Hi.
We are designing a PETSc application that will employ a SNES solver on a
multiphysics problem whose jacobian will have a 2x2 block form, say
A=[A00,A01;A10,A11]. We already have code for the top left block A_00 (a
MatShell and a related Shell preconditioner) that we wish to reuse. We
could implement the other blocks as Shells or assembled matrices. We'd
like also to compare our method with existing ones, so we'd like to be
quite flexible in the choice of KSP and PC within the SNES. (To this
end, implementing an assembled version of the A00 and the other blocks
would be easy)
I am assuming that, in order to have one or more shell blocks, the full
jacobian should be a nested matrix, and I am wondering what is the best
way to design the code.
We are going to use DMDA's to manipulate Vecs for both variable sets, so
the DMComposite approach of
https://www.mcs.anl.gov/petsc/petsc-current/src/snes/tutorials/ex28.c.html
is intriguing, but I have read in the comments that it has issues with
MatNest type.
My next guess would be to create the four submatrices ahead and then
insert them in a MatNest, like in the Stokes example of
https://www.mcs.anl.gov/petsc/petsc-current/src/snes/tutorials/ex70.c.html.
However, in order to have shell blocks I guess it is almost mandatory to
have the matrix partitioned among cpus as the Vecs are and I don't
understand how Vecs end up being partitioned in ex70.
We could
- create a DMComposite and create the Vecs with it
- get the local sizes of the Vecs and subVecs for the two variable groups
- create the matrix as in ex70, using the shell type where/when needed,
but instead of
MatSetSizes(matblock, NULL, NULL, globalRows, globalCols)
call
MatSetSizes(matblock, localRows, localCols, NULL, NULL)
using the local sizes of the subvectors.
Does this sound a viable approach? Or do you have some different
suggestions?
Thanks
Matteo
