[petsc-users] Which type of matrix do I use to define my own interpolation operators in PCMG?

[Ben Yee]

Thank you for the reply.

If I understand the example correctly, you are suggesting that I define my
interpolation matrix implicitly by defining the MATOP_MULT and
MATOP_MULT_TRANSPOSE_ADD
operations. In my case, I want the coarse grid operators defined via the
Galerkin process, so would I also have to define the MATOP_PTAP operation?
Also, is there a more convenient PETSc matrix type that I can use? My
interpolation operators can easily be represented in matrix form, and it
seems a bit unusual to have to define the matrix operations
MATOP_MULT, MATOP_MULT_TRANSPOSE_ADD,
and MATOP_PTAP myself. (Perhaps you are suggesting that defining these
operations without explicitly constructing the matrix is more
computationally efficient?)

On Mon, Aug 21, 2017 at 6:00 PM, Jed Brown <jed at jedbrown.org> wrote:

> Ben Yee <bcyee at umich.edu> writes:
>
> > Hi,
> >
> > I was wondering what type of matrix I should use if I want to define my
> own
> > interpolation matrix in PCMG.
> >
> > I don't have any DM objects, and I wanted to provide the matrix entries
> to
> > the interpolation matrix manually.  Moreover, I want the coarse grid
> > operators to be defined via the Galerkin process, so I only need to
> define
> > the interpolation operator.  The fine grid problem/operator is defined
> as a
> > parallel sparse matrix using MATMPIAIJ.  My interpolation operator is
> also
> > parallel and sparse -- does that mean I should also use MATMPIAIJ for my
> > interpolation operator?
> >
> > I did some digging but I couldn't find any examples where the
> > interpolation/restriction operators in PETSc were defined explicitly by
> the
> > user.
>
> src/ksp/pc/examples/tests/ex5.c
>
> > I also found the documentation for the matrix type MATMAIJ (
> > http://www.mcs.anl.gov/petsc/petsc-current/docs/
> > manualpages/Mat/MATMAIJ.html#MATMAIJ), which indicates that it is a
> > specialized matrix for interpolation/restriction operations.  However,
> > I also noticed that the description for MATMAIJ indicates that it will
> > interpolate each component the same way independently.  I do have a
> > multicomponent problem, but I was hoping to interpolate each component
> > differently -- does that mean I can't use the MATMAIJ matrix type?
>
> Correct, MAIJ applies the Kronecker product of a scalar interpolation
> with the identity so it acts the same on each component.  It's more
> efficient if you want each component treated the same way.
>
> > If it is recommended that I use the MATMAIJ matrix type, I would like
> some
> > clarification regarding the MatCreateMAIJ function.  In particular, I'm
> not
> > really sure how the input matrix "A" (first argument of MatCreateMAIJ) is
> > supposed to be -- the description of MatCreateMAIJ says "the AIJ matrix
> > describing the action on blocks," but I don't know what that means.  The
> > use of MatCreateMAIJ in ex48.c is not really clear to me.
> >
> > Any guidance would be much appreciated.  Thanks!
> >
> > --
> > Ben Yee
> >
> > NERS PhD Candidate, University of Michigan
> > B.S. Mech. & Nuclear Eng., U.C. Berkeley
>



-- 
Ben Yee

NERS PhD Candidate, University of Michigan
B.S. Mech. & Nuclear Eng., U.C. Berkeley
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