Some linear systems may be ill-conditioned and probably PETSc's LU is having a
hard time with them. I would suggest installing PETSc with --download-mumps and
run with MUMPS as the linear solver, without the st_pc_factor_shift* options.
See section 3.4.1 of SLEPc's manual.
Let us know if this helps.
> El 6 mar 2018, a las 23:32, Habib <abuabib2...@yahoo.com> escribió:
> Hi Everyone,
> I hope this is the right medium to post my question as it is related to
> I have just installed slepc4py with complex scaler and I intend to use it to
> solve large sparse generalised eigenvalue problems that result from the
> stability of flows that can be described by linearised Navier-Stokes
> equations. For my problem, Ax = kBx, matrices A and B are non-Hermitian, B,
> in particular, is singular and I am interested in eigenvalue with maximum
> real part which could be positive if the flow is unstable or negative for a
> stable flow. Following the steps described in exp1.py, I wrote a code for
> Non-Hermitian Generalised Eigenvalue problem. I test the code on a problem
> that is stable and with known solution using Shift and Invert transformation
> with complex shift value and the solution seems okay but I have the following
> concerns that I would be grateful if you could clarify on.
> (1) If I used a shift value that is close to the solution (which I already
> know for this test problem), the code converge at the correct eigenvalue but
> the computed relative error is very large. I was wondering why the error is
> large and the implication on my eigenvectors. How can this be corrected?
> Below is a typical command line option I entered and the results I got from
> python ComputeEigenValueUsingSlepc4Python.py -eps_nev 1 -eps_tol 1e-10
> -st_type sinvert -eps_target -105.01+252.02i -eps_converged_reason
> -eps_conv_abs -st_pc_factor_shift_type NONZERO -st_pc_factor_shift_amount
> *** SLEPc Solution Results ***
> Number of iterations of the method: 1
> Solution method: krylovschur
> Number of requested eigenvalues: 1
> Stopping condition: tol=1e-10, maxit=23923
> Number of converged eigenpairs 1
> k ||Ax-kx||/||kx||
> ----------------- ------------------
> -106.296653+251.756509 j 3.64763e+11
> (2) Since my goal is to use the code to test the stability of flows in which
> I have no idea of what the maximum eigenvalue would be, I tried solving the
> problem I stated in 1 with different target values that are not close to the
> eigenvalue, but it was not successful. The code kept running for a very long
> time that I had to cancel it. With a target value of zero, I had convergence
> in finite time but to a spurious-like eigenvalue. Any suggestion on how I
> could go about getting the true eigenvalue for my main problem for which I
> have no idea of what a close target value to the maximum value would be and
> considering that matrix B is singular?
> Looking forward to your suggestions.
> Department of Chemical Engineering,
> Ahmadu Bello University, Zaria
> Samaru Campus,
> Kaduna State, Nigeria