[Nek5000-users] Problems in getting eigenvalues using ARNOLDI
nek5000-users at lists.mcs.anl.gov
nek5000-users at lists.mcs.anl.gov
Thu Nov 8 04:44:31 CST 2018
For me it does not make sense to discuss something on our mailing list which is not part of Nek5000.
Cheers,
Stefan
-----Original message-----
> From:nek5000-users--- via Nek5000-users <nek5000-users at lists.mcs.anl.gov>
> Sent: Thursday 8th November 2018 11:37
> To: nek5000-users at lists.mcs.anl.gov
> Subject: Re: [Nek5000-users] Problems in getting eigenvalues using ARNOLDI
>
> Hi Alok,
>
> First of all I think you should
> increase the number of steps per Arnoldi iteration (p109) even
> more, for example multiplying it by 4. The columns 2 and 3 (
> re(RITZ) and im(RITZ)) show that the operator seen by ARPACK is
> close to identity, all the Ritz values are close to 1.
>
> I forgot to mention this earlier, but
> it might also converge faster if you increase the Krylov space
> size p111 to 120 (four times the number of eigenvalues that you
> request).
>
> Regarding the 0 frequency modes, I
> often see them related to boundaries. I am not exactly sure where
> they come from. It is difficult to say anything without seeing
> what the eigenvectors look like.
>
> Regards,
> Guillaume
>
> On 30/10/2018 06:40, nek5000-users---
> via Nek5000-users wrote:
> Hi Guillaume,
>
> I tried with the help of your valuable suggestions. I am
> getting dominant Eigenvalue with time period 8.34 which is
> very much close to the literature. However, I require 30
> Eigen values by setting P112=30 and P111=90. Below is the
> eigenvalues I am getting after many restarts.
>
> re(RITZ);
> im(RITZ)
> ln|RITZ|;
> arg(RITZ)
> 1 0.991128702238537
> 0.150881402754817 1.272083634754888E-002
> 0.755360071443281
> 2 0.991128702238537
> -0.150881402754817 1.272083634754888E-002
> -0.755360071443281
> 3 0.991728721496092
> 1.806383192432841E-002 -4.069909517841635E-002
> 9.106237555496137E-002
> 4 0.991728721496092
> -1.806383192432841E-002 -4.069909517841635E-002
> -9.106237555496137E-002
> 5 0.989791831070271
> 3.446186469202143E-002 -4.827437507304033E-002
> 0.174016133198715
> 6 0.989791831070271
> -3.446186469202143E-002 -4.827437507304033E-002
> -0.174016133198715
> 7 0.987601103156919
> 5.049392478862426E-000 -5.585540570484418E-002
> 0.255416865677410
> 8 0.987601103156919
> -5.049392478862426E-002 -5.585540570484418E-002
> -0.255416865677410
> 9 0.995627135254111
> 0.000000000000000E+000 -2.191226841613384E-002
> 0.000000000000000E+000
> 10 0.995700191328997
> 0.000000000000000E+000 -2.154539716426180E-002
> 0.000000000000000E+000
> 11 0.995229254767405
> 0.000000000000000E+000 -2.391080780851450E-002
> 0.000000000000000E+000
> 12 0.995434205850176
> 0.000000000000000E+00 -2.288124611941097E-002
> 0.000000000000000E+000
> 13 0.994877066906734
> 0.000000000000000E+000 -2.568050152041379E-002
> 0.000000000000000E+000
> 14 0.994526533813701
> 0.000000000000000E+000 -2.744250243633435E-002.
> 0.000000000000000E+000
> 15 0.994024234181460
> 0.000000000000000E+000 -2.996846079257938E-002.
> 0.000000000000000E+000
> 16 0.992886352948494
> 0.000000000000000E+000 -3.569534837742794E-002
> 0.000000000000000E+000
> 17 0.993531725861019
> 0.000000000000000E+000 -3.244642035911912E-002
> 0.000000000000000E+000
> 18 0.992269436061858
> 0.000000000000000E+000 -3.880299821483946E-002
> 0.000000000000000E+000
> 19 0.991568951835935
> 0.000000000000000E+000 -4.233395244633451E-002
> 0.000000000000000E+000
> 20 0.991491977086931
> 0.000000000000000E+000 -4.272211373739676E-002
> 0.000000000000000E+000
> 21 0.991513431383682
> 0.000000000000000E+000 -4.261392292430112E-002
> 0.000000000000000E+000
> 22 0.991180149347166
> 0.000000000000000E+00 -4.429487878603097E-002
> 0.000000000000000E+000
> 23 0.991284115416627
> 0.000000000000000E+000 -4.377045031887505E-002
> 0.000000000000000E+000
> 24 0.990874009258556
> 0.000000000000000E+000 -4.583943845265666E-002
> 0.000000000000000E+000
> 25 0.990632850108536
> 0.000000000000000E+000 -4.705648774052894E-002
> 0.000000000000000E+000
> 26 0.990852910254318
> 0.000000000000000E+000 -4.594590622089855E-002.
> 0.000000000000000E+000
> 27 0.990206173286647
> 0.000000000000000E+000 -4.921050845320660E-002
> 0.000000000000000E+000
> 28 0.990051445648789
> 0.000000000000000E+000 -4.999185950921724E-002
> 0.000000000000000E+000
> 29 0.989332783273003
> 0.000000000000000E+000 -5.362259677015029E-002
> 0.000000000000000E+000
> 30 0.989848247701740
> 0.000000000000000E+000 -5.101816376314156E-002
> 0.000000000000000E+000
> 31 0.989278105749528
> 0.000000000000000E+000 -5.389893975295782E-002
> 0.000000000000000E+000
>
> I am unable to understand the reason behind getting so
> many Eigenvalues with zero imaginary part/rotation. Please
> help.
>
> Regards,
>
> On Wed, Oct 3, 2018 at 2:54 PM <nek5000-users at lists.mcs.anl.gov <mailto:nek5000-users at lists.mcs.anl.gov>>
> wrote:
> Hi,
>
> What
> is your time step? I calculated the spectrum of the
> cylinder flow a while ago at Re=44 and I got an angular
> frequency of 0.7278, which corresponds to a period of
> 8.63.
> It
> is possible that 40 time steps per Arnoldi iteration is
> too small; a good start is to integrate for 1/10th of
> the period, so dt*p109 = 0.8 approximately. I used 120
> time steps at dt=4.2e-3 but it may be faster with more
> steps.
> It
> depends on which frequencies you want to resolve; if you
> integrate for a short time your operator is close to
> identity and all eigenvalues are close to 1, but if you
> integrate for too long then the frequencies of the
> eigenvalues you are interested in will be aliased.
>
> I
> think you could try decreasing p021 and p022 to maybe
> 1e-10 or 1e-12 and see if helps, too.
>
> Best,
> Guillaume
>
> On
> 03/10/2018 07:24, nek5000-users at lists.mcs.anl.gov <mailto:nek5000-users at lists.mcs.anl.gov>
> wrote:
> Hi Guillaume,
>
> Thanks for your reply. My reply to
> your queries is as below:-
>
> 1) I am getting unstable pair of
> Eigen values with growth rate around
> 0.02.
> 2) Solver tolerance that I used are
> ;
> 7.00000 p020
> NORDER
> 0.100000E-09 p021 DIVERGENCE
> 0.100000E-09. p022 HELMHOLTZ
> 0.00000 p023
> NPSCAL
> 0.100000E-09 p024 TOLREL
> 0.100000E-04 p025 TOLABS
> 1.00000E-05. p113 : ARNOLDI:
> arpack tolerance
>
>
> 3) Boundary conditions are :
>
> I am using sponge strength at inlet
> and outlet with following details in
> .rea file
> 1.00000 p119 : SPONGE
> STRENGTH
> 25.0000 p120 : SPONGE TOTAL
> WIDTH
> 3.00000 p121 : SPONGE DROP
> WIDTH (INFLOW)
> 5.00000 p122 : SPONGE RISE
> WIDTH (OUTFLOW)
> the sponge function and its cal is
> detailed in userf subroutine of .usr
> file
>
> Also following is defined in .usr
> file
> c-----------------------------------------------------------------------
> subroutine userbc
> (ix,iy,iz,iside,eg)
>
> include 'SIZE'
> include 'NEKUSE' !
> UX, UY, UZ, TEMP, X, Y
> include 'PARALLEL' !
> GLLEL
>
>
> integer e,eg
>
> c velocity
> c e = GLLEL(eg)
> UX = 0.0
> UY = 0.0
> UZ = 0.0
>
> c t
> TEMP=0.0
>
> return
> end
> c-----------------------------------------------------------------------
> subroutine useric
> (ix,iy,iz,ieg)
>
> include 'SIZE'
> include 'NEKUSE' !
> UX, UY, UZ, TEMP, Z
> integer idum
> save idum
> data idum / 0 /
>
> real eps
>
> if (idum.eq.0) idum = 99 +
> nid
> eps = 0.1
>
> c velocity
> c random distribution
> UX = eps*(ran1(idum)-0.50)
> UY = eps*(ran1(idum)-0.50)
> UZ = eps*(ran1(idum)-0.50)
>
> c t
> TEMP=0
>
> return
> end
>
>
> 40.0000 p109 : ARNOLDI:
> frequency of calling arn_solve
> 4.00000 p110 : ARNOLDI:
> maximal number of arnoldi cycles
> 90.0000 p111 : ARNOLDI: size
> of Krylov space
> 30.0000 p112 : ARNOLDI:
> number of eigenvectors
>
>
> If I am increasing the Krylov
> subspace then will I get Eigen values at
> lesser restart ?
>
> Kindly help please as I am new to
> this. Thanks in advance.
>
> Alok Mishra
> Research Scholar
> Computational Propulsion Lab
> Aerospace Department IIT Kanpur
> +91-8795844555
>
> _______________________________________________
> Nek5000-users mailing list
> Nek5000-users at lists.mcs.anl.gov <mailto:Nek5000-users at lists.mcs.anl.gov>
> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users <https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users>
>
> _______________________________________________
> Nek5000-users mailing list
> Nek5000-users at lists.mcs.anl.gov <mailto:Nek5000-users at lists.mcs.anl.gov>
> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users <https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users>
> <br clear="all" />
>
> --
> Alok Mishra
> Research Scholar
> Computational Propulsion Lab
> Aerospace Department IIT Kanpur
> +91-8795844555
>
> _______________________________________________
> Nek5000-users mailing list
> Nek5000-users at lists.mcs.anl.gov <mailto:Nek5000-users at lists.mcs.anl.gov>
> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users <https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users>
>
> _______________________________________________
> Nek5000-users mailing list
> Nek5000-users at lists.mcs.anl.gov
> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
More information about the Nek5000-users
mailing list