Re: [firedrake] eigenvalue problems with SLEPc

7 Dec 2016

      Hello Lawrence,

Thanks!  

I see that one major difference is you don't try and ask for the imaginary eigenavlue of magnitude 3.14 but for the eigenvalue of that magnitude. Since the eigenvalues are purely imaginary that is a clever way to get around that. Yes, that's working brilliantly.

However, I now see that my plots are just plotting zero.  I guess that means that I did something silly.  Maybe I can get your advice?

Using getEigenpair below we get petsc matrices vr an vi.  If we can convert say vr to em_real, then we can split it and plot the different fields.  Unfortunately, what worked in the QG code didn't seem to work here.  

# Find eigenvalues an eigenvectors
vr, vi = petsc_a.getVecs()
for i in range(nconv):
    lam = es.getEigenpair(i, vr, vi)
    print lam
    eval_real.append(lam.real)
    eval_imag.append(lam.imag)

    u_real, eta_real = em_real.split()
    #u_imag, eta_imag = em_imag.split()

    p = plot(eta_real)
    p.show()

What do you suggest we try?

Cheers, Francis

------------------
Francis Poulin
Associate Professor
Department of Applied Mathematics
University of Waterloo

email:           fpoulin@uwaterloo.ca
Web:            https://uwaterloo.ca/poulin-research-group/
Telephone:  +1 519 888 4567 x32637

________________________________________
From: firedrake-bounces@imperial.ac.uk [firedrake-bounces@imperial.ac.uk] on behalf of Lawrence Mitchell [lawrence.mitchell@imperial.ac.uk]
Sent: Wednesday, December 07, 2016 10:20 AM
To: firedrake@imperial.ac.uk
Subject: Re: [firedrake] eigenvalue problems with SLEPc

On 07/12/16 14:46, Francis Poulin wrote:
...
Hello Lawrence,
Thanks for the reply.
1) Sadly no.  I commented out the lines because they weren't
working.  If you uncomment them you will see that plotting gives an
error.
Traceback (most recent call last): File "basin_modes_sw.py", line
86, in <module> p = plot(eta_real) File
"/home/fpoulin/software/firedrake/src/firedrake/firedrake/plot.py",
line 125, in plot raise TypeError("Unexpected type") TypeError:
Unexpected type
Aha, I see, I was confusing which code I was looking at.
...
2) The version that I have posted now uses lapack and when I run
that i get numbers I believe.  Some zero eigenavalues but the first
non-zero ones have an imaginary part of 3.14, and then they
increase.
...
The fact that lapack gives the correct answers tells me that the
weak form is set up correctly.  The problem is that when I use
krylovschur, which is fast, specify we want a target imaginary,
with value 3.14, it gives the eigenvalue with the largest
magnitude.  I know that these are the easiest to converge to but
SLEPc should allow us to pick a target.  I am not sure if the
options are being set correctly.
opts.setValue("eps_type", "krylovschur")
opts.setValue("eps_spectrum", "target imaginary")
opts.setValue("eps_tol", 1e-10) opts.setValue("spectral_shift",
3.14)
No, I don't think this is right.

If I use:

opts.setValue("eps_gen_non_hermitian", None)
opts.setValue("st_pc_factor_shift_type", "NONZERO")
# opts.setValue("eps_type", "lapack")
opts.setValue("eps_type", "krylovschur")
opts.setValue("eps_target_magnitude", None)
opts.setValue("eps_target", 3.14)
opts.setValue("eps_tol", 1e-10)
opts.setValue("st_type", "sinvert")

Then I can converge a few eigenvalues around 3.14i

Does that work for you?

Cheers,

Lawrence