[petsc-users] Fwd: Convergence problems

[Oliver Browne]

To Whom It May Concern,

I am using petsc to solve an eigenvalue problem

  Jq = oq

I am obtaining the Jacobian matrix, J, from solving

F(x) = 0

and by numerically perturbing the solution to give

J = dF(x)/dx = F(x + delta) + F(x) / delta             (1)

I use the PETSc to solve Ax=b in the Arnoldi iteration to build the 
Hessenberg matrix.

For small problems (1000 DoF) I obtain accurate results in a timely 
fashion by using ILU(2) and GMRES.

However, when I move to bigger problems (60000 Dof) I can't get the 
GMRES to converge. 5 GMRES steps take an HOUR (it is incredible!!!). I 
have tried modifying the levels for ILU but with no success and a few 
different preconditioners. I have also tried some of the MatGetOrdering 
to improve the stability. I believe that it is down to the structure of 
my matrix, because I have tried similar size matrices obtained from a 
different code which creates the analytical Jacobian (has a different 
topology), of which I can get a convergence to GMRES in about 3 mins. I 
have attached a figure showing the structure of the matrix for a smaller 
problem but obtained with equation (1) above.

I would be very grateful if you could give me some advice in choosing a 
different preconditioner/solver etc or anything else which could help.

Thanks in advance

Olls
-------------- next part --------------
A non-text attachment was scrubbed...
Name: MatrixStructure.png
Type: image/png
Size: 60505 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20140319/f2f19cd4/attachment-0001.png>