[petsc-users] Roles of ksp_type and pc_type

[Massimiliano Leoni]

Hi petsc-users,
  I am relatively new to PETSc and so a few things that you'd call obvious 
still puzzle me. I hope someone can help me clarify this.

Consider the system Ax = b and
        KSPSetOperators(ksp,A,A,...);

now, please correct me wherever I'm wrong:
[1] if I set -ksp_type preonly, -pc_type lu   it solves Ax = b with direct LU 

[2] if I set -ksp_type preonly, -pc_type hypre   it solves Px = b where P is    
        the AMG preconditioner of A build by HYPRE
        § Question: how does PETSc solve this?

[3] if I set -ksp_type gmres, -pc_type hypre   it solves Ax = b as
        P^{-1}Ax = P^{-1}b with gmres, where P is again the AMG prec build by   
        
        HYPRE.

[4] suppose I have the classic Stokes matrix A = [[C,B^T],[B,O]] and want to    
        use the block preconditioner P = [[C,O],[O,Mp/nu]]. What I'm doing now 
is
        KSPSetOperators(ksp,A,P,...);
        set ksp_type gmres, pc_type fieldsplit, inner ksps gmres and inner pcs  
        
        hypre, so I expect PETSc to solve Pz = r by blocks,
        C z_u = r_u first, as in [3]
        Mp/nu z_p = r_p later, again as in [3]
        Is this what is actually happening?

[5] what happens instead if I set, in the same situation,
        ksp_type preonly, pc_type fieldsplit, inner ksps gmres and inner pcs ?
        I expect PETSc to solve Px = b with a block method as before. [This     
        
        doesn't actually solve Stokes].

I'm sorry for the many questions, I am trying to go through the User Manual 
and will be glad if anyone points me to further resources.

Thanks in advance for any help,
Massimiliano