Thank you for the email, Zak,
I have not looked into continuation methods for this problem yet, and
I'd love to hear your thoughts on it!
The problem I have is two-fold:
1. Obtaining the eigenvectors of the system
K.v = lam*M.v
where the K and M are stiffness and mass matrices coming from a
finite element model without any Dirichlet boundary conditions
(i.e., having 6 Rigid body modes) and with a few RBE3 constraints
(introducing degrees of freedom with "zero mass" in the mass
matrix). So the system has, in addition to the 6 rigid body modes, a
few "spurious" null vectors coming from these RBE3 constraints
(which are enforced using Lagrange multipliers).
2. Conducting a linear solve of the system:
K.x = b
where K is from above.
What I'm trying to do with both of these is to conduct a
Hurty/Craig-Bampton Component Mode Synthesis, which is like a Schur
Condensation with a few "fixed interface modal" DoFs added to the
reduced system.
So both can be solved by obtaining the vectors that span the null space
of the system.
I've created two separate threads for the two problems because I felt
both are slightly different questions. But I understand now that the
whole thing boils down to obtaining the nullspaces.
Thank you,
Nidish
On 8/17/20 1:33 PM, zakaryah wrote:
Hi Nidish,
I may not fully understand your problem, but it sounds like you could
benefit from continuation methods. Have you looked into this? If it's
helpful, I have some experience with this and I can discuss with you
by email.
Cheers, Zak
On Mon, Aug 17, 2020 at 2:31 PM Nidish <n...@rice.edu
<mailto:n...@rice.edu>> wrote:
Thankfully for this step, the matrix is not dense. But thank you.
Nidish
On 8/17/20 8:52 AM, Jose E. Roman wrote:
>
>> El 17 ago 2020, a las 14:27, Barry Smith <bsm...@petsc.dev
<mailto:bsm...@petsc.dev>> escribió:
>>
>>
>> Nidish,
>>
>> Your matrix is dense, correct? MUMPS is for sparse matrices.
>>
>> Then I guess you could use Scalapack
http://netlib.org/scalapack/slug/node48.html#SECTION04323200000000000000
to do the SVD. The work is order N^3 and parallel efficiency may
not be great but it might help you solve your problem.
>>
>> I don't know if SLEPc has an interface to Scalapack for
SVD or not.
> Yes, SLEPc (master) has interfaces for ScaLAPACK and Elemental
for both SVD and (symmetric) eigenvalues.
>
> Jose
>
>> Barry
>>
>>
>>
>>
>>
>>
>>
>>> On Aug 17, 2020, at 2:51 AM, Jose E. Roman <jro...@dsic.upv.es
<mailto:jro...@dsic.upv.es>> wrote:
>>>
>>> You can use SLEPc's SVD to compute the nullspace, but it has
pitfalls: make sure you use an absolute convergence test (not
relative); for the particular case of zero singular vectors,
accuracy may not be very good and convergence may be slow (with
the corresponding high computational cost).
>>>
>>> MUMPS has functionality to get a basis of the nullspace, once
you have computed the factorization. But I don't know if this is
easily accessible via PETSc.
>>>
>>> Jose
>>>
>>>
>>>
>>>> El 17 ago 2020, a las 3:10, Nidish <n...@rice.edu
<mailto:n...@rice.edu>> escribió:
>>>>
>>>> Oh damn. Alright, I'll keep trying out the different options.
>>>>
>>>> Thank you,
>>>> Nidish
>>>>
>>>> On 8/16/20 8:05 PM, Barry Smith wrote:
>>>>> SVD is enormously expensive, needs to be done on a full
dense matrix so completely impractical. You need the best tuned
iterative method, Jose is the by far the most knowledgeable about
that.
>>>>>
>>>>> Barry
>>>>>
>>>>>
>>>>>> On Aug 16, 2020, at 7:46 PM, Nidish <n...@rice.edu
<mailto:n...@rice.edu>> wrote:
>>>>>>
>>>>>> Thank you for the suggestions.
>>>>>>
>>>>>> I'm getting a zero pivot error for the LU in slepc while
calculating the rest of the modes.
>>>>>>
>>>>>> Would conducting an SVD for just the stiffness matrix and
then using the singular vectors as bases for the nullspace work? I
haven't tried this out just yet, but I'm wondering if you could
provide me insights into whether this will.
>>>>>>
>>>>>> Thanks,
>>>>>> Nidish
>>>>>>
>>>>>> On 8/16/20 2:50 PM, Barry Smith wrote:
>>>>>>> If you know part of your null space explicitly (for
example the rigid body modes) I would recommend you always use
that information explicitly since it is extremely expensive
numerically to obtain. Thus rather than numerically computing the
entire null space compute the part orthogonal to the part you
already know. Presumably SLEPc has tools to help do this, naively
I would just orthogonalized against the know subspace during the
computational process but there are probably better ways.
>>>>>>>
>>>>>>> Barry
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>> On Aug 16, 2020, at 11:26 AM, Nidish <n...@rice.edu
<mailto:n...@rice.edu>> wrote:
>>>>>>>>
>>>>>>>> Well some of the zero eigenvectors are rigid body modes,
but there are some more which are introduced by
lagrange-multiplier based constraint enforcement, which are non
trivial.
>>>>>>>>
>>>>>>>> My final application is for a nonlinear simulation, so I
don't mind the extra computational effort initially. Could you
have me the suggested solver configurations to get this type of
eigenvectors in slepc?
>>>>>>>>
>>>>>>>> Nidish
>>>>>>>> On Aug 16, 2020, at 00:17, Jed Brown <j...@jedbrown.org
<mailto:j...@jedbrown.org>> wrote:
>>>>>>>> It's possible to use this or a similar algorithm in
SLEPc, but keep in mind that it's more expensive to compute these
eigenvectors than to solve a linear system. Do you have a
sequence of systems with the same null space?
>>>>>>>>
>>>>>>>> You referred to the null space as "rigid body modes".
Why can't those be written down? Note that PETSc has convenience
routines for computing rigid body modes from coordinates.
>>>>>>>>
>>>>>>>> Nidish <
>>>>>>>> n...@rice.edu <mailto:n...@rice.edu>
>>>>>>>>> writes:
>>>>>>>>
>>>>>>>> I just use the standard eigs function
(https://www.mathworks.com/help/matlab/ref/eigs.html
>>>>>>>> ) as a black box. I think it uses a lanczos type method
under the hood.
>>>>>>>>
>>>>>>>> Nidish
>>>>>>>>
>>>>>>>> On Aug 15, 2020, 21:42, at 21:42, Barry Smith <
>>>>>>>> bsm...@petsc.dev <mailto:bsm...@petsc.dev>
>>>>>>>>> wrote:
>>>>>>>>
>>>>>>>> Exactly what algorithm are you using in Matlab to get the
10 smallest
>>>>>>>> eigenvalues and their corresponding eigenvectors?
>>>>>>>>
>>>>>>>> Barry
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Aug 15, 2020, at 8:53 PM, Nidish <n...@rice.edu
<mailto:n...@rice.edu>
>>>>>>>>> wrote:
>>>>>>>> The section on solving singular systems in the manual
starts with
>>>>>>>>
>>>>>>>> assuming that the singular eigenvectors are already known.
>>>>>>>>
>>>>>>>>
>>>>>>>> I have a large system where finding the singular
eigenvectors is not
>>>>>>>>
>>>>>>>> trivially written down. How would you recommend I proceed
with making
>>>>>>>> initial estimates? In MATLAB (with MUCH smaller
matrices), I conduct an
>>>>>>>> eigensolve for the first 10 smallest eigenvalues and take the
>>>>>>>> eigenvectors corresponding to the zero eigenvalues from
this. This
>>>>>>>> approach doesn't work here since I'm unable to use SLEPc
for solving
>>>>>>>>
>>>>>>>>
>>>>>>>> K.v = lam*M.v
>>>>>>>>
>>>>>>>> for cases where K is positive semi-definite (contains a
few "rigid
>>>>>>>>
>>>>>>>> body modes") and M is strictly positive definite.
>>>>>>>>
>>>>>>>>
>>>>>>>> I'd appreciate any assistance you may provide with this.
>>>>>>>>
>>>>>>>> Thank you,
>>>>>>>> Nidish
>>>>>>>>
>>>>>> --
>>>>>> Nidish
>>>> --
>>>> Nidish
--
Nidish
--
Nidish
