 residual = 4.356401e-05
>          iter: 400 residual = 3.333877e-05
>          iter: 500 residual = 1.901319e-05
>          iter: 600 residual = 1.574073e-05
>          iter: 700 residual = 1.438600e-05
>          iter: 800 residual = 1.372764e-05
>          iter: 900 residual = 1.351302e-05
>          iter: 1000 residual = 1.335775e-05
> ***************************************************************
> Warning: maximum number of iterations exceeded without convergence
> Solver: gmres
> number of iterations: 1000
> Recursive residual = 3.6551e-08
>
> The convergence rate at iteration > 200 is very slow. In this case, what
> should I do to improve the convergence rate of Gmres?
>
> BR
> Bui
>
>
>


-- 
With Best Regards !
Giang Bui
To learn and to excel
-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://software.sandia.gov/pipermail/trilinos-users/attachments/20130628/7990061c/attachment.html