[Trilinos-Users] AztecOO convergence

[Ramsey, James J CIV (US)]

From: trilinos-users-bounces at software.sandia.gov [trilinos-users-bounces at software.sandia.gov] on behalf of Hoang Giang Bui [hgbk2008 at gmail.com]

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?

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Without knowing more about the particular system that you are trying to solve, it's really hard to say. Obviously, how well a solver works depends upon, for example, how well-conditioned the matrix of your linear system is.

Also, it might be useful to know whether you tried not using a preconditioner at first (for testing purposes at least) or if you had tried the preconditioners that come with AztecOO instead of a user-defined one.