[petsc-users] Custom Matrix- and Vector-Class

[Markus Mayr]

Dear list,

I would like to use PETSc's linear solver for matrix free methods, but I think that I need to create a custom vector type in order to write an efficient matrix-vector multiplication. First, this is my problem:

I would like to solve a system of linear equations

  /   A  |  B   \    /  x  \   /  a  \
  | -----+----- | *  | --- | = | --- |
  \   C  |  D   /    \  y  /   \  b  /

The problem is that only A is a PETSc matrix. For the other matrices, an external library provides a matrix-vector multiplication for PETSc vectors. I would like to use GMRES to solve this system.

If I would like to use GMRES, I have to provide a matrix-vector multiplication for the whole matrix, right?. A, B, C, D and all vectors involved are distributed across the same set of processes. This is why I think it would be inefficient to use PETSc's MPIVec vector class. Is it? Or can I obtain the required parts of the vector efficiently, i.e. with little communication operations involved?

I think, it would be the best solution, to write a vector class myself, that contains an array of PETSc vector. I took a look at the PETSc source code and it does not look too hard, but first:

1.) I wanted to get some feedback, because I am a beginner with PETSc and there might be a way to do this in PETSc more easily.
2.) I do not know which functions I have to implement in order to get GMRES to work. Is there a comprehensive list or something? Or does PETSc return meaningful error messages about missing functions?
3.) If you do not mind, could you give a short example how new vector classes are created once the vector operations struct is created? I could not find this yet.

Thanks for your help!

Best regards,
Markus Mayr