[Trilinos-Users] AztecOO convergence

[Heroux, Mike]

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