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.
Barry
> On Aug 17, 2020, at 2:51 AM, Jose E. Roman <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> 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> 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> 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> 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
>>>>>>> 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
>>>>>>> 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
>>>>>>> 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
>
