[petsc-users] ASM with matrix-free method

[Matthew Knepley]

On Thu, Feb 2, 2017 at 8:55 AM, Sonia Pozzi <sonia.pozzi at usi.ch> wrote:

> Dear Barry,
>
> At the moment I’m dealing with the following problem.
>
> Suppose I want to solve Sx=b, where is a product of matrices. In
> particular inside it contains also an inverse of a matrix.
> To compute the action of S I have created a shell matrix, but know I would
> like to apply the ASM as preconditioner.
>

Are you using a Schur complement? Have you looked at


http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/MatCreateSchurComplement.html


> Citing your words as answer to a previous similar question:
>
> *Thu Jan 13 13:14:47 CST 2011*
> *Is it possible use ASM and/or FieldSplit with a matrix-free method?*
>
> "Yes, BUT the algorithms are coded around MatGetSubMatrix() and or MatGetSubMatrices() so to do matrix free you need to have code that applies "part" of the operator at a time (that is you cannot just have a matrix vector product that applies the entire operator to the entire vector. Once you have the ability to apply "part" of the operator at a time you need to code up a MATSHELL that responds appropriately to MatGetSubMatrix() and or MatGetSubMatrices() and returns new matrix-free shell matrices that apply only "their" part of the operator. This is non-trivial for many people but possible."
>
>
> Could you be so kind to explain me better how, or do you have some code
> that is doing something similar?
>
> ASM says "I will take a block of your operator and invert it", but we do
not know how to take a block of your MATSHELL
because it only provides the action on a vector. You could

  a) Also provide MatGetSubmatrix() or MAtGetSubmatrices() for your
MATSHELL as Barry says

  b) Make a matrix M that is an approximation to your MATSHELL, perhaps
using the block diagonal portions of the inverse
      so that you can explicitly give the values. Then pass M in as the
preconditioner matrix for the solver.

  c) Use Chebyshev or some matrix-free preconditioner instead of ASM

  Thanks,

    Matt

> Regards,
>
> Sonia
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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