[petsc-users] Increasing ILU robustness

Jed Brown jedbrown at mcs.anl.gov
Sun Apr 21 10:56:20 CDT 2013

Hugo Gagnon <opensource.petsc at user.fastmail.fm> writes:

> Linear elasticity, 

Smoothed aggregation is a good choice.

> which yields symmetric positive definite matrices.

Note that ILU can produce negative pivots for SPD matrices.  See Kershaw
1978 or src/ksp/pc/examples/tutorials/ex1.c for a 4x4 example.

> So I guess I could reformulate my question to: what is the
> solver/preconditioner combination that is "best" suited for this kind
> of problem?  I tried Anton suggestion and gave BCGS a shot but
> although it does seem to work it converges very slowly.  Using the
> gamg preconditioner blows up:

What do you mean "blows up"?  Does this problem have sufficient boundary
conditions to be non-singular?  For elasticity, you should set the "near
null space" (rigid body modes) using MatSetNearNullSpace (and perhaps

Once this is set, you can compare PCGAMG to PCML.

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