"QA means quality assurance.", which has nothing to do with the technical discussions here.
However, I take this opportunity to promote http://aspiritech.org, an non-profit organization with a mission to provide employment on *QA* for high functioning individuals on the Autism Spectrum. Hong On Thu, Aug 9, 2012 at 12:28 PM, Jinquan Zhong <jzhong at scsolutions.com>wrote: > Hope this is not too technical. J**** > > ** ** > > **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/20120809/0075b63e/attachment.html>
