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
