[petsc-users] Example code of linear solve of a block matrix system in Fortran

[Thomas S. Chyczewski]

All,

I'm relatively new to PETSc and have relied pretty heavily on the example codes included in the distribution to figure out the finer points of using the PETSc library that I couldn't deduce from the manual. One thing I can't figure out is how to solve block matrix systems and I couldn't find an example in Fortran. I'm writing a 2D incompressible CFD solver so I have a 3x3 block Imax*Jmax system. The closest I've come to finding an example is ex19.c in the snes directory, but that is in c and for the nonlinear solver.

I have been able to run PETSc but unwrapping the block matrix into a monolithic system. But the manual says "Block matrices represent an important class of problems in numerical linear algebra and offer the possibility of far more efficient iterative solvers than just treating the entire matrix as black box." However, in the FAQs I saw a comment that PETSc scans the AIJ matrices for rows that have the same column layout and can deduce if it's a block system and use the more efficient solvers. I also saw in the archives for this email list a thread where it seems workaround for building fields in a Fortran code is discussed ("Back to struct in Fortran to represent field with dof > 1"), so I'm beginning to suspect building a block system in Fortran might not be straight forward.

All that being said, my questions:

Is there a significant advantage to building the block system as opposed to the analogous monolithic system if PETSc can figure out that it's a block system? Can you confirm that PETSc does figure this out?
If there is an advantage to loading the matrix as a block matrix, is there an example Fortran code that builds and solves a linear block system?

Thanks,
Tom C

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