[petsc-users] Customizeing MatSetValuesBlocked(...)

[Jinquan Zhong]

Hope this is not too technical. ☺


**Jed, A’=[A^-1 U B], not the transpose of A.

I understand that it's not the transpose. I still don't have a clue what the notation [A^{-1} U B] means. I would think it means some block decomposed thing, but I don't think you mean just adding columns or taking a product of matrices. Using some standard mathematical notation would help.

>> A’=[A^-1 U B] means matrix A’ consists all elements from A^-1, the inverted A, and all elements from B.  One simple equation is

           K=[Kst] =A’ = ASSEMBLE_ij (A^-1_ij) + ASSEMBLE_i’j’(B_i’j’),  here (s,t), (i,j) and (i’,j’) = different index sets

i.e., entry K_st= A^-1_st+ B_st,
 = 0 when A^-1_st=0 and B_st=0
=  A^-1_st when B_st =0
=  B_st when A^-1_st =0

  We need to solve for A’*x=b. A is dense matrix.

Where does A come from? Why is it dense?


>> A comes from wave propagation.  It is dense since it denotes a function of Green function.


** As I mentioned A’=K is the assembled global matrix using the rule K=A’=SIGMA_ij (A^-1_ij)+SIGMA_i’j’(B_i’j’) from FEM.  Here, SIGMA_ij (A^-1_ij) denotes the assembling process for A^-1_ij  into K according the DOFs of each node in the FEM model,

Is A^{-1} an operator on some subdomain? Are you trying to implement a substructuring algorithm? What is B physically?

>> NO.  A^{-1} denotes the inverted A.  B is a sparse matrix of much larger order.

Then there is no way A^{-1} should be stored as a dense matrix.

o   It is stored as a dense matrix in scalapack.  It stays in the same way in cores as scalapack finishes its inversion.  We could define A^-1 as dense matrix in PETSc.
It should not be done this way. A^{-1} should not be stored explicitly. Store the sparse finite element matrix A. Then when you want to "apply A^{-1}", solve with the sparse matrix.

 ** Jed, you are getting close to understand the problem related to QA.  A has to be inverted explicitly.  A^-1 has to be known entry by entry such that each entry in B could be assembled with A^-1 to form A’=K.  This is a requirement beyond technical issue.  This is a QA issue.

What does QA stand for? Can you explain why B needs the entries of A^{-1}?

>> QA means quality assurance.  It is a procedure to ensure product quality.  In Eq.

K=A’=ASSEMBLE_ij (A^-1_ij)+ ASSEMBLE_i’j’(B_i’j’)

Entry B_i’j’ and A^-1_ij may or may not locate at the same row and col.  That why we need explicitly each entry in B_i’j’ and A^-1_ij to assemble K.  The big picture is that K is the final sparse matrix we need to solve K*x=A’*x=b.  However, K indexed by (s,t) needs to be constructed in terms of dense matrix A and sparse matrix B using index sets (i,j) and (i’,j’).
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120809/7ed746d3/attachment-0001.html>