Everybody is correct.

  Using the extremely sparse, nearly diagonal MPI matrix will have a bit more overhead than doing the rotations on the elements due to the needed MPI check and general use of  a sparse-sparse-sparse matrix vector product. But if a code does not have support for the local transformations the extra cost of the the sparse matrix operation will be trivial relative to the rest of computations and so is fine to use. 

  Barry


On May 31, 2021, at 1:00 PM, Sanjay Govindjee <s_g@berkeley.edu> wrote:

In our FEA code we perform the rotations at the local level, before assembly so that it is easy to apply the boundary conditions, then unrotate locally after solution to get the usual Cartesian components.  Somehow this seems more efficient than doing this globally, but perhaps I am missing something.
-sanjay

    
On 5/31/21 9:33 AM, Matthew Knepley
      wrote:

    

    

      
      

        
On Mon, May 31, 2021 at 11:12 AM Stefano Zampini
          <stefano.zampini@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@lbl.gov> ha
                scritto:

              

              

                

                  


                  

                  

                  

                    
On Mon, May 31,
                      2021 at 9:20 AM Michael Wick <michael.wick.1980@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