[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
>                 
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> 
>         -- 
> Alok Mishra
> Research Scholar 
> Computational Propulsion Lab 
> Aerospace Department IIT Kanpur
> +91-8795844555
>       
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