[petsc-users] ASM with matrix-free method

[Sonia Pozzi]

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.

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?


Regards,

Sonia
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