[petsc-users] PCMG with matrix-free operators accessing DMDA

[Valeria Mele]

Hi everyone,
this time I am using PETSc to do something that is more complicated than my
usual and I want to do it at the highest possible abstraction level.

To put it in a nutshell, my intent is to build a parallel multigrid to
solve a linear system via DM, KSP and PCMG (I would like to use DMMG but
probably I should have the same problems or more).

I created the distributed object, *da*, with DMDACreate3d, even if it is
distributed (as yet) only in the x-dimension and has 3 dof.
Then I create the KSP (type KSPRICHARDSON) and set the nonzero initial
guess and PCMG as preconditioner. Here I start to tune the MG.

The point is that I need to define all the operators as matrix-free, since
they will do several operations on *x* to obtain *y*, and I am not familiar
with the way to access all the elements or informations in the two levels
involved and/or among the processors with a so-high level interface.

So please (please please please please) tell me if I correctly understand
the mechanism or I am on the wrong way and clear my doubts.

That is, let's say that my operation for the shell are:

   - *A_mult(Mat mat,Vec x, Vec y) *//coefficients matrix

in this case the level is only one but should I write it taking into
account only the local data (I think so) and accessing them via the
informations in *da*?

For example, if I use DMDAVecGetArray, DMDAVecGetCorners (or
DMDAGetGhostCorners) and DMDAVecRestoreArray, will they retrieve
informations from the right level each time (I am pretty sure that in some
official examples it is done in this way)?

Or should I handle just *Vec*s as local structures with their usual indices
(through VecGetArray and VecRestoreArray)?

   - *P_mult(Mat mat,Vec x, Vec y) *//interpolation matrix that is NOT
   conceptually the traspose of Restriction

in this case *x* and *y* will be from two different levels (respectively L
and L+1), so, if I retrieve informations from the *da*... how can I access
the two at different levels?

I am sorry if it seems that they are trivial questions, and I will be
grateful to anyone will help me.

Thanks a lot,
Valeria






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PhD Valeria Mele

University of Naples Federico II
Department of Mathematics and Applications "R. Caccioppoli"
Complesso Universitario M.S. Angelo, Via Cinthia
80126 Naples
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