[petsc-users] fieldsplit - preconditioner mix

[Lukasz Kaczmarczyk]

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.

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