[petsc-users] Fwd: Convergence problems

[Oliver Browne]

The problem at the moment is building the Hessenberg matrix. Once I have 
that I find the eigenvalues with LAPACK.

So I am solving

x = (J^I)b with PETSc (ILU and GMRES) for the first column of the 
Hessenberg matrix and for the big problem (Dof = 64000) I can't get it 
to converge.

Regards,

---
Oliver Browne
Ph.D. Student
School of Aeronautics (E.T.S.I.A.)
Universidad Politécnica de Madrid
Tel No: (0034) 913 366 326 ext: 201

http://matap.dmae.upm.es/numat/index.php/people/mod-fellow-in?persona=oliver
http://www.anade-itn.eu/index.php/people/fellow-information

On 19-03-2014 18:17, Jose E. Roman wrote:
> 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