You can use MatCreateMFFD 
https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/ 
<https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/> MatMFFDSetFunction 
MatSetFromOptions MatMFFDSetBase and provide the matrix to KSP. Note you will 
need to use -pc_type none or provide your own custom preconditioner with 
https://petsc.org/main/docs/manualpages/PC/PCSHELL/ 
<https://petsc.org/main/docs/manualpages/PC/PCSHELL/>



> On May 24, 2022, at 1:21 PM, Tu, Jiannan <jiannan...@uml.edu> wrote:
> 
> I want to use a matrix-free matrix to solve a large linear equation system 
> because the matrix is too large to be stored. Petsc user manual describes 
> matrix-free method for SNES with examples. The matrix-free matrices section 
> explains how to set up such a matrix, but I can't find any example of 
> matrix-free method with KSP. I am wondering how to apply the method to KSP 
> iterative solver in parallel.
> 
> I greatly appreciate your help for me to understand this topic. 
> 
> Jiannan Tu

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