[Trilinos-Users] AztecOO convergence

[Hoang Giang Bui]

Dear Mike,

Thanks for the comment. After scaling of my system, the condition 
improved significantly and now the AztecOO works well, both with 
BICGSTAB and GMRES.

Best regards
Giang Bui



On 06/25/2013 05:20 PM, Heroux, Mike 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
>
>