[petsc-users] fieldsplit - preconditioner mix

[Matthew Knepley]

On Tue, Nov 1, 2016 at 6:21 AM, Lukasz Kaczmarczyk <
Lukasz.Kaczmarczyk at glasgow.ac.uk> wrote:

> Hello,
>
> I solve problems of identifying forces on the surface, which are results
> in displacements (measured) on some other surface. This technique is used
> in cell engineering where we can observe the movement of dots through
> transparent gels. That is unknown to us is tractions on the surface and
> stresses in the body.
>
> The body is composed of two materials, which two orders difference in
> stiffness.
>
> We constructed problem which gives the stable solution, works great with
> direct solvers like mumps or superlu_dist, however, we have the problem
> with scalability, for a larger number of processors and DOFs (>1m).
>
> The general system which we solving looks like this,
> [ K K K 0 ][u]=[0]
> [ K K K C ][u]=[0]
> [ K K K 0 ][u]=[0]
> [ 0 0 B 0 ][L]=[0]
>
> I am trying to use PCFIELDSPLIT however I have the problem which the best
> mix of preconditioners and set-up. I can converge for a very small problem,
> but overall efficiency is far from perfect.  Note that matrices C, B are
> small compared to the block of K matrices. Block of  K matrices is positive
> define and symmetric. Note that [0 0 B]*[ 0 C 0]^T = 0.
>

Always start from a known position. Can you run full Schur complement with
an exact solve for K and very accurate solve for the Schur block? Does it
converge in 1 iterate? That is the first step. Then you need to look at the
two block solves. Generally, the hard part is solving the Schur block. Do
you
know what would be a good preconditioner? It looks like it could be worth
directly forming your Schur complement.

  Thanks,

     Matt


> Anyone have any advise what I can do with this.
>
> The full code can bee seen here
> http://mofem.eng.gla.ac.uk/mofem/html/cell__forces_8cpp.html
>
> Kind regards
> Lukasz




-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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