"mingled" is not a very useful term. How about using an actual equation so we
can have some clue what you mean.
o I agree. It is hard to have an accurate equation to for the structure of
A?. But if you are familiar with FEM, you may know global stiffness matrix
K=SIGMA_ij( K_ij ), the assembling process of elemental stiffness. Here A?=K.
This cannot be true because you say A' is the larger part sparse and part dense
matrix. Maybe you mean A rather than A'?
**Jed, A?=[A^-1 U B], not the transpose of A. We need to solve for A?*x=b. A
is dense matrix. B is a sparse matrix. Therefore, A? is a sparse matrix when
the rule K=A?=SIGMA_ij (A^-1_ij)+SIGMA_i?j?(B_i?j?) applies.
o We partition the FEM domain into two physical pieces due to different
operations they are defined for. After completing each operation, we need to
operate on A^-1_ij and B_i?j? such that we can have K=A?=SIGMA_ij
(A^-1_ij)+SIGMA_i?j?(B_i?j?).
The sum of the inverses are not the inverses of the sum. Can you back up
further to explain what underlying problem you are trying to solve?
** 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, so does SIGMA_i?j?(B_i?j?). in this application, A^-1
and B have different indices sets. Some of them may locate at the same
locations in K.
If you have an "inverse" floating around, what sort of operator is it the
inverse of.
? A is a double complex matrix we have generated from a practical application
using FEM.
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.
o Another constraint we have is we have to use direct solver for QA purposes.
This brings up the needs to convert the dense matrix into MATAIJ or MATMPIAIJ.
However, in PETSc, converting dense matrix-formatted A^-1 into MATAIJ/
MATMPIAIJ also takes lots of time.
Choose the right tool for the job. When I cook dinner tonight, I plan to use a
stove and a frying pan instead of a dump truck radiator and 200 feet of 18
gauge copper wire woven into a basket.
** That why I came here for. PETSc is the right tool for solver in the last
step A?*x=b. However, due to the differences in addressing the matrix between
PETSc and ScaLAPACK, I am asking for the kind help from this community to
current issue.
-------------- next part --------------
An HTML attachment was scrubbed...
URL:
<http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120809/18c3ecf1/attachment.html>
