[petsc-users] Fwd: [petsc-maint] A question on Schur complement

[saturday luis]

Thanks, Barry!

Do you have any suggestions on solving the B^tB matrix? I noticed the
solver option LSQR but haven't tried it yet.

Luis



2018-01-26 11:25 GMT-08:00 Smith, Barry F. <bsmith at mcs.anl.gov>:

>
>
> > On Jan 26, 2018, at 1:18 PM, saturday luis <luis.saturday at gmail.com>
> wrote:
> >
> > Hi PETSc team:
> >
> > I want to consult for a good way of doing an approximated Schur
> complement matrix. So I just want to handle a matrix in the format C + B^t
> B, or sometimes B^t B.
> >
> > An easy way is to run with the MatCreateSchurComplement to create C +
> B^t inv A B, wherein A is an identity matrix. The downside is that the
> matrix free style does not allow for algebraic preconditioners.
> >
> > Another way is to generate the matrix B^t B. For my case, I checked the
> sparsity of the resulting matrix from MatMatMult and it is pretty sparse
> still. I found a similar approach in
> > http://www.mcs.anl.gov/petsc/petsc-current/src/snes/examples
> /tutorials/ex70.c.html
> > where the B^t B matrix is created explicitly (line 367-388). However,
> there is a line of comment saying  " in real life this matrix would be
> build directly without MatMatMult". So I just want to ask the best way of
> assemblying and solving the B^t B matrix.
>
>    Using the product is best.  You can ignore the comment.
>
>    The comment is attempting to indicate that one can build the matrix
> from which the preconditioner is to be constructed by explicitly forming a
> matrix based on the specific problem at hand.
>
>    Barry
>
>
> >
> > Thanks,
> >
> > Luis
>
>
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