[petsc-users] [petsc-maint] Performing a coordinate system rotation for the stiffness matrix

[Matthew Knepley]

On Mon, May 31, 2021 at 11:12 AM Stefano Zampini <stefano.zampini at gmail.com>
wrote:

> Mike
>
> as long as P is a sparse matrix with compatible rows and cols (i.e.
> rows(P)= cols(A) = rows (A)) , MatPtAP will compute the result.
>

Stefano and Mark are correct. This will work.

I implemented the same thing in my code in a different way. I put this
transformation into the mapping between local and global vector spaces. The
global degrees of
freedom are the ones you want for boundary conditions (normal and
tangential to the boundary), and I eliminate the ones that are constrained.
The local degrees of
freedom are the normal Caresian ones, and these are used for assembly. The
map is used when I execute DMGlobalToLocal() and DMLocalToGlobal(). There
is an
example of me doing this in SNES ex71, Poiseuille flow in a tilted channel.

  Thanks,

      Matt


> Il giorno lun 31 mag 2021 alle ore 16:52 Mark Adams <mfadams at lbl.gov> ha
> scritto:
>
>>
>>
>> On Mon, May 31, 2021 at 9:20 AM Michael Wick <michael.wick.1980 at gmail.com>
>> wrote:
>>
>>> Hi PETSc team:
>>>
>>> I am considering implementing a skew roller boundary condition for my
>>> elasticity problem. The method is based on this journal paper:
>>> http://inside.mines.edu/~vgriffit/pubs/All_J_Pubs/18.pdf
>>>
>>> Or you may find the method in the attached Bathe's slides, pages 9 -10.
>>>
>>> Roughly speaking, a (very) sparse matrix T will be created which takes
>>> the shape [ I, O; O, R], where R is a 3x3 rotation matrix. And the original
>>> linear problem K U = F will be modified into (T^t K T) (T^t U) = T^t F. In
>>> doing so, one can enforce a roller boundary condition on a slanted surface.
>>>
>>> I think it can be an easy option if I can generate the T matrix and do
>>> two matrix multiplications to get T^t K T. I noticed that there is a
>>> MatPtAP function. Yet, after reading a previous discussion, it seems that
>>> this function is not designed for this purposes (
>>> https://lists.mcs.anl.gov/pipermail/petsc-users/2018-June/035477.html).
>>>
>>
>> Yes, and no. It is motivated and optimized for a Galerkin coarse grid
>> operator for AMG solvers, but it is a projection and it should be fine. If
>> not, we will fix it.
>>
>> We try to test our methods of "empty" operators , but I don't know
>> if MatPtAP has ever been tested for super sparse P. Give it a shot and see
>> what happens.
>>
>> Mark
>>
>>
>>>
>>> I assume I can only call MatMatMult & MatTransposeMatMult to do this
>>> job, correct? Is there any existingly PETSc function to do T^t K T in one
>>> call?
>>>
>>> Thanks,
>>>
>>> Mike
>>>
>>>
>
> --
> Stefano
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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