[petsc-users] Fwd: Convergence problems

[Jose E. Roman]

El 19/03/2014, a las 18:03, Oliver Browne escribió:

> 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<MatrixStructure.png>

Are you using SLEPc for the eigenvalue problem? Which eigenvalues do you want? Are you using GMRES for the shift-and-invert solve?

Jose