Thank you for your feedback.
> -coupledsolve_pc_type fieldsplit
> -coupledsolve_pc_fieldsplit_0_fields 0,1,2
> -coupledsolve_pc_fieldsplit_1_fields 3
> -coupledsolve_pc_fieldsplit_type schur
> -coupledsolve_pc_fieldsplit_block_size 4
> -coupledsolve_fieldsplit_0_ksp_converged_reason
> -coupledsolve_fieldsplit_1_ksp_converged_reason
> -coupledsolve_fieldsplit_0_ksp_type gmres
> -coupledsolve_fieldsplit_0_pc_type fieldsplit
> -coupledsolve_fieldsplit_0_pc_fieldsplit_block_size 3
> -coupledsolve_fieldsplit_0_fieldsplit_0_pc_type ml
> -coupledsolve_fieldsplit_0_fieldsplit_1_pc_type ml
> -coupledsolve_fieldsplit_0_fieldsplit_2_pc_type ml
>
> Is it normal, that I have to explicitly specify the block size
> for each
> fieldsplit?
>
>
> No. You should be able to just specify
>
>
> -coupledsolve_fieldsplit_ksp_converged
> -coupledsolve_fieldsplit_0_fieldsplit_pc_type ml
>
>
> and same options will be applied to all splits (0,1,2).
>
> Does this functionality not work?
>
>
It does work indeed, but what I actually was referring to, was the use
of
-coupledsolve_pc_fieldsplit_block_size 4
-coupledsolve_fieldsplit_0_pc_fieldsplit_block_size 3
Without them, I get the error message
[0]PETSC ERROR: PCFieldSplitSetDefaults() line 468
in /work/build/petsc/src/ksp/pc/impls/fieldsplit/fieldsplit.c Unhandled
case, must have at least two fields, not 1
I thought PETSc would already know, what I want to do, since I
initialized the fieldsplit with
CALL PCFieldSplitSetIS(PRECON,PETSC_NULL_CHARACTER,ISU,IERR)
etc.
>
>
> Are there any guidelines to follow that I could use to avoid
> taking wild
> guesses?
>
>
> Sure. There are lots of papers published on how to construct robust
> block preconditioners for saddle point problems arising from Navier
> Stokes.
> I would start by looking at this book:
>
>
> Finite Elements and Fast Iterative Solvers
>
> Howard Elman, David Silvester and Andy Wathen
>
> Oxford University Press
>
> See chapters 6 and 8.
>
As a matter of fact I spent the last days digging through papers on the
regard of preconditioners or approximate Schur complements and the names
Elman and Silvester have come up quite often.
The problem I experience is, that, except for one publication, all the
other ones I checked deal with finite element formulations. Only
Klaij, C. and Vuik, C. SIMPLE-type preconditioners for cell-centered,
colocated finite volume discretization of incompressible
Reynolds-averaged Navier–Stokes equations
presented an approach for finite volume methods. Furthermore, a lot of
literature is found on saddle point problems, since the linear system
from stable finite element formulations comes with a 0 block as pressure
matrix. I'm not sure how I can benefit from the work that has already
been done for finite element methods, since I neither use finite
elements nor I am trying to solve a saddle point problem (?).
>
> > Petsc has some support to generate approximate pressure
> schur
> > complements for you, but these will not be as good as the
> ones
> > specifically constructed for you particular discretization.
>
> I came across a tutorial (/snes/examples/tutorials/ex70.c),
> which shows
> 2 different approaches:
>
> 1- provide a Preconditioner \hat{S}p for the approximation of
> the true
> Schur complement
>
> 2- use another Matrix (in this case its the Matrix used for
> constructing
> the preconditioner in the former approach) as a new
> approximation of the
> Schur complement.
>
> Speaking in terms of the PETSc-manual p.87, looking at the
> factorization
> of the Schur field split preconditioner, approach 1 sets
> \hat{S}p while
> approach 2 furthermore sets \hat{S}. Is this correct?
>
>
>
> No this is not correct.
> \hat{S} is always constructed by PETSc as
> \hat{S} = A11 - A10 KSP(A00) A01
But then what happens in this line from the
tutorial /snes/examples/tutorials/ex70.c
ierr = KSPSetOperators(subksp[1], s->myS, s->myS);CHKERRQ(ierr);
It think the approximate Schur complement a (Matrix of type Schur) gets
replaced by an explicitely formed Matrix (myS, of type MPIAIJ).
>
> You have two choices in how to define the preconditioned, \hat{S_p}:
>
> [1] Assemble you own matrix (as is done in ex70)
>
> [2] Let PETSc build one. PETSc does this according to
>
> \hat{S_p} = A11 - A10 inv(diag(A00)) A01
>
Regards,
Fabian
>
>
